H∞ Optimal Controller Design With Closed-Loop Positive Real Constraints

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
L. Hewing ◽  
S. Leonhardt ◽  
P. Apkarian ◽  
B. J. E. Misgeld
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Controller Synthesis ◽  
Optimal Controller ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Positive Real ◽  
Promising Tool ◽  
Control Framework ◽  
Real Constraint

Positive real constraints on the closed-loop of linear systems guarantee stable interaction with arbitrary passive environments. Two such methods of H∞ optimal controller synthesis subject to a positive real constraint are presented and demonstrated on numerical examples. The first approach is based on an established multi-objective optimal control framework using linear matrix inequalities and is shown to be overly restrictive and ultimately infeasible. The second method employs a sector transformation to substitute the positive real constraint with an equivalent H∞ constraint. In two examples, this method is shown to be more reliable and displays little change in the achieved H∞ norm compared to the unconstrained design, making it a promising tool for passivity-based controller design.

Advanced gain scheduledH∞controller for robotic manipulators

Robotica ◽  
2002 ◽  
Vol 20 (5) ◽  
pp. 537-544
Author(s):  
Zhongwei Yu ◽  
Huitang Chen ◽  
Peng-Yung Woo
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Robotic Manipulators ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Vertex Set ◽  
Parameter Dependent ◽  
Gain Scheduled ◽  
Upper Boundary

SummaryA conservatism-reduced design of a gain scheduled output feedbackH∞controller for ann-joint rigid robotic manipulator, which integrates the varying-parameter rate without their feedback, is proposed. The robotic system is reduced to a 1inear parameter varying (LPV) form, which depends on the varying-parameter. By using a parameter-dependent Lyapunov function, the design of a controller, which satisfies the closed-loopH∞performance, is reduced to a solution of the parameterized linear matrix inequalities (LMIs) of parameter matrices. With a use of the concept of “multi-convexity”, the solution of the infinite LMIs in the varying-parameter and its rate space is reduced to a solution of the finite LMIs for the vertex set. The proposed controller eliminates the feedback of the varying-parameter rate and fixes its upper boundary so that the conservatism of the controller design is reduced. Experimental results verify the effectiveness of the proposed design.

Substructural Multiobjective H∞ Controller Design for Large Flexible Structures: A Divide-and-Conquer Approach Based on Linear Matrix Inequalities

2005 ◽  
Vol 219 (5) ◽  
pp. 319-334 ◽  
Author(s):  
O Toker ◽  
M Sunar
Keyword(s):  
Linear Matrix Inequalities ◽  
Closed Loop ◽  
Controller Design ◽  
Flexible Structures ◽  
Computation Time ◽  
Divide And Conquer ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Static Condensation

In this paper, a novel substructural approach is proposed and successfully implemented for H∞ robust controller design for large flexible structures. It is assumed that sensors and actuators are discrete and located at some nodal points of the structure. In general, a finite element method (FEM)-based modelling approach results in a matrix differential equation of large dimensions. As the dimension becomes larger and larger controller design algorithms require more and more computation time, and start to have numerical problems. To cope with these difficulties, there are many known techniques in the literature, including the decentralized- and substructural-type methods. In this paper, a substructural-type approach based on the static condensation principle is adopted and the H∞ optimal controller design problem for large flexible structures is studied. The key point in the present approach is that the static condensation is performed in the abstract state space. Geometric information about the flexible structure is utilized in deciding how to do the state decomposition, then H∞ optimal controllers are designed at the substructure level, and finally a global controller is assembled for the whole structure. To improve the convergence of the algorithm, a multi-objective H∞ optimization approach is adopted. More precisely, while forcing the closed-loop poles to be in a given convex region to ensure fast dynamics, and hence improve the convergence of the substructural iterations, the H∞ objective function is minimized to achieve maximum robustness. The main advantage of this approach is that both the H∞ objective and the constraints on closed-loop poles can be expressed as a convex problem and formulated as linear matrix inequalities (LMIs), which can be solved easily, e.g. by LMI Toolbox of MATLAB. Overall, the proposed approach results in a reduction in computation time and improvements in numerical reliability as the problem of large size is decomposed into several smaller-size problems. The accuracy and effectiveness of the substructural H∞ control technique are tested on benchmark problems, and effects of structural non-linearities are studied.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

scholarly journals Design of delay observer-based controllers for uncertain time-lag systems

1999 ◽  
Vol 5 (2) ◽  
pp. 121-137 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Mohamed Zribi
Keyword(s):  
Uncertain Systems ◽  
Closed Loop ◽  
Time Lag ◽  
Linear Matrix ◽  
Time Lags ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Delayed Measurements ◽  
Uncertain Time ◽  
Theoretical Developments

In this paper, the problem of designing observers and observer-based controllers for a class of uncertain systems with input and state time lags is considered. We construct delay-type observers in which both the instantaneous as well as the delayed measurements are utilized. Using feedback control based on the reconstructed state, the behavior of the closed-loop system is investigated. It is established that the uncertain time-lag system with delay observer-based control is asymptotically stable. Expressions for the gain matrices are given based on two linear-matrix inequalities. A numerical example is given to illustrate the theoretical developments.

Fixed-order ℋ∞ controller design for MIMO systems via polynomial approach

2018 ◽  
Vol 41 (7) ◽  
pp. 1985-1992 ◽  
Author(s):  
Bilal Erol ◽  
Akın Delibaşı
Keyword(s):  
Traditional Method ◽  
Controller Design ◽  
Mimo Systems ◽  
Linear Matrix ◽  
Main Difficulty ◽  
Matrix Inequalities ◽  
Central Polynomial ◽  
Fixed Order ◽  
Inner Approximation ◽  
Associated Solution

This paper presents a fixed-order [Formula: see text]∞ controller design based on linear matrix inequalities for multi-input–multi-output systems. The main difficulty in the development of a fixed-order controller design is that the associated solution set of the problem is defined in a non-convex cluster, and that makes the problem computationally intractable. The convex inner approximation is used to deal with this non-convexity. The proposed controller design approach is applied to some elegant numerical problems taken from various previous works. To show the effectiveness of the proposed method, the full-order [Formula: see text]∞ controller and fixed-order controllers are constructed for these models using the traditional method and popular toolboxes, respectively. Furthermore, in this paper, some strategies for choosing the central polynomial, which is the main conservatism of the proposed method, are discussed.

Non-Fragile Decentralized Control for the Uncertain Singular Large-Scale Systems with Time-Delay

2011 ◽  
Vol 317-319 ◽  
pp. 2204-2207
Author(s):  
Dong Mei Yang ◽  
Qing Sun
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Decentralized Control ◽  
Large Scale ◽  
Controller Design ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Large Scale Systems ◽  
System With Time Delay

This paper is concerned with the non-fragile decentralized controller design problem for uncertain singular large-scale system with time-delay. Sufficient condition for the controller is expressed in terms of linear matrix inequalities(LMIs). When this condition is feasible, the desired controller can be obtained with additive gain perturbations and multiplicative gain perturbations. Finally, a numerical example is also given to illustrate the effectiveness.

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