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.

scholarly journals Output feedback controller design for polynomial linear parameter varying system via parameter-dependent Lyapunov functions

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769032 ◽  
Author(s):  
Xiaobao Han ◽  
Zhenbao Liu ◽  
Huacong Li ◽  
Xianwei Liu
Keyword(s):  
Output Feedback ◽  
Optimization Problem ◽  
Controller Design ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Output Feedback Controller ◽  
Parameter Varying ◽  
Parameter Dependent

This article presents a new output feedback controller design method for polynomial linear parameter varying model with bounded parameter variation rate. Based on parameter-dependent Lyapunov function, the polynomial linear parameter varying system controller design is formulated into an optimization problem constrained by parameterized linear matrix inequalities. To solve this problem, first, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameter-dependent Lyapunov function, controller, and object coefficient matrices. Then, the control solving problem was reduced to a normal convex optimization problem with linear matrix inequalities constraint on a newly constructed convex polyhedron. Moreover, a parameter scheduling output feedback controller was achieved on the operating condition, which satisfies robust performance and dynamic performances. Finally, the feasibility and validity of the controller analysis and synthesis method are verified by the numerical simulation.

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.

Vibration control of base-isolated structures using mixed H2/H∞ output-feedback control

2009 ◽  
Vol 223 (6) ◽  
pp. 809-820 ◽  
Author(s):  
H R Karimi ◽  
M Zapateiro ◽  
N Luo
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
Design Methodology ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
Building Structures ◽  
Matrix Inequalities ◽  
Closed Loop System

A mixed H2/ H∞ output-feedback control design methodology for vibration reduction of base-isolated building structures modelled in the form of second-order linear systems is presented. Sufficient conditions for the design of a desired control are given in terms of linear matrix inequalities. A controller that guarantees asymptotic stability and a mixed H2/ H∞ performance for the closed-loop system of the structure is developed, based on a Lyapunov function. The performance of the controller is evaluated by means of simulations in MATLAB/Simulink.

scholarly journals Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State-Derivative Feedback

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Emerson R. P. da Silva ◽  
Edvaldo Assunção ◽  
Marcelo C. M. Teixeira ◽  
Luiz Francisco S. Buzachero
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Polytopic Uncertainties ◽  
Parameter Dependent ◽  
Finsler’S Lemma ◽  
Time Linear

The motivation for the use of state-derivative feedback instead of conventional state feedback is due to its easy implementation in some mechanical applications, for example, in vibration control of mechanical systems, where accelerometers have been used to measure the system state. Using linear matrix inequalities (LMIs) and a parameter-dependent Lyapunov functions (PDLF) allowed by Finsler’s lemma, a less conservative approach to the controller design via state-derivative feedback, is proposed in this work, with and without decay rate restriction, for continuous-time linear systems subject to polytopic uncertainties. Finally, numerical examples illustrate the efficiency of the proposed method.

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.

scholarly journals Gain scheduled controller design for thermo-optical plant

2014 ◽  
Vol 24 (3) ◽  
pp. 333-349 ◽  
Author(s):  
Vojtech Veselý ◽  
Jakub Osuský ◽  
Ivan Sekaj
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Design Method ◽  
Feedback Gain ◽  
Small Gain ◽  
Gain Scheduled Controller ◽  
The Stability ◽  
Gain Scheduled ◽  
Siso Systems

Abstract This paper presents a gain scheduled controller design for MIMO and SISO systems in the frequency domain using the genetic algorithms approach. The proposed method is derived from the M-delta structure of closed loop MIMO (SISO) systems and the small gain theory is exploited to obtain the stability condition. An example of real system illustrates the effectiveness of the proposed output feedback gain scheduled controller design method and also the possibility to improve its performance using the genetic algorithm

An LMI Optimization Approach to the Design of Structured Linear Controllers Using a Linearization Algorithm

2003 ◽  
Author(s):  
Jeongheon Han ◽  
Robert E. Skelton
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Matrix Inequalities ◽  
Lmi Optimization ◽  
Fixed Order ◽  
H2 Performance ◽  
Linear Controllers

This paper presents a new algorithm for the design of linear controllers with special constraints imposed on the control gain matrix. This so called SLC (Structured Linear Control) problem can be formulated with linear matrix inequalities (LMI’s) with a nonconvex equality constraint. This class of prolems includes fixed order output feedback control, multi-objective controller design, decentralized controller design, joint plant and controller design, and other interesting control problems. Our approach includes two main contributions. One is that many design specifications such as H∞ performance, generalized H2 performance including H2 performance, l∞ performance, and upper covariance bounding controllers are described by a similar matrix inequality. A new matrix variable is introduced to give more freedom to design the controller. Indeed this new variable helps to find the optimal fixed-order output feedback controller. The second contribution uses a linearization algorithm to search for a solution to the nonconvex SLC problems. This has the effect of adding a certain potential function to the nonconvex constraints to make them convex. Although the constraints are added to make functions convex, those modified matrix inequalities will not bring significant conservatism because they will ultimately go to zero, guaranteeing the feasibility of the original nonconvex problem. Numerical examples demonstrate the performance of the proposed algorithms and provide a comparison with some of the existing methods.

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