An LMI-based optimization approach for integrated plant/output-feedback controller design

2012 American Control Conference (ACC), 2012

The robust filter design and the robust feedforward controller design are particular cases of a larger class of problems: the robust open-loop problems. In this article, we consider a class of uncertain open-loop plants, where a filter needs to be designed to ensure that the plant satisfies chosen specifications. The representation of uncertainties is made in a very general framework: the Linear Fractional Transformation (LFT). Associated with the Dynamic Integral Quadratic Constraints framework, it allows the consideration of many classes of structured uncertainties. This paper proves that the design of a filter ensuring a robust L2-gain or H2 performance for the complete plant can be expressed as a convex optimization problem involving Linear Matrix Inequalities Constraints which can be solved using an efficient algorithm.

Journal of the Franklin Institute, 2014

In this paper, the problem of designing an LPV state-feedback controller for uncertain LPV systems that can guarantee some desired bounds on the H 1 and the H 2 performances and that satisfies some desired constraints on the closed-loop poles location is considered. In the proposed approach, the vector of varying parameters is used to schedule between uncertain LTI systems. The resulting idea consists in using a double-layer polytopic description so as to take into account both the variability due to the parameter vector and the uncertainty. The first polytopic layer manages the varying parameter and is used to obtain the vertex uncertain systems, where the vertex controllers are designed. The second polytopic layer is built at each vertex system so as to take into account the model uncertainties and add robustness into the design step. Under some assumptions, the problem reduces to finding a solution to a finite number of LMIs, a problem for which efficient solvers are available nowadays. The solution to the multiobjective design problem is found both in the case when a single fixed Lyapunov function is used and when multiple parameter-varying Lyapunov functions are used. The validity and performance of the theoretical results are demonstrated through a numerical example.

IEEE Transactions on Automatic Control, 2000

Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as an LMI using KYP Lemma. This parameterization is a convex innerapproximation of the whole non-convex set of stabilizing controllers and depends on the choice of a central polynomial. It is shown that with an appropriate choice of the central polynomial, the set of all stabilizing fixed-order controllers that place the closed-loop poles of a polytopic system in a disk centered on the real axis, can be outbounded with some LMIs. These LMIs can be used for robust pole placement of polytopic systems.

Dynamic Systems and Control, Volumes 1 and 2, 2003

This paper presents a new algorithm for the design of linear controllers with special constraints imposed on the control gain matrix. This so called SLC (Structured Linear Control) problem can be formulated with linear matrix inequalities (LMI’s) with a nonconvex equality constraint. This class of prolems includes fixed order output feedback control, multi-objective controller design, decentralized controller design, joint plant and controller design, and other interesting control problems. Our approach includes two main contributions. One is that many design specifications such as H∞ performance, generalized H2 performance including H2 performance, l∞ performance, and upper covariance bounding controllers are described by a similar matrix inequality. A new matrix variable is introduced to give more freedom to design the controller. Indeed this new variable helps to find the optimal fixed-order output feedback controller. The second contribution uses a linearization algorithm to sea...

BACKGROUND: Robust methods aim to achieve robust performance and/or stability in the presence of bounded modeling errors.OBJECTIVE: dual problem in which uncertainty enters a filter at the plant output.RESULTS: A solution to this problem could be obtained, when parametric uncertainties are involved and a class of static multipliers is used. In view of the fact that the general robust output feedback problem is largely open, it is a challenging research question which kind of interconnections of uncertain systems can be handled by convex optimization in the LMI framework.CONCLUSION: It is found that the only structural property needed for a synthesis solution to exist in terms of LMIs, is the fact that the transfer matrix from control input to measurement output is not affected by uncertainty.

2006 IEEE/PES Transmission & Distribution Conference and Exposition: Latin America, 2006

Integrated design is based on the idea of including dynamic constraints such as stability or controllability, on the early stages of process design. Hence not only the system's parameter are calculated but also a controller. In this work we present a methodology to Integrated Design that allows to compute the optimal parameters of the system, along with its controller, in this case a PID. The system to design may be non linear with non linear constraints. To compute the controller we use LMIs and the controller calculated is robust since some uncertainty may be explicitly considered on the plant model. The methodology is applied to a non linear hydraulic system where

42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)

This paper presents a new algorithm for the design of linear controllers with special structural constraints imposed on the control gain matrix. This so called SLC (Structured Linear Control) problem can be formulated with linear matrix inequalities (LMI's) with a nonconvex equality constraint. This class of problems includes fixed order output feedback control, multi-objective controller design, decentralized controller design, joint plant and controller design, and other interesting control problems. Our approach includes two main contributions. The first is that many design specifications are described by a similar matrix inequality. A new matrix variable is introduced to give more freedom to design the controller. Indeed this new variable helps to find the optimal fixedorder output feedback controller. The second contribution is to propose a linearization algorithm to search for a solution to the nonconvex SLC problems. This has the effect of adding a certain potential function to the nonconvex constraints to make them convex. The convexified matrix inequalities will not bring significant conservatism because they will ultimately go to zero, guaranteeing the feasibility of the original nonconvex problem. Numerical examples demonstrate the performance of the proposed algorithms and provide a comparison with some of the existing methods.

… 2001. Proceedings of …, 2001

This paper examines the plant and controller optimization problems. One can solve these problems sequentially, iteratively, using a nested (or bi-level) strategy, or simultaneously. Unlike the nested and simultaneous strategies, the sequential and iterative strategies fail to guarantee system-level optimality. This is because the plant and controller optimization problems are coupled. This coupling is introduced using a simple experiment. To prove it theoretically, the necessary conditions for combined plant and controller optimality are derived. These combined optimality conditions differ from the individual sets of necessary conditions for plant and controller optimality by a coupling term that reflects the plant design's influence on the plant dynamics and control input constraints.

52nd IEEE Conference on Decision and Control, 2013

In this paper, a new approach to fixed-order H∞ and H2 output feedback control of MIMO discrete-time systems with polytopic uncertainty is proposed. The main idea of this approach is based on the definition of SPR-pair matrices and the use of some instrumental matrices which operates as a tool to overcome the original non-convexity of fixed-order controller design. Then, stability condition as well as H∞ and H2 performance constraints are presented by a set of linear matrix inequalities with linearly parameter dependent Lyapunov matrices. An iterative algorithm for update on the instrumental matrices is developed, that monotonically converges to a suboptimal solution. Simulation results show the effectiveness of the proposed approach.

1986

This paper presents a design method for simultaneous optimization of a large number of controller and plant parameters of high-order linear time-invariant systems. User-friendly supervision and control of several design objectives is achieved through an interactive graphics-supported design process. The application of the design package for optimal matching of construction and controller parameters is demonstrated in great detail taking as an example a vehicle model with actively controlled tandem wheel suspension.