Multi-objective Robust Control Research Articles

Multi Objective Robust Active Vibration Control for Flexure Jointed Struts of Stewart Platforms via H∞ and μ Synthesis

Active vibration control is needed for future space telescopes, space laser communication and other precision sensitive payloads which require ultra-quiet environments. A Stewart platform based hybrid isolator with 6 hybrid struts is the effective system for active/passive vibration isolation over 5–250 Hz band. Using an identification transfer matrix of the Stewart platform, the coupling analysis of six channels is provided. A dynamics model is derived, and the rigid mode is removed to keep the signal of pointing control. Multi objective robust H∞ and μ synthesis strategies, based on singular values and structured singular values respectively, are presented, which simultaneously satisfy the low frequency pointing and high frequency disturbance rejection requirements and take account of the model uncertainty, parametric uncertainty and sensor noise. Then, by performing robust stability test, it is shown that the two controllers are robust to the uncertainties, the robust stability margin of H∞ controller is less than that of μ controller, but the order of μ controller is higher than that of H∞ controller, so the balanced controller reduction is provided. Additionally, the μ controller is compared with a PI controller. The time domain simulation of the μ controller indicates that the two robust control strategies are effective for keeping the pointing command and isolating the harmonic and stochastic disturbances.

Robust multi-objective control for the station keeping of the interferometric cartwheel

Groups of satellites flying in formation require maintaining the specific relative geometry of the formation with high precision. This requirement implies to consider the problem of relative station keeping in a renewed framework. In this framework, issues related to the derivation of reliable relative models as well as to the peculiarity of the synthesis problems must be jointly considered. This paper presents some preliminary results of a robust multi-objective control approach applied to the station keeping of a low Earth observation system, i.e. the interferometric cartwheel, patented by CNES. This wheel is made up of three receiving spacecrafts, which follow an emitting Earth observation radar satellite. The particular geometry of this formation of satellites leads to the derivation of a simplified uncertain state-space model. Atmospheric drag perturbations are included in the linearized equations of the relative motion and the atmospheric density part of the definition of the atmospheric drag force is considered to be uncertain due to its dependence upon the solar activity. In the first part of the paper, an uncertain polytopic state-space model is derived. The second part describes the station keeping strategy of the formation. The station keeping strategy is performed using pure passive actuators. Due to the high stability of the relative eccentricity of the formation, only the relative semi major axis has to be controlled. Differential drag due to a differential orientation of the solar panel is used here to control relative altitude. A robust multi-objective control strategy via state-feedback is developed and tested as autonomous orbit controller. These results are analyzed via highly non linear simulations performed on a platform of CNES.

Robust decentralized controller with multi-objective performance design for stochastic large-scale systems via linear matrix inequalities approach

The present paper focuses on a class of stochastic large-scale interconnected systems with norm-bounded and time-varying parameter uncertainties. The problem addressed is the design of a robust decentralized controller such that the corresponding interconnected closedloop system satisfies certain multi-objective performance requirements for all admissible uncertainties. The objectives of this robust design consist of individual state variance limitation, white noise attenuation constraints on H∞ norm, and pole placement specification. Suffcient conditions, based on a quadratic Lyapunov function, for multi-objective robustness are derived in terms of linear matrix inequalities (LMIs). It is shown that the problem of multi-objective robust decentralized control can be solved and the effectiveness of the proposed approach is illustrated by a numerical example.

Solving and visualizing nonlinear parametric constraints in control based on quantifier elimination

We present a new method with a software tool for parametric robust control synthesis by symbolic-numeric computation. The method is a parameter space approach and it is especially effective for analysis and design of fixed-structure controllers of rational type, which encompass PI and PID controllers. The real quantifier elimination (QE), which is one of the recent progresses in the symbolic computation, plays a key role in our development. The QE-based approach can uniformly deal with a lot of important design specifications for robust control such as frequency restricted H ∞ norm constraints, stability (gain/phase) margin and stability radius specifications, and pole location requirement by reducing such specifications to a particular type of formulae called a “sign definite condition (SDC)”. This is also useful for improving the efficiency of QE computations since we can utilize an efficient QE algorithm specialized to the SDC using the Sturm-Habicht sequence. We have developed a MATLAB toolbox for robust parametric control based on a parameter space approach accomplished by QE. The QE-based parameter space approach and numerical simulation of performances for specific controller parameter values taken from a controller parameter space are integrated conveniently in our toolbox with the assistance of a graphical user interface (GUI). With our toolbox the feasible regions of controller parameters are visualized in a parameter space for the controllers with three or two parameters. This enables control engineers to achieve multi-objective robust controller synthesis smoothly. We also discuss how to merge the numerical computation and the symbolic operation to make our new design methods more efficient in practical control design.

Boîte à outils « robust multi-objective control » - version 1. Fondements théoriques de RoMulOC et son utilisation illustrée sur des exemples

For the past ten years the formalism of Linear Matrix Inequalities has lead to many results for robust analysis and synthesis. One major characteristic of these results is the variety of performances and uncertain models that may be tackled. Although every individual result may be easily coded we felt necessary to gather all the results in a unique toolbox. It allows to put in evidence the complementarity of all these results developed separately. This paper is devoted to the first version of the Robust Multi-Objective Control toolbox. It is

Multi-objective robust controller synthesis for discrete-time systems with convex polytopic uncertain domain

Multi-objective robust controller synthesis for discrete-time systems with convex polytopic uncertain domain

Mixed Gl2/GH2 multi-channel multi-objective control synthesis for discrete time systems

This paper proposes a new approach for multi-objective robust control. The approach extends the standard generalized l2 (Gl2) and generalized H2 (GH2) conditions to a set of new linear matrix inequality (LMI) constraints based on a new stability condition. A technique for variable parameterization is introduced to the multi-objective control problem to preserve the linearity of the synthesis variables. Consequently, the multi-channel multi-objective mixed Gl2/GH2 control problem can be solved less conservatively using computationally tractable algorithms developed in the paper.

