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.

Robust Gain-Scheduling Output Feedback Control With Noisy Scheduling Parameters

2015 ◽  
Author(s):  
Ali Khudhair Al-Jiboory ◽  
Guoming Zhu
Keyword(s):  
Output Feedback ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Gain Scheduling ◽  
Linear Matrix ◽  
Synthesis Methods ◽  
Matrix Inequalities ◽  
Feedback Controllers ◽  
Comparison Results ◽  
H2 Performance

Robust Gain-Scheduling (RGS) control strategy has been considered in this paper. In contrast to the conventional gain-scheduling synthesis methods, the scheduling parameters are assumed to be inexactly measured. This is a practical assumption since measurement noise is inevitable even with very accurate sensors. Multi-simplex modeling approach was used to model the scheduling parameters and their uncertainties in a convex domain. Sufficient conditions in terms of Parametrized Linear Matrix Inequalities (PLMIs) for synthesizing dynamic output-feedback controllers are derived. The resulting controller not only guarantees robust stability and H2 performance but also ensures robustness against scheduling parameters uncertainties. The effectiveness of the developed conditions is demonstrated through numerical example with simulation and comparisons with existing approaches from literature. The comparison results confirm that the developed approach outperforms the existing ones considerably.

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.

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.

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 Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3285
Author(s):  
Andreas Rauh ◽  
Swantje Romig
Keyword(s):  
Linear Matrix Inequalities ◽  
Output Feedback ◽  
Output Feedback Control ◽  
Iterative Solution ◽  
Simultaneous Optimization ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Optimization Task ◽  
State Observers

Linear matrix inequalities (LMIs) have gained much importance in recent years for the design of robust controllers for linear dynamic systems, for the design of state observers, as well as for the optimization of both. Typical performance criteria that are considered in these cases are either H2 or H∞ measures. In addition to bounded parameter uncertainty, included in the LMI-based design by means of polytopic uncertainty representations, the recent work of the authors showed that state observers can be optimized with the help of LMIs so that their error dynamics become insensitive against stochastic noise. However, the joint optimization of the parameters of the output feedback controllers of a proportional-differentiating type with a simultaneous optimization of linear output filters for smoothening measurements and for their numeric differentiation has not yet been considered. This is challenging due to the fact that the joint consideration of both types of uncertainties, as well as the combined control and filter optimization lead to a problem that is constrained by nonlinear matrix inequalities. In the current paper, a novel iterative LMI-based procedure is presented for the solution of this optimization task. Finally, an illustrating example is presented to compare the new parameterization scheme for the output feedback controller—which was jointly optimized with a linear derivative estimator—with a heuristically tuned D-type control law of previous work that was implemented with the help of an optimized full-order state observer.

Modified Sky-Hook Control of a Semi-Active Suspension System Using H∞ Robust Control Theory

2009 ◽  
Author(s):  
Mohammad Saber Fallah ◽  
Rama Bhat ◽  
Wen-Fang Xie
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
Controller Design ◽  
Kinematic Model ◽  
Three Dimensional ◽  
Output Feedback Control ◽  
Suspension System ◽  
Linear Matrix ◽  
Control Force ◽  
The Stability

The main focus of the present paper is on the design of a modified sky-hook control of a semi-active Macpherson suspension system by means of H∞ Output Feedback Control (OFC) theory. To this end, a new dynamic model, incorporating the kinematics of the suspension system, is used for the controller design. The combination of a Linear Matrix Inequality (LMI) solver and Genetic Algorithm (GA) is adopted to regulate the static output feedback control gain so that the stability conditions are fulfilled and control objectives are achieved. Meanwhile, a three-dimensional kinematic model of the system is incorporated to investigate the influence of the control force variation on the steering, handling and stability of the vehicle. A geometric relation of the vehicle roll center is employed to study one more extra aspect of the comfort and stability of the vehicle. The results show that the proposed controller improves the kinematic and dynamic performances of the suspension well compared with those of the passive system. Moreover, it is concluded that a superior stability of the vehicle during the cornering can be achieved by adjusting the height of the vehicle roll center passively so that the stability of the vehicle is improved while the forward motion specifications can be modified by an appropriate suspension control design.

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