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  • 1.
    Ankelhed, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Partially Augmented Lagrangian Method for Low Order H-Infinity Controller Synthesis Using Rational Constraints2011Report (Other academic)
    Abstract [en]

    When designing robust controllers, H-infinity synthesis is a common tool touse. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.

    The approach used in this work is based on formulating the constraint onthe maximum order of the controller as a polynomial (or rational) equation.This equality constraint is added to the optimization problem of minimizingan upper bound on the H-innity norm of the closed loop system subjectto linear matrix inequality (LMI) constraints. The problem is then solvedby reformulating it as a partially augmented Lagrangian problem where theequality constraint is put into the objective function, but where the LMIsare kept as constraints.

    The proposed method is evaluated together with two well-known methodsfrom the literature. The results indicate that the proposed method hascomparable performance in most cases, especially if the synthesized con-troller has many parameters, which is the case if the system to be controlledhas many input and output signals.

  • 2.
    Ankelhed, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Partially Augmented Lagrangian Method for Low Order H-Infinity Controller Synthesis Using Rational Constraints2012In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 57, no 11, p. 2901-2905Article in journal (Refereed)
    Abstract [en]

    This technical note proposes a method for low order H-infinity synthesis where the constraint on the order of the controller is formulated as a rational equation. The resulting nonconvex optimization problem is then solved by applying a partially augmented Lagrangian method. The proposed method is evaluated together with two well-known methods from the literature. The results indicate that the proposed method has comparable performance and speed.

  • 3.
    Ankelhed, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Primal-Dual Method for Low Order H-Infinity Controller Synthesis2010In: Proceedings of Reglermöte 2010, Lund, 2010Conference paper (Other academic)
    Abstract [en]

    When designing robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.

    The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. By using the fact that the polynomial (or rational) is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex function is to be minimized over a convex set defined by linear matrix inequalities.

    The proposed method is evaluated together with a well-known method from the literature. The results indicate that the proposed method performs slightly better.

  • 4.
    Ankelhed, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Primal-Dual Method for Low Order H-Infinity Controller Synthesis2010Report (Other academic)
    Abstract [en]

    When designing robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.

    The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. By using the fact that the polynomial (or rational) is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex function is to be minimized over a convex set defined by linear matrix inequalities.

    The proposed method is evaluated together with a well-known method from the literature. The results indicate that the proposed method performs slightly better.

  • 5.
    Ankelhed, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Primal-Dual Method for Low Order H-Infinity Controller Synthesis2009In: Proceedings of the 48th IEEE Conference on Decision and Control held jointly with the 28th Chinese Control Conference, IEEE , 2009, p. 6674-6679Conference paper (Refereed)
    Abstract [en]

    When designing robust controllers, H-infinity synthesisis a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex,even when the order of the system is low.

    The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. By using the fact that the polynomial (or rational) is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex function is to be minimized over a convex set defined by linear matrix inequalities.

    The proposed method is evaluated together with a wellknown method from the literature. The results indicate that the proposed method performs slightly better.

  • 6.
    Ankelhed, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Quasi-Newton Interior Point Method for Low Order H-Infinity Controller Synthesis2011In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 6, p. 1462-1467Article in journal (Refereed)
    Abstract [en]

    This technical note proposes a method for low order H-infinity synthesis where the constraint on the order of the controller is formulated as a rational equation. The resulting nonconvex optimization problem is then solved by applying a quasi-Newton primal-dual interior point method. The proposed method is evaluated together with a well-known method from the literature. The results indicate that the proposed method has comparable performance and speed.

  • 7.
    Ankelhed, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Additional Numerical Results for the Quasi-Newton Interior Point Method for Low Order H-Infinity Controller Synthesis2010Report (Other academic)
    Abstract [en]

    Here we present numerical results and timings obtained using our quasi-Newton interior point method on a set of 44 systems. We were not able to include these results in the article due to limited amount of space. Also results from our evaluation of HIFOO on the same systems are included.

  • 8.
    Ankelhed, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Suboptimal Model Reduction using LMIs with Convex Constraints2006Report (Other academic)
    Abstract [en]

    An approach to model reduction of LTI systems using Linear Matrix Inequalities (LMIs) in an H-infinity framework is presented, where non-convex constraints are replaced with stricter convex constraints thus making it suboptimal. The presented algorithms are compared with the Optimal Hankel reduction algorithm, and are shown to achieve better results (i.elower H-infinity errors) in cases where some of the Hankel singular values are close, but not equal to each other.

