Robust dynamical compensator design for discrete-time linear periodic systems

This paper presents as its main result a new and efficient method for the design of optimal dynamic compensators for linear multivariable control systems. The discussion starts with a fresh look into the design of optimal constant gain output feedback. In this context, three new ideas are introduced that prove their usefulness particularly in the dynamic compensator case: (1) deterministic measurement disturbances are included in the formulation of the underlying optimization problem, (2) the relationship between a deterministic and a stochastic optimal control problem is shown, (3) by proper modifications of the quadratic cost function, the effort involved in the numerical solution of the optimal output feedback problem is considerably reduced. Furthermore, a canonical form is introduced for the dynamic compensator and an algorithm is developed for the numerical computation of its free parameters. It is based on quasi-newtonian gradient methods and an efficient line search procedure. Some features of the new design method are demonstrated by means of a non-trivial benchmark taken from the literature.

This paper considers discrete-time Floquet transformations, by which a discrete-time periodic linear system can be transformed to a time-invariant one. The previous researches have made clear when a discrete-time periodic system has its Floquet transformations and also it is known that the system has a lot of Floquet transformations if it has one. This paper defines three new similarities between two Floquet transformations, clarifies some relations among those similarities, and also makes clear how a set of all Floquet transformations can be split into a finite number of equivalence classes.

Model matching for discrete-time periodic systems with time-varying relative degree and order

This paper presents a robust linear dynamic compensator design algorithm for linear uncertain systems whose parameters vary within given bounded sets. The algorithm explicitly incorporates the structure of the uncertainty into the design procedure and utilizes the elemental perturbation bounds developed recently. The special cases of linear state feedback and measurement feedback controllers are considered and the relative trade offs are discussed. The design algorithm is illustrated with the help of a simple example.

An algebraic theory of linear periodic discrete-time (LPDT) systems is developed in terms of a periodic polynomial matrix description (PMD) and in a dynamics (module) structure defined over a non-commutative, non-integral and non-principal ideal ring /spl Rscr/ (the ring of periodic polynomials). Various properties of matrices and modules over /spl Rscr/ are explored, and links between algebraic properties of LPDT systems such as reachability, controllability are established directly in the periodic PMD and /spl Rscr/-module descriptions; i.e., without using the technique of lifting a LPDT system to its associated linear time-invariant (LTI) ones. The advantage of such characterizations is to show that LPDT systems are not index-invariant only for a class-that we characterize-of non-reversible time systems and that, except for this class of systems, the parametrization of all stabilizing controllers can be constructed similarly to LTI systems. Furthermore, one shows that for the class of non-reversible time systems above-mentioned, it is not possible to extract a canonical part like for LTI systems.

This paper considers a subclass of hybrid systems, which is the discrete-time linear switching systems whose changes in the dynamics are determined by exogenous, uncontrollable events, and resets are present. In the presence of uncertain parameter and non-symmetrical constrained control, based on the results of nominal linear switching systems, a necessary and sufficient condition to test the robustness of a state feedback controller is given. The candidate state feedback controller for this test is that stabilizing nominal discrete-time linear switching systems. Also, the method in this paper can be extended to the case which has state constraints. At last, a numerical example is presented to illustrate the technique.

This paper researches and analyzes the modeling of electro-hydraulic proportional servo system to improve the characteristics of forging hydraulic servo control system and meet their requirements of forging a variety of materials. Based on robust compensator design, PID control strategy is proposed with uncertain disturbance of hydraulic press hydraulic servo system and the response characteristics of the system is simulated and analyzed. The results show that hydraulic press servo system which uses robust compensator has better performance than the traditional PID control and the chattering is eliminated. The test results and simulation results are compared by building simulation test system of 60MN hydraulic press electro-hydraulic proportional control system.

In this paper a basis is developed for the systematic design of linear multivariable discrete-time tracking systems for plants with inaccessible states, which thus extends the results for discrete-time plants with accessible states previously obtained by Bradshaw and Porter (1975). The design method is illustrated by the presentation of the results of computer simulation studies.

The linear continuous-time systems to be discussed are described by state space models with structured time-varying uncertainties. First, the explicit maximal perturbation bound for maintaining quadratic Lyapunov stability of the closed-loop systems is presented. Then, a robust design method is proposed. Given an open-loop, nominal system with information of the uncertainty structure, the proposed robust design method produces a linear constant output feedback control law which maximizes the perturbation bound for maintaining quadratic Lyapunov stability. Both the optimal results for robust analysis and robustness design can be obtained by using an efficient numerical algorithm (e.g. minimax of MATLAB) with analytic gradients given in this paper. Examples are investigated in some detail to show the improvements and advantages of the proposed methods over previous ones.

A contraction property for state feedback design of linear discrete-time systems

This paper studies the design of uncertain linear discrete-time Networked Control Systems over imperfect communication channels with time-varying data loss. This leakage is modeled as stochastic parameter and norm-bounded uncertainties. In addition, this paper defines the necessary conditions for the design of the dynamic output feedback controller; subsequently, an iterative LMI approach is specified to compute the controller state parameters. The simulation results show that the designed controller improves the H∞ disturbance attenuation performance of the concerned uncertain system.

The classical row-by-row decoupling problem with stability by the use of a dynamic compensator is studied for linear periodic discrete-time systems. The necessary and sufficient conditions for the existence of a solution are found, and a design procedure of the dynamic compensator (including a feedback subcompensator and a pre-subcompensator) is provided by the sufficiency proof, also for the case of a dead-beat requirement for the state free response.

This article deals with a new representation of linear discrete-time periodic systems. This representation, based on the time-varying z-transform, turns out to be highly efficient in the field of automatic control, when an appropriate choice of the sampling period is made. This representation permits to extend many well-known theorems, in particular, the initial- and final-value theorems, to the case of these systems and to predict the presence of limit cycles. Finally, this representation can be used to establish an extension of the Nyquist criterion to the feedback discrete-time periodic systems.

This brief revisits the problem of the semiglobal stabilization of discrete-time linear periodic systems with bounded controls. First, a new state feedback solution based on a parametric periodic Riccati equation is established to solve the problem under the condition that the open-loop characteristic multipliers are strictly inside or on the unit circle. Different from our early solution based on the parametric periodic Lyapunov equation, this new solution does not require any state transformation on the open-loop system and is theoretically more appealing. Second, an output feedback solution is presented in this brief, which complements the two state feedback solutions. Third, as a periodic system model, the multirate sampled-data system is considered, and the problem of semiglobal stabilization for such a system subject to input saturation is solved. In doing so, the connections between the semiglobal stabilizability of the original continuous-time system and of the multirate sampled-data system are established. A numerical example is worked out to illustrate the effectiveness of the proposed design.

SummaryThis paper presents the design of output feedback controllers for discrete‐time (DT) linear systems. New sufficient LMI conditions are derived for designing static and controllers using decomposition of an auxiliary matrix. The decomposition facilitates linearization of nonlinear term of reduced size to obtain linear matrix inequality criteria. This leads to less conservative results as shown in the numerical examples. In addition, the proposed static output feedback criteria is also used for designing dynamic output feedback controllers for DT systems. Furthermore, a comparative study is also made for the proposed design method with the results existing in the literature. Finally, a DT static output feedback controller is designed for a quarter‐car suspension system. Simulation results are provided to show the efficacy of the proposed design method.