Robust Suboptimal Control Research Articles

Adaptive suboptimal robust control of the first-order plant

For a linear first-order plant, consideration was given to minimization of the deviation of its output from the specified value in an uncertain environment. Both the parameters of the plant itself and the upper bounds of the external disturbances and operator perturbations in output and control were assumed to be unknown. The suboptimal adaptive control was constructed on the basis of an approximate solution of the problem of optimal identification from the measurement data where the performance of the problem of control was used as an identification criterion.

Design of suboptimal robust controllers under unknown weights of perturbations

In the classical formulations of the problems of design of the robust optimal controllers, the equations of the nominal plant and the weights of the permissible perturbations are assumed to be known. In the present paper, consideration was given to a nonclassical formulation of the design problem where the weights of perturbations are assumed to be unknown and subject to estimation from the measurement data. The multivariable discrete-time controlled plant was described by a given transfer matrix with perturbations in the irreducible factors and a bounded external perturbation. The problem of determination with a predefined accuracy of the perturbation weights that are best coordinated with the measurements and of their corresponding suboptimal controller was solved.

ROBUST MODEL PREDICTIVE CONTROL FOR SWITCHED PIECEWISE LINEAR HYBRID SYSTEMS

This paper investigates the robust tracking and regulation control problems for discrete-time, switched piecewise linear hybrid systems affected by parameter variations. In particular, the main question addressed is related to the existence of a controller such that the closedloop system exhibits an attainable desired behavior under all possible parameter variation. Checking attainability and calculating the state space regions for which a robust control is assured despite the uncertainty is performed using a polyhedral approach. A model predictive control law derived from a quadratic cost function minimization is further examined as a simple and fast sub-optimal robust control. An application of the proposed technique to a two-tank benchmark is finally presented.

Limitations of linear control of thermal convection in a porous medium

The ability of linear controllers to stabilize the conduction (no-motion) state of a saturated porous layer heated from below and cooled from above is studied theoretically. Proportional, suboptimal robust (H∞) and linear quadratic Gaussian (H2) controllers are considered. The proportional controller increases the critical Rayleigh number for the onset of convection by as much as a factor of 2. Both the H2 and H∞ controllers stabilize the linearized system at all Rayleigh numbers. Although all these controllers successfully render negative the real part of the linearized system’s eigenvalues, the linear operator of the controlled system is non-normal and disturbances undergo substantial growth prior to their eventual, asymptotic decay. The dynamics of the nonlinear system are examined as a function of the disturbance’s amplitude when the system is subjected to the “most dangerous disturbances.” These computations provide the critical amplitude of the initial conditions above which the system can no longer be stabilized. This critical amplitude decreases as the Rayleigh number increases. To facilitate extensive computations, we examine two-dimensional convection in a box containing a saturated porous medium, heated from below and cooled from above, as a model system. The heating is provided by a large number of individually controlled heaters. The system’s state is estimated by measuring the temperature distribution at the box’s midheight. All the controllers considered here render the linearized, controlled system’s operator non-normal. The transient amplification of disturbances limits the “basin of attraction” of the nonlinear system’s controlled state. By appropriate selection of a controller, one can minimize, but not eliminate, the controlled, linear system’s non-normality.

ROBUST MODEL PREDICTIVE CONTROL FOR PIECEWISE AFFINE SYSTEMS SUBJECT TO BOUNDED DISTURBANCES

This paper investigates the robust tracking and regulation control problems for discrete-time, piecewise affine systems subject to bounded disturbances. In particular, the main question addressed is related to the existence of a controller such that the closed-loop system exhibits an attainable desired behavior under all possible disturbances. Checking attainability and calculating the state space regions for which a robust control is assured despite the disturbance is performed using a polyhedral approach. A model predictive control law derived from a quadratic cost function minimization is further examined as a fast sub-optimal robust control. An application of the proposed technique to a two-tank benchmark is finally presented.

Design of robust gain-scheduled PI controllers for nonlinear processes

Gain-scheduling has proven to be a successful design methodology in many engineering applications. However, in the absence of a sound theoretical analysis, these designs come with no guarantees of robust stability, performance or even nominal stability of the overall gain-scheduled deign. This paper presents such an analysis for one type of nonlinear gain-scheduled control system based on the process input for nonlinear chemical processes. A methodology is also proposed for the design and optimization of the robust gain-scheduled PI controller. Conditions which guarantee robust stability and performance are formulated as a finite set of linear matrix inequalities (LMIs) and hence, the resulting problem is numerically tractable. Issues of modeling error and input-saturation are explicitly incorporated into the analysis. A simulation study of a nonlinear continuous stirred tank reactor (CSTR) process indicates that this approach can produce efficient sub-optimal robust gain-scheduled controllers.

Iterative design of robust controllers under unknown bounded perturbation norms

A suboptimal robust controller for a multidimensional linear stationary nominal system with output- and control-operator perturbations and a bounded external perturbation is designed. Perturbation norms (weights) are assumed to be unknown and estimated from measurement data. The quality index of the closed-loop control system is taken to be the worst ??-norm for the output of the system in the class of admissible perturbations. The quality index for systems in the class of linear stationary stabilizing controllers is a fractional linear function of induced norms of transfer matrices of the closed-loop system and perturbation norms. The classical design of suboptimal robust controllers under known perturbation norms is reduced to a standard ?1-optimization problem, and optimal estimation of unknown perturbation norms is reduced to a linear programming problem. Therefore, the iterative sequential method of controller design and perturbation norm estimation is used as a heuristic method for designing suboptimal robust controllers under unknown perturbation norms. Modeling results corroborate the effectiveness of this method.