  • 9.
    Axelsson, Patrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Norrlöf, Mikael
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    H-Controller Design Methods Applied to One Joint of a Flexible Industrial Manipulator2013Report (Other academic)
    Abstract [en]

    Control of a flexible joint of an industrial manipulator using H design methods is presented. The considered design methods are i) mixed-H design, and ii) H loop shaping design. Two different controller configurations are examined: one uses only the actuator position, while the other uses the actuator position and the acceleration of end-effector. The four resulting controllers are compared to a standard PID controller where only the actuator position is measured. The choices of the weighting functions are discussed in details. For the loop shaping design method, the acceleration measurement is required to improve the performance compared to the PID controller. For the mixed-H method it is enough to have only the actuator position to get an improved performance. Model order reduction of the controllers is briefly discussed, which is important for implementation of the controllers in the robot control system.

  • 10.
    Axelsson, Patrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Norrlöf, Mikael
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    H-Controller Design Methods Applied to One Joint of a Flexible Industrial Manipulator2014In: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Boje, Edward and Xia, Xiaohua, International Federation of Automatic Control , 2014, p. 210-216Conference paper (Refereed)
    Abstract [en]

    Control of a flexible joint of an industrial manipulator using H design methods is presented. The considered design methods are i) mixed-H design, and ii) H loop shaping design. Two different controller configurations are examined: one uses only the actuator position, while the other uses the actuator position and the acceleration of end-effector. The four resulting controllers are compared to a standard PID controller where only the actuator position is measured. The choices of the weighting functions are discussed in details. For the loop shaping design method, the acceleration measurement is required to improve the performance compared to the PID controller. For the mixed-H method it is enough to have only the actuator position to get an improved performance. Model order reduction of the controllers is briefly discussed, which is important for implementation of the controllers in the robot control system.

  • 11.
    Axelsson, Patrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Norrlöf, Mikael
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Single Joint Control of a Flexible Industrial Manipulator using H Loop Shaping2012Report (Other academic)
    Abstract [en]

    Control of a flexible joint of an industrial manipulator using H loop shaping design is presented. Two controllers are proposed; 1) H loop shaping using the actuator position, and 2) H loop shaping using the actuator position and the acceleration of end-effector. The two controllers are compared to a standard PID controller where only the actuator position is measured. Using the acceleration of the end-effector improves the nominal performance. The performance of the proposed controllers is not significantly decreased in the case of model error consisting of an increased time delay or a gain error.

  • 12.
    Axelsson, Patrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Pipeleers, Goele
    Katholieke Universiteit, Leuven, Belgium.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Norrlöf, Mikael
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    H Synthesis Method for Control of Non-linear Flexible Joint Models2013Report (Other academic)
    Abstract [en]

    An H synthesis method for control of a flexible joint, with non-linear spring characteristic, is proposed. The first step of the synthesis method is to extend the joint model with an uncertainty description of the stiffness parameter. In the second step, a non-linear optimisation problem, based on nominal performance and robust stability requirements, has to be solved. Using the Lyapunov shaping paradigm and a change of variables, the non-linear optimisation problem can be rewritten as a convex, yet conservative, LMI problem. The method is motivated by the assumption that the joint operates in a specific stiffness region of the non-linear spring most of the time, hence the performance requirements are only valid in that region. However, the controller must stabilise the system in all stiffness regions. The method is validated in simulations on a non-linear flexible joint model originating from an industrial robot.

  • 13.
    Axelsson, Patrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Pipeleers, Goele
    Katholieke Universiteit, Leuven, Belgium.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Norrlöf, Mikael
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    H Synthesis Method for Control of Non-linear Flexible Joint Models2014In: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Boje, Edward and Xia, Xiaohua, International Federation of Automatic Control , 2014, p. 8372-8377Conference paper (Refereed)
    Abstract [en]

    An H synthesis method for control of a flexible joint, with non-linear spring characteristic, is proposed. The first step of the synthesis method is to extend the joint model with an uncertainty description of the stiffness parameter. In the second step, a non-linear optimisation problem, based on nominal performance and robust stability requirements, has to be solved. Using the Lyapunov shaping paradigm and a change of variables, the non-linear optimisation problem can be rewritten as a convex, yet conservative, LMI problem. The method is motivated by the assumption that the joint operates in a specific stiffness region of the non-linear spring most of the time, hence the performance requirements are only valid in that region. However, the controller must stabilise the system in all stiffness regions. The method is validated in simulations on a non-linear flexible joint model originating from an industrial robot.

