Tsuyoshi Kiyama

Generalized sector synthesis of output feedback control with anti-windup structure

This paper considers the control synthesis problem for linear time invariant (LTI) continuous-time systems with actuator saturation nonlinearities. The control architecture is standard; a nominal LTI output feedback with an anti-windup (AW) mechanism. Traditional approaches have focused on AW synthesis where the nominal controller is first designed to achieve a local performance in the linear region of the actuators and then the AW compensator is added to guarantee stability/performance properties when the actuators saturate. In contrast, this paper proposes a synthesis method to design both the nominal controller and the AW compensator simultaneously. Using the generalized sector (GS) approach in the multiplier setting, a sufficient condition is given in terms of linear matrix inequalities so that a given ellipsoid is synthesized as a domain of attraction for the closed-loop system. Our result is shown to include the existing results on the simultaneous circle synthesis and the anti-windup GS synthesis as special cases. This paper also shows that the direct feed-through term in the AW compensator does not contribute to enlarging the achievable domain of attraction within the multiplier GS framework.

A design procedure of output regulation problems for anti-windup control systems

This paper considers an output regulation problem for a linear time invariant continuous-time system with saturation nonlinearities and/or an anti-windup control system which consists of controlled objects, servocompensators following the internal model principle, and dynamic output feedback, anti-windup and feedforward controllers. This problem is mainly concerned with perfect tracking and/or rejection of exogenous signals generated by some external systems. This paper proposes a convex design procedure which allows us to design dynamic output feedback, anti-windup and feedforward controllers simultaneously based on the existing output regulatable conditions. Our proposed design procedure guarantees a local stability and achieves the desired output regulation performance in a specific state space domain (a domain of quadratic performance). It is pointed out that our derived conditions can be recast as the linear matrix inequality (LMI) conditions permitting the existence of an algebraic loop from the output to the input of the saturation nonlinearities

On the relation between analysis and synthesis conditions for discrete-time systems with saturation nonlinearities

This paper considers linear time-invariant (LTI) discrete-time systems with saturation and/or dead-zone nonlinearities, and proposes analysis and synthesis methods of a regional l2performance and/or a pole placement based on a quadratic Lyapunov function via a generalized sector and a polytopic approach. In particular, a new domain of l2performance is defined by a region of initial states of the system considering the l2performance and/or the pole placement. For analysis, the problems based on the two approaches can be recast as linear matrix inequality (LMI) optimization ones respectively, and in the special case of single saturation or single dead-zone nonlinearity, it is proved that the generalized sector approach is exactly the same as the polytopic approach. Similarly, for synthesis, the problem based on the generalized sector approach can be recast as an LMI optimization problem where the outputs of the nonlinearities are assumed to be available for control. Next, the relation is clarified that the analysis and synthesis conditions can be reduced to the corresponding conditions for the continuous-time systems as the sampling period goes to zero. Finally, it is pointed out that our LMI-based approach is helpful through a numerical example designing anti-windup control systems.

A solvability condition of general robust control problems

This paper is concerned with the robust well-posedness problem which is an extension of a general robust control problem. We derive a new solvability condition of the problem in the form of a linear matrix inequality (LMI) condition adding a rank condition. The condition is still nonconvex due to the existence of the rank condition. However, it can be checked approximately with the alternating projection method, and the approach might be more efficient than the existing methods from the viewpoint of computation.

RELIABILITY AND EFFICIENCY OF EXTENDED LINEARIZATION ALGORITHMS FOR GENERAL ROBUST CONTROL PROBLEMS

Abstract This paper proves that a certain class of nonconvex matrix inequalities is equivalent to linear matrix inequalities (LMIs) plus a nonconvex rank constraint. From the equivalence, this paper proposes two heuristic algorithms, that is extended linearization algorithms, to solve LMIs with a rank constraint using LMI-based approach. Reliability and efficiency of the algorithms are investigated statistically, and then extensive numerical experiments will indicate that the algorithms have decent performances from the viewpoint of computation in comparison with the existing method: the standard alternating projection method. It is also important that our approaches can be applied to a large number of other rank-minimization problems over LMIs, for example, the robust well-posedness problem which is an extension of general robust control problems.

