Low‐order H∞ controller design on the frequency domain by partial optimization

In this paper, an optimization method of low‐order multivariable controllers for H_∞ control is proposed. Starting from a low‐order stabilizing controller, our method gives a sequence of controllers for which the H_∞ norm performance index is monotonically non‐increasing by tuning the numerator coefficient matrices of the low‐order controller. This controller class includes multivariable PID controllers. The proposed method is a descent method where the feasible direction is calculated by solving a linear matrix inequality that represents a sufficient condition for the H_∞ criterion for each frequency. Usefulness is shown by two numerical examples. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust Controller Design And Pid Tuning For Multivariable Processes

In this paper, a robust controller design method is first formulated to deal with both performance and robust stability specifications for multivariable processes. The optimum problem is then dealt with using a loop‐shaping H_∞ approach, which gives a sub‐optimal solution. Then a PID approximation method is proposed to reduce a high‐order controller. The whole procedure involves selecting several parameters and the computation is simple, so it serves as a PID tuning method for multivariable processes. Examples show that the method is easy to use and the resulting PID settings have good time‐domain performance and robustness.     

Non-fragile robust H ∞ control for uncertain spacecraft rendezvous system with pole and input constraints

This article investigates the robust H _∞ control problem for a class of spacecraft rendezvous systems with parameter uncertainties and subject to input constraint, pole constraint and external and controller perturbations. Based on the Lyapunov theory, a sufficient condition for the existence of the non-fragile robust state-feedback controller is given in terms of linear matrix inequalities (LMIs). Then, proper non-fragile controller design can be cast as a convex optimisation problem subject to LMI constraints. With the obtained controller, the spacecraft rendezvous mission can be accomplished. An illustrative example is provided to show the effectiveness of the proposed control design method.     

Non-fragile control of fuzzy affine dynamic systems via piecewise Lyapunov functions

This paper addresses the robust H_∞ static output feedback (SOF) controller design problem for a class of uncertain fuzzy affine systems that are robust against both the plant parameter perturbations and controller gain variations. More specifically, the purpose is to synthesize a non-fragile piecewise affine SOF controller guaranteeing the stability of the resulting closed-loop fuzzy affine dynamic system with certainH_∞ performance index. Based on piecewise quadratic Lyapunov functions and applying some convexification procedures, two different approaches are proposed to solve the robust and non-fragile piecewise affine SOF controller synthesis problem. It is shown that the piecewise affine controller gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples are given to illustrate the effectiveness of the proposed methods.     

Non-fragile H∞ dynamic output feedback control for uncertain Takagi–Sugeno fuzzy systems with time-varying delay

This paper mainly focuses on the problem of non-fragile H_∞ dynamic output feedback control for a class of uncertain Takagi–Sugeno fuzzy systems with time-varying state delay. Based on a new type of Lyapunov–Krasovskii functional without ignoring any subtle integral terms in the derivatives, a less conservative dynamic output feedback controller with additive gain variations is designed, which guarantees that the closed-loop fuzzy system is asymptotically stable and satisfies a prescribed H_∞-performance level. Furthermore, the obtained parameter-dependent conditions are given in terms of solution to a set of linear matrix inequalities, which improve some existing relevant results. Finally, numerical examples are given to illustrate the effectiveness and merits of the proposed method.     

Finite-time H∞ control of periodic piecewise linear systems

In this paper, the finite-time stability, stabilisation, L₂-gain and H_∞ control problems for a class of continuous-time periodic piecewise linear systems are addressed. By employing a time-varying control scheme in which the time interval of each subsystem constitutes a number of basic time segments, the finite-time controllers can