  • 14.
    Glad, Torkel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Enqvist, Martin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Controllers for Amplitude Limited Model Error Models2005In: Proceedings of the 16th IFAC World Congress, 2005, p. 662-662Conference paper (Refereed)
    Abstract [en]

    In this paper, systems where information about model accuracy is contained in a model error model are considered. The validity of such a model is typically restricted to input signals that are limited in amplitude. It is then natural to require the same amplitude restriction when designing controllers. The resulting implications for controller design are investigated in both the continuous and the discrete time case.

  • 15.
    Glad, Torkel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Enqvist, Martin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Controllers for Amplitude Limited Model Error Models2005Report (Other academic)
    Abstract [en]

    In this paper, systems where information about model accuracy is contained in a model error model are considered. The validity of such a model is typically restricted to input signals that are limited in amplitude. It is then natural to require the same amplitude restriction when designing controllers. The resulting implications for controller design are investigated in both the continuous and the discrete time case.

  • 16.
    Glad, Torkel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robustness Guarantees for Linear Control Designs with an Estimated Nonlinear Model Error Model2004Report (Other academic)
    Abstract [en]

    Much attention in robust identification and control has been focused on linear low order models approximating high order linear systems. We consider the more realistic situation with a linear model approximating a nonlinear system. We describe how a nonlinear model error model can be developed, that allows a complete linear design process that results in a closed loop system with performance robustness guarantees (in terms of gain from disturbance to output) against the nonlinear error. Clearly the design can be successful only if the linear model is a reasonably good approximation of the system. A particular aspect of the design process is to define a workable definition of 'practical stability' for robust control design, with possible non-linear model errors. We use affine norms for that purpose.

  • 17.
    Glad, Torkel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robustness Guarantees for Linear Control Designs with an Estimated Nonlinear Model Error Model2004In: International Journal of Robust and Nonlinear Control, ISSN 1049-8923, E-ISSN 1099-1239, Vol. 14, no 11, p. 959-970Article in journal (Refereed)
    Abstract [en]

    Much attention in robust identification and control has been focused on linear low order models approximating high order linear systems. We consider the more realistic situation with a linear model approximating a nonlinear system. We describe how a nonlinear model error model can be developed, that allows a complete linear design process that results in a closed loop system with performance robustness guarantees (in terms of gain from disturbance to output) against the nonlinear error. Clearly the design can be successful only if the linear model is a reasonably good approximation of the system. A particular aspect of the design process is to define a workable definition of 'practical stability' for robust control design, with possible non-linear model errors. We use affine norms for that purpose.

  • 18.
    Glad, Torkel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Uncertain LTI-Models for Linear Control Design of Nonlinear Systems2007Report (Other academic)
    Abstract [en]

    Much attention in robust identification and control has been focused on linear low order models approximating high order linear systems. We consider the more realistic situation with a linear model approximating a non-linear system. We describe how a linear time invariant (LTI) model with unstructured uncertainty, i.e. a "band" of Nyquist curves can be developed using a non-linear model error model. Applying standard linear robust control design to this uncertain LTI model will lead to a (non-linear) closes loop system with performance robustness guarantees (in terms of gain from disturbances to output) well in line with the objectives of the linear design. Clearly the design can be successful only if the linear model is a reasonable good approximation of the system. A particular aspect of the design process is to define a workable definition of "practical stability" for robust control design, with possibly non-linear model errors. We use affine power norms for that purpose.

  • 19.
    Gunnarsson, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    McKelvey, Tomas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Matrix Algebra Package for Mathematica1999Report (Other academic)
  • 20.
    Hansson, Anders
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Stability Analysis of Nonlinear Systems using Frozen Stationary Linearization2004In: Proceedings of the 2004 American Control Conference, 2004, p. 424-428Conference paper (Refereed)
    Abstract [en]

    This work discusses how to compute stability regions for nonlinear systems with slowly varying parameters using frozen stationary linearization. It is shown that larger stability regions can be obtained as compared to traditional approaches using recent stability results for linear parameter-varying systems.