THE RELATION BETWEEN POLYTOPIC AND MULTIPLIER APPROACHES FOR ANTI - WINDUP CONTROL SYNTHESIS

Abstract This paper is concerned with regional stabilization: a domain of attraction for anti-windup control systems by a polytopic approach and a multiplier one respectively. In particular, the paper considers integrated stabilizing synthesis problems of dynamic output feedback controllers and anti-windup ones depending on the two approaches. The paper indicates that both synthesis problems can be recast as linear matrix inequality (LMI) optimization problems, where, for the synthesis, the outputs of the saturation elements are assumed to be available for the control. Finally, the paper clarifies the inclusion relation between the two synthesis conditions and systematical meanings of the conditions.

Limitation and Effectiveness of Polytopic Approach for Saturating Control

Abstract We propose quadratic performance analysis and state feedback synthesis methods based on a polytopic approach for linear time invariant systems with saturation. In the analysis case, the polytopic approach is theoretically less conservative than both the circle criterion and the existing linear analysis. However, in the synthesis case, the synthesis condition with the polytopic approach is theoretically equivalent to one with the circle criterion or the linear analysis in the meaning of the same achievable quadratic performance levels despite obtaining different state feedback controllers respectively. Finally, we propose a synthesis method making use of effectiveness of the polytopic approach.

Generalized sector synthesis of reduced-order output feedback controllers for discrete-time servosystems with control input saturation

This paper considers linear time-invariant discrete-time servosystems with control input saturation nonlinearities represented by δ-operator, and proposes a design method of discrete-time output feedback controllers satisfying a regional summational quadratic performance for the systems based on the generalized sector approach. For a given discrete-time servocompensator, the method assumes the output of the nonlinearities to be available for the control, and then it is an integrated design of discrete-time reduced-order dynamic output feedback and anti-windup compensators where each of their orders is the number of available plant states less than the plant order. This paper recasts the design problem using the method as a convex optimization problem based on linear matrix inequalities and linear matrix equations. Furthermore, it is pointed out that the performance achievable by the full-order compensator with the same generalized plant order is exactly the same as that by the reduced-order compensator.

l 2 Performance Synthesis via Polynomial Parameter-Dependent Switching State Feedback Control for Constrained Systems

This paper proposes a switching control method based on error systems from multi-equilibrium points of constrained systems using homogeneous polynomial parameter-dependent saturating state feedback gains. First, mufti-equilibrium points are calculated from the origin to a steady state in state space regions. Next, analysis and synthesis conditions of the domain of lscr2 performance for the systems can be recast as parameter-dependent matrix inequality conditions via the polytopic approach for the saturation. In particular, the parameter-dependent conditions are reduced to necessary and sufficient parameter-independent matrix inequality conditions based on Polyas theorem. Hence, the state feedback gains are designed by derived synthesis linear matrix inequality conditions using off-line computation, and the gains are applied to the system by on-line computation of a proposed switching algorithm. Finally, it is confirmed through a numerical example that the proposed switching control is definitely helpful.

L∞ PERFORMANCE ANALYSIS/SYNTHESIS FOR CONTINUOUS-TIME CONTROL SYSTEMS WITH ACTUATOR SATURATION UNDER L∞ BOUNDED DISTURBANCE

Abstract This paper considers anti-windup control systems and/or linear time invariant continuous-time systems with actuator saturation under persistent disturbances bounded in L ∞ norm. Our objective is to design dynamic output feedback controllers and anti-windup ones simultaneously that, in the presence of disturbances, causes closed-loop system trajectories starting from a larger invariant set to converge to a smaller invariant set guaranteed with the L ∞ performance. The invariant sets are expressed by a level set of quadratic Lyapunov functions. In synthesis, the effectiveness in the case when their Lyapunov variables are different from the common Lyapunov variable will be point out.