Design of Sub-Optimal Robust Gain-Scheduled PI Controllers

A methodology is proposed for the analysis and design of a robust gain-scheduled PI controller for nonlinear chemical processes. The stability and performance tests can be formulated as a finite set of linear matrix inequalities (LMI) and hence, the resulting problem is numerically tractable. Input saturation and model error are explicitly incorporated into the analysis. A simulation study of a nonlinear CSTR (continuous stirred tank reactor) process indicates that this approach can provide useful sub-optimal robust controllers.

Decentralized Robust Fuzzy Sliding Mode Control Design of Interconnected Uncertain System

We present a fuzzy approach to design a robust suboptimal control for decentralized interconnected system. We denote the non-linear interactions between the sub-systems are uncertain and in many real-life situation it can be represented by the differences of actual behavior from nominal description of sub-systems (e, é). Fuzzy sliding mode control is designed hr sub-system to track the prespecified trajectory in phase plane (e, é) according it’s states (x,x´). Fuzzy adaptation is proposed for tuning closed-related control subsystem on the sliding surface toward new equilibrium points. The adaptation strategy is determined by rule bases based on considering controller as PID controller with variable structure, switching between different PID settings with different inputs (e, é).

Design of the l1-suboptimal Robust Controller for the Linear Object with Nonstructured Uncertainty

Design of the i>l1-suboptimal robust controller for the linear discrete scalar object with constrained external perturbation and nonstructured operator perturbation in input and control was considered. The worst value of the i>l∞-norm of object output in the class of admissible perturbations was regarded as the performance index of the control system. The problem of designing the optimal robust controller was interpreted in the geometric terms, and an algorithm to design the suboptimal controller was proposed. A numerical example was used to demonstrate effciency of the algorithm, the ways to improving it, and the differences between the suboptimal robust controllers with structured and nonstructured operator perturbations.

Low Order Suboptimal Robust Controller Design for Systems with Structured Uncertainty

Abstract This paper considers the problem of designing robust controllers for linear plants affected by rank one real perturbations. The main objective of the paper is to use a convex parameterization of robustly stabilizing controllers for optimizing the stability margin over an assigned class of low complexity controllers. In fact, it is well known that if no constraints on the controller structure are imposed, the complexity of the resulting optimal controller is usually excessive. In this paper, a procedure is proposed which allows one to select a suboptimal controller within a fixed class, by solving a sequence of linear matrix inequalities feasibility problems. Several application examples are reported to discuss the performance of the proposed procedure.

Design of suboptimal H/sup ∞/ excitation controllers

This paper presents a method to design power system suboptimal robust excitation controllers based on H/sup /spl infin// control theory. The suboptimal controller results from additional constraints that are imposed on the standard optimal H/sup /spl infin// solution. Global stability constraints are incorporated into the H/sup /spl infin// algorithm to ensure stability of the interconnected system under decentralized control. Furthermore, a Lyapunov-based index is used to evaluate the robustness properties of the closed loop. In order to obtain a reduced order controller, the method of balanced truncation is used. The suboptimal H/sup /spl infin// controllers are output feedback controllers. These controllers posses superior robustness as compared to a conventional PSS and optimal H/sup /spl infin// controllers.

Suboptimal Ellipsoidal Boundin for Simple Robust Control in Self-Tuning Robust Control

This paper considers ellipsoidal parameter bounding for self-tuning robust control of a sampled process using a controller which is performance robust with respect to this feasible process parameter set. This parameter set is obtained by an ellipsoidal parameter bounding method using unknown but bounded disturbance with known bounds. The ellipsoidal method used is based on a criterion specifically chosen for suboptimal robust control. A comparison with the minimum volume method demonstrates the advantage of this approach.

063 Performance recovery approach to H∞ robust sub-optimal control

Abstract The paper is concerned with H∞ robust sub-optimal control problem for linear time invariant systems with structural uncertainties. The main result shows that if there exists a state feedback gain matrix which ensures H∞ robust sub-optimality of the closed loop system, then the robust performance achieved by the state feedback can be asymptotically recovered by a controller with high gain observer.

State feedback performance recovery via an observer in [formula omitted] robust control

The paper is concerned with H ∞ robust suboptimal control problem for linear time-invariant systems with structural uncertainties. The main result shows that if there exists a state feedback gain matrix which ensures H ∞ robust suboptimally of the closed-loop system, then the robust performance achieved by the state feedback can be asymptotically recovered by a controller with high-gain observer.

Performance Recovery Approach to H∞ Robust Sub-optimal Control

The paper is concerned with H∞ robust sub-optimal control problem for linear time invariant systems with structural uncertainties. The main result shows that if there exists a state feedback gain matrix which ensures H∞ robust sub-optimality of the closed loop system, then the robust performance achieved by the state feedback can be asymptotically recovered by a controller with high gain observer.

065 Synthesis of a robust suboptimal controller based on the optimality minimax criteria

065 Synthesis of a robust suboptimal controller based on the optimality minimax criteria

Riccati 不等式の負定余裕と時変パラメータ摂動に対する <i>H</i><sub>∞</sub>ロバスト準最適制御

Riccati 不等式の負定余裕と時変パラメータ摂動に対する <i>H</i><sub>∞</sub>ロバスト準最適制御

Design of a Trajectory Insensitive Regulator With Prescribed Degree of Stability

The paper outlines an approach for designing a trajectory insensitive optimal linear quadratic regulator (LQR) with prescribed degree of stability for uncertain plants. The state trajectory insensitivity to structural uncertainties is achieved by designing a robust suboptimal controller of proportional state, and proportional derivative of state type. The prescribed degree of stability is obtained by appropriate modification of the quadratic cost functional. The proposed method is superior to some recent approaches as far as the computational complexity and robustness are concerned.