  • 21.
    Hansson, Anders
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Stability Analysis of Nonlinear Systems using Frozen Stationary Linearization2003Report (Other academic)
    Abstract [en]

    This work discusses how to compute stability regions for nonlinear systems with slowly varying parameters using frozen stationary linearization. It is shown that larger stability regions can be obtained as compared to traditional approaches using recent stability results for linear parameter-varying systems.

  • 22.
    Hansson, Jörgen
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wallin, Ragnar
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ståhl-Gunnarsson, Karin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Karlsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Clearance of Flight Control Laws for Time-Varying Parameters2003Report (Other academic)
    Abstract [en]

    In this article exponential stability of the closed loop for the Saab AB VEGAS model controlled by a gain-scheduled linear fractional transformation controller is investigated for time-varying Mach-number. The analysis is based on parameter-dependent Lyapunov-functions which are obtained by investigating feasibility of linear matrix inequalities.

  • 23.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Finite Frequency method for µ-Analysis1995In: Proceedings of the 3rd European Control Conference, 1995, Vol. 1, p. 171-176Conference paper (Refereed)
    Abstract [en]

    This paper presents and discusses a method for assuring an upper bound of the structured singular value (µ), by treating the frequency as a real parametric uncertainty on continuous time systems. Using this approach a complete frequency interval can be covered in one µ-computation. By subdividing the frequency range and using a pruning scheme an efficient and accurate method is obtained for computing an upper bound of a dynamic system. The method is composed of existing µ-methods and branch and bound schemes.

  • 24.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Finite Frequency Method for µ-Analysis1994Report (Other academic)
    Abstract [en]

    This paper presents and discusses a method for assuring an upper bound of the structured singular value (µ), by treating the frequency as a real parametric uncertainty on continuous time systems. Using this approach a complete frequency interval can be covered in one µ-computation. By subdividing the frequency range and using a pruning scheme an efficient and accurate method is obtained for computing an upper bound of a dynamic system. The method is composed of existing µ-methods and branch and bound schemes.

  • 25.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Nonlinear Application of a Lyapunov Technique for Assuring Global Performance Bounds1994In: Proceedings of the 1994 American Control Conference, 1994, Vol. 3, p. 954-958 vol.1Conference paper (Refereed)
    Abstract [en]

    In this paper we consider the stability and performance problem of nonlinear systems using a Lyapunov technique. The upper or lower bounds can be provided assuming that a Lyapunov function satisfies a Hamiltonian inequality for all admissible states. Also, suboptimal control laws with guaranteed performance bounds can be derived with this technique. The technique has been applied on rate and attitude control for sounding rockets. As an example, a rate control algorithm is elaborated showing the main ideas presented in this paper: (1) the Lyapunov function provides a global performance bound; (2) a control law is derived based on the Lyapunov function; and (3) the candidate Lyapunov function is parametrized and improved bounds are obtained using parameter optimization.

  • 26.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Nonlinear Application of a Lyapunov Technique for Assuring Global Performance Bounds1994Report (Other academic)
    Abstract [en]

    In this paper we consider the stability and performance problem of nonlinear systems using a Lyapunov technique. The upper or lower bounds can be provided assuming that a Lyapunov function satisfies a Hamiltonian inequality for all admissible states. Also, suboptimal control laws with guaranteed performance bounds can be derived with this technique. The technique has been applied on rate and attitude control for sounding rockets. As an example, a rate control algorithm is elaborated showing the main ideas presented in this paper: (1) the Lyapunov function provides a global performance bound; (2) a control law is derived based on the Lyapunov function; and (3) the candidate Lyapunov function is parametrized and improved bounds are obtained using parameter optimization.

  • 27.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    An IQC-Based Stability Criterion for Systems with Slowly Varying Parameters1999In: Proceedings of the 14th IFAC World Congress, 1999, Vol. F, p. 525-530Conference paper (Refereed)
    Abstract [en]

    An integral quadratic constraints (IQC) is introduced for stability analysis of linear systems with slowly varying parameters. The parameters are assumed to be bounded and with bounded derivatives. Other types of uncertainties can be included in the problem. The new criterion yields less conservative bounds than previously proposed criteria.

