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  • 1.
    Ankelhed, Daniel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    On design of low order H-infinity controllers2011Doctoral thesis, monograph (Other academic)
    Abstract [en]

    When designing controllers with robust performance and stabilization requirements, H-infinity synthesis is a common tool to use. These controllers are often obtained by solving mathematical optimization problems. The controllers that result from these algorithms are typically of very high order, which complicates implementation. Low order controllers are usually desired, since they are considered more reliable than high order controllers. However, if a constraint on the maximum order of the controller is set that is lower than the order of the so-called augmented system, the optimization problem becomes nonconvex and it is relatively difficult to solve. This is true even when the order of the augmented system is low.

    In this thesis, optimization methods for solving these problems are considered. In contrast to other methods in the literature, the approach used in this thesis is based on formulating the constraint on the maximum order of the controller as a rational function in an equality constraint. Three methods are then suggested for solving this smooth nonconvex optimization problem.

    The first two methods use the fact that the rational function is nonnegative. The problem is then reformulated as an optimization problem where the rational function is to be minimized over a convex set defined by linear matrix inequalities (LMIs). This problem is then solved using two different interior point methods.

    In the third method the problem is solved by using a partially augmented Lagrangian formulation where the equality constraint is relaxed and incorporated into the objective function, but where the LMIs are kept as constraints. Again, the feasible set is convex and the objective function is nonconvex.

    The proposed methods are evaluated and compared with two well-known methods from the literature. The results indicate that the first two suggested methods perform well especially when the number of states in the augmented system is less than 10 and 20, respectively. The third method has comparable performance with two methods from literature when the number of states in the augmented system is less than 25.

  • 2.
    Ankelhed, Daniel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    On low order controller synthesis using rational constraints2009Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In order to design 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 plant, the problem is no longer convex and it is then relatively hard to solve. These problems become very complex, even when the order of the system to be controlled is low.

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

    To solve this optimization problem, two methods have been proposed. The first method is a barrier method and the second one is a method based on a primal-dual framework. These methods have been evaluated on several problems and compared with a well-known method found in the literature. To motivate this choice of method, we have made a brief survey of available methods available for solving the same or related problems.

    The proposed methods emerged as the best methods among the three for finding lower order controllers with the same or similar performance as the full order controller. When the aim is to find the lowest order controller with no worse than +50% increase in the closed loop H-infinity norm, then the three compared methods perform equally well.

  • 3.
    Ankelhed, Daniel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Utvärdering av DC-labben2006Report (Other academic)
    Abstract [en]

    I denna rapport jämförs två olika metoder för att ta fram en modell för att kunna reglera en DC-motor med lead-lagreglering. I den ena metoden identifieras två parametrar i en given modell av andra ordningen, medan i den andra metoden skattas ett antal punkter i ett bodediagram direkt med hjälp av frekvensanalys. Resultaten indikerar att de två metoderna är ungefär likvärdiga för den process som studerats.

  • 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 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.

  • 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 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.

  • 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 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.

  • 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.
    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.

  • 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.
    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.

  • 9.
    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.

  • 10.
    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.

  • 11.
    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.

  • 12.
    Nielsen, Isak
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ankelhed, Daniel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Axehill, Daniel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Low-rank Modifications of Riccati Factorizations with Applications to Model Predictive Control2013In: Proceedings of 52nd IEEE Conference on Decision and Control, IEEE conference proceedings, 2013, p. 3684-3690Conference paper (Refereed)
    Abstract [en]

    In optimization algorithms used for on-line Model Predictive Control (MPC), the main computational effort is spent while solving linear systems of equations to obtain search directions. Hence, it is of greatest interest to solve them efficiently, which commonly is performed using Riccati recursions or generic sparsity exploiting algorithms. The focus in this work is efficient search direction computation for active-set methods. In these methods, the system of equations to be solved in each iteration is only changed by a low-rank modification of the previous one. This highly structured change of the system of equations from one iteration to the next one is an important ingredient in the performance of active-set solvers. It seems very appealing to try to make a structured update of the Riccati factorization, which has not been presented in the literature so far. The main objective of this paper is to present such an algorithm for how to update the Riccati factorization in a structured way in an active-set solver. The result of the work is that the computational complexity of the step direction computation can be significantly reduced for problems with bound constraints on the control signal. This in turn has important implications for the computational performance of active-set solvers used for linear, nonlinear as well as hybrid MPC.

1 - 12 of 12
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