Multi-Objective Robust Control of an Evaporation Process

In this paper, a new multi-objective robust control design approach is applied to an evaporation process. The new approach, proposed in (Yan and Cao, 2002) extends the standard generalized-12 (G12) control problem based on a new Lyaponov stability condition to a set of new linear matrix inequality (LMI) constraints such that the multi-objective robust control problem associated with robust stability and robust performance objectives can be less conservatively solved using computationally tractable algorithms. A comparison of simulation results with controllers designed by different techniques demonstrates the superiority of the new method.

Design of PID-type controllers using multiobjective genetic algorithms

Abstract The design of a PID controller is a multiobjective problem. A plant and a set of specifications to be satisfied are given. The designer has to adjust the parameters of the PID controller such that the feedback interconnection of the plant and the controller satisfies the specifications. These specifications are usually competitive and any acceptable solution requires a tradeoff among them. An approach for adjusting the parameters of a PID controller based on multiobjective optimization and genetic algorithms is presented in this paper. The MRCD (multiobjective robust control design) genetic algorithm has been employed. The approach can be easily generalized to design multivariable coupled and decentralized PID loops and has been successfully validated for a large number of experimental cases.

MRCD: a genetic algorithm for multiobjective robust control design

A genetic algorithm (GA) for the class of multiobjective optimization problems that appears in the design of robust controllers is presented in this paper. The design of a robust controller is a trade-off problem among competitive objectives such as disturbance rejection, reference tracking, stability against unmodeled dynamics, moderate control effort and so on. However, general methodologies for solving this class of design problems are not easily encountered in the literature because of the complexity of the resultant multiobjective problems. In this paper, a recently developed class of GAs, multiobjective GAs, are used to solve robust control design problems. Here, a new algorithm, called multiobjective robust control design, has been proposed. The structure and operators of this algorithm have been specifically developed for control design problems. The performace of the algorithm is evaluated by solving several test cases and is also compared to the standard algorithms used for the multiobjective design of robust controllers.

Multiobjective Robust Control of Flexible Structure with Observer

In this paper the multiobjective robust control method for the vibration control of flexible structure is studied. The parameter uncertainty of the system is formulated as a H∞ optimal problem and the state feedback H2/H∞ mixed norm control with pole placement constraint is solved by LMI (linear matrix inequalities). Robustness of observer to the parameters uncertainty of system matrix is also formulated as a H∞ optimal problem with pole placement constraints and solved by LML. Simulation results show that this controller design approach is robustness under large parameters perturbation

Analysis and synthesis of the robust impulse-to-peak performance

Analysis and synthesis methods are proposed to guarantee upper bounds on the worst-case peak values of impulse responses in the presence of plant perturbations. The results provide solutions to a class of the multi-objective robust control problems with time-domain specifications, including servo/tracking and disturbance attenuation problems. The analysis problem and the synthesis problem both reduce to tractable linear matrix inequality problems. The proposed synthesis method is illustrated for a simple mechanical system with preview action.

Observer-based controller for robust pole clustering in a vertical strip and disturbance rejection in structured uncertain systems

This paper presents an observer-based multi-objective robust feedback controller to achieve robust pole clustering within a vertical strip and disturbance rejection with an H∞-norm constraint for the uncertain linear systems. The systems of interest include both matched and mismatched uncertain linear systems with structured uncertainties existing in both the system and input matrices. The controller is obtained by solving two Riccati equations (one for the controller and the other for the observer) and checking three conditions (two for robust pole clustering). A set of tuning parameters is incorporated to enhance flexibility in finding the controller. © 1998 John Wiley & Sons, Ltd.

Multiobjective Robust Control Toolbox for LMI-Based Control

This paper presents a public domain toolbox built on top of the software LMITOOL and the Semidefinite Programming package. The Multiobjective Robust Control Toolbox is a collection of synthesis LMI-based tools for a large class of nonlinear uncertain systems. It provides solutions for the robust state- and output-feedback controller synthesis under various specifications. These specifications include performance requirements via α-stability, L2-gain bounds and command input and outputs bounds.

Multiobjective robust control of LTI systems subject to unstructured perturbations

We consider a multiobjective robust controller synthesis problem for an LTI system subject to unstructured perturbations. Our design specifications include robust stability, robust performance ( H 2-norm) bounds and time-domain bounds (output and command input peak). We derive sufficient conditions, based on a single quadratic Lyapunov function, for the existence of an LTI controller such that the closed-loop system satisfies all specifications simultaneously. These conditions can be numerically checked using finite-dimensional, convex optimization over LMIs, associated with a two-dimensional search. When considering only a subset of the specifications, we recover previous results from the literature, such as those obtained in mixed H 2/ H ∞ control.

Robust Multiobjective LTI Control Design for Systems with Structured Perturbations

We consider a multiobjective robust controller synthesis problem for an LTI system subject to structured perturbations. Our design specifications include robust stability, robust performance (H2-norm) bounds and time-domain bounds (output and command input peak). We derive sufficient conditions, based on a single quadratic Lyapunov function, for the existence of an LTI controller such that the closed-loop system satisfies all specifications simultaneously. These nonconvex conditions can be numerically checked with an efficient LMI-based heuristic. We illustrate our results on a three-parameter mass/spring system.