  • 28.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    An IQC-Based Stability Criterion for Systems with Slowly Varying Parameters1997Report (Other academic)
    Abstract [en]

    An integral quadratic constraints (IQC) is introduced for stability analysis of linear systems with slowly varying parameters. The parameters are assumed to be bounded and with bounded derivatives. Other types of uncertainties can be included in the problem. The new criterion yields less conservative bounds than previously proposed criteria.

  • 29.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    An LFT Parameterization of Lyapunov Functions1995In: Proceedings of the 2nd Russian Swedish Control Conference, 1995, p. 23-27Conference paper (Other academic)
  • 30.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    An Uncertainty Approach to µ Analysis1996In: Proceedings of the 13th IFAC World Congress, 1996, Vol. H, p. 65-70Conference paper (Refereed)
    Abstract [en]

    e present a concept for µ analysis and synthesis with varying uncertainties. We assume that the uncertainties are unknown by bounded and with bounded rate of variation. The approach taken here is to augment the uncertainty block with its derivative. This can be achieved using appropriate dynamic multipliers. The approach fits nicely in the µ framework and D-K-iteration-like methods can be used for synthesis.

  • 31.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    An Uncertainty Augmentation Approach to Varying µ Analysis1995Report (Other academic)
    Abstract [en]

    We present a concept for µ analysis and synthesis with varying uncertainties. We assume that the uncertainties are unknown by bounded and with bounded rate of variation. The approach taken here is to augment the uncertainty block with its derivative. This can be achieved using appropriate dynamic multipliers. The approach fits nicely in the µ framework and D-K-iteration-like methods can be used for synthesis.

  • 32.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Applications of Mixed µ-Synthesis using the Passivity Approach1995In: Proceedings of the 3rd European Control Conference, 1995, Vol. 1, p. 165-170Conference paper (Refereed)
    Abstract [en]

    This paper presents mixed synthesis using a D-K like method inspired by passivity theorem. The method is illustated on two similar examples showing the virtues of the mixed approach.

  • 33.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Applications of Mixed µ-Synthesis Using the Passivity Approach1994Report (Other academic)
    Abstract [en]

    This paper presents mixed synthesis using a D-K like method inspired by passivity theorem. The method is illustated on two similar examples showing the virtues of the mixed approach.

  • 34.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Applications of Real-µ Gain Scheduling1996In: Proceedings of the 35th IEEE Conference on Decision and Control, 1996, p. 1666-1671 vol.2Conference paper (Refereed)
    Abstract [en]

    A pitch-axis controller is designed for a missile using linear functional transformation (LFT) synthesis with real uncertainties. Gain scheduling in two variables, angle of attack and Mach number, are used. The example illustrates the linearization of a nonlinear model as well as LFT parametrization and synthesis

  • 35.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Employing Kronecker Canonical Form for H-infinity Synthesis Problems2011Report (Other academic)
    Abstract [en]

    The Kronecker canonical form (KCF) can be employed when solving H-infinity synthesis problem. The KCF structure reveals variables that can be eliminated in the semidefinite program that defines the controller. The structure can also be used to remove states in the controller without sacrificing performance. In order to find the KCF structure, we can transform the relevant matrices to a generalized upper triangular (Guptri) form using orthogonal transformations. Thus, we can avoid finding the KCF structure explicitly, which is a badly conditioned problem.

  • 36.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Employing Kronecker Canonical Form for LMI-Based H-infinity Synthesis Problems2012In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 57, no 8, p. 2062-2067Article in journal (Refereed)
    Abstract [en]

    The Kronecker canonical form (KCF) can be employed when solving H-infinity synthesis problem. The KCF structure reveals variables that can be eliminated in the semidefinite program that defines the controller. The structure can also be used to remove states in the controller without sacrificing performance. In order to find the KCF structure, we can transform the relevant matrices to a generalized upper triangular (Guptri) form using orthogonal transformations. Thus, we can avoid finding the KCF structure explicitly, which is a badly conditioned problem.

  • 37.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering. Linköping University, Faculty of Science & Engineering.
    Generalized Riccati Equations for Hinfinity Synthesis2015Report (Other academic)
    Abstract [en]

    Conditions for the existence of controllers for lineartime-varying (LTV) systems is given. The closed loop performance isspecified in terms of energy gain, which also includes terminalconstraints. The conditions can be formulated either as linear matrixinequalities (LMIs) or as solutions to Riccati differental equationswith algebraic constraints.

  • 38.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    IQC Synthesis based on Inertia Constraints1999In: Proceedings of the 14th IFAC World Congress, 1999, Vol. G, p. 163-168Conference paper (Refereed)
    Abstract [en]

    Integral quadratic constraints (IQC:s) can be used for proving stability of systems with uncertainties and nonlinearities. Similarly, IQC:s can also be used for controller synthesis. Necessary and sufficient conditions for the existence of such a controller is derived. These conditions include linear matrix inequalities (LMI:s) and matrix inertia specifying the number of negative eigenvalues of a matrix. In general, these conditions are non-convex. Connections to bilinear matrix inequalities and LMI:s with rank constraints are also given.

  • 39.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    IQC Synthesis based on Inertia Constraints1998Report (Other academic)
    Abstract [en]

    Integral quadratic constraints (IQC:s) can be used for proving stability of systems with uncertainties and nonlinearities. Similarly, IQC:s can also be used for controller synthesis. Necessary and sufficient conditions for the existence of such a controller is derived. These conditions include linear matrix inequalities (LMI:s) and matrix inertia specifying the number of negative eigenvalues of a matrix. In general, these conditions are non-convex. Connections to bilinear matrix inequalities and LMI:s with rank constraints are also given.

  • 40.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    LTV Model Reduction with Upper Error Bounds2006Report (Other academic)
    Abstract [en]

    A new approach for computing upper error bounds for reduced-order models of linear time-varying systems is presented. It is based on a transformation technique of the Hankel singular values using positive-real, odd incremented functions. By applying such time-varying functions, the singular values to be removed can be forced to become equal and constant, so that they can be reduced. Two variations of this method are proposed: one for finite-time horizons and the other for infinite-time problems including periodic systems.

  • 41.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    LTV Model Reduction With Upper Error Bounds2009In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 54, no 7, p. 1450-1462Article in journal (Refereed)
    Abstract [en]

    A new approach for computing upper error bounds for reduced-order models of linear time-varying systems is presented. It is based on a transformation technique of the Hankel singular values using positive-real, odd incremented functions. By applying such time-varying functions, the singular values to be removed can be forced to become equal and constant, so that they can be reduced. Two variations of this method are proposed: one for finite-time horizons and the other for infinite-time problems including periodic systems.

  • 42.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Methods for robust gain scheduling1995Doctoral thesis, monograph (Other academic)
    Abstract [en]

    This thesis considers the analysis of systems with uncertainties and the design of controllers to such systems. Uncertainties are treated in a relatively broad sense covering gain-bounded elements that are not known a priori but could be available to the controller in real time.

    The uncertainties are in the most general case norm-bounded operators with a given block-diagonal structure. The structure includes parameters, linear time-invariant and time-varying systems as well as nonlinearities. In some applications the controller may have access to the uncertainty, e.g. a parameter that depends on some known condition.

    There exist well-known methods for determining stability of systems subject to uncertainties. This thesis is within the framework for structured singular values also denoted by μ.  Given a certain class of uncertainties, μ is the inverse of the size of the smallest uncertainty that causes the system to become unstable. Thus, μ is a measure of the system's "structured gain".  In general it is not possible to compute μ exactly, but an upper bound can be determined using efficient numerical methods based on linear matrix inequalities.

    An essential contribution in this thesis is a new synthesis algorithm for finding controllers when parametric (real) uncertainties are present. This extends previous results on μ synthesis involving dynamic (complex) uncertainties.  Specifically, we can design gain scheduling controllers using the new μ synthesis theorem, with less conservativeness than previous methods. Also, algorithms for model reduction of uncertainty systems are given.

    A gain scheduling controller is a linear regulator whose parameters are changed as a function of the varying operating conditions. By treating nonlinearities as uncertainties, μ methods can be used in gain scheduling design. In the discussion, emphasis is put on how to take into consideration different characteristics of the time-varying properties of the system to be controlled. Also robustness and its relation with gain scheduling are treated.

    In order to handle systems with time-invariant uncertainties, both linear systems and constant parameters, a set of scalings and multipliers are introduced. These are matched to the properties of the uncertainties. Also, multipliers for treating uncertainties that are slowly varying, such that the rate of change is bounded, are introduced. Using these multipliers the applicability of the analysis and synthesis results are greatly extended.

  • 43.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Model reduction from an H∞/LMI perspective1994Report (Other academic)
    Abstract [en]

    This paper treats the problem of approximating a´n nth order continuous system by a system of order k  n Optimal solutions minimizing´the H􀀀 norm exist for k n 􀀀 This paper presents an iterative twostep LMI method for improving the H􀀀 model error compared to Hankel norm reduction As an intermediate step the algorithm nds a generalized balanced realization such that the n􀀀k Hankel singular values coincide

  • 44.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Model reduction using LMIs1994In: Proceedings of the 33rd IEEE Conference on Decision and Control, 1994, p. 3217-3222 vol.4Conference paper (Refereed)
    Abstract [en]

    This paper treats the problem of approximating an nth order continuous system by a system of order k<n. Optimal solutions minimizing the H norm of the approximation error exist for k=0, n-1. This paper presents an iterative two-step LMI method for improving the H model error compared to Hankel norm reduction.

  • 45.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Model Reduction using LMIs1994Report (Other academic)
    Abstract [en]

    This paper treats the problem of approximating an nth order continuous system by a system of order k<n. Optimal solutions minimizing the H norm of the approximation error exist for k=0, n-1. This paper presents an iterative two-step LMI method for improving the H model error compared to Hankel norm reduction.

  • 46.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    On Polynomial Coefficients and Rank Constraints2009Report (Other academic)
    Abstract [en]

    Rank constraints on matrices emerge in many automatic control applications. In this short document we discuss how to rewrite the constraint into a polynomial equations of the elements in a the matrix. If addition semidefinite matrix constraints are included, the polynomial equations can be turned into an inequality. We also briefly discuss how to implement these polynomial constraints.

  • 47.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    On Polynomial Coefficients and Rank Constraints2008Report (Other academic)
    Abstract [en]

    Rank constraints on matrices emerge in many automatic control applications. In this short document we discuss how to rewrite the constraint into a polynomial equations of the elements in a the matrix. If addition semidefinite matrix constraints are included, the polynomial equations can be turned into an inequality. We also briefly discuss how to implement these polynomial constraints.

  • 48.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    On Synthesis of Practically Valid Gain-Scheduled Controllers2003Report (Other academic)
    Abstract [en]

    Abstract Sucient conditions for the existence of a gain scheduled controller for LPV systems is presented. It is shown that it is always possible to, and a controller that depends on the parameters but which is independent of the rate of parameter variation. The conditions are three LMIs, which are similar to the conditions used for standard H1 synthesis problems. In the general case, the controller needs to have twice as many states as the original system. If a lower-order controllers is searched for, a rate- independent controller still resists a convex formulation.

  • 49.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Parameter Dependent Lyapunov Functions Based on Linear Fractional Transformation1999In: Proceedings of the 14th IFAC World Congress, 1999, Vol. F, p. 537-542Conference paper (Refereed)
    Abstract [en]

    A parameter dependent Lyapunov function is introduced for stability analysis of linear systems with slowly varying parameters. The Lyapunov function is a quadratic form using a linear fractional transformation (LFT) of the parameters. The parameters are assumed to be bounded and with bounded derivatives. Other types of uncertainties can be included in the problem.The new criterion yields less conservative bounds than previously proposed criteria.

  • 50.
    Helmersson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    State-Space Methods for µ-Analysis1994Report (Other academic)
    Abstract [en]

    This paper discusses state-space methods for analyzing stability of continuous time linear systems subject to structured uncertainties. Four types of uncertainties are discussed: linear parametric and dynamic uncertainties (real and complex µ) and nonlinear parametric and dynamic uncertainties. The method employs LMIs equipped with a scaling matrix adapted to the type of uncertainty. For parametric uncertainties conservativeness is reduced by branch and bound schemes. Different types of uncertainties can be mixed in this approach. The problem is convex except for the linear dynamic (complex µ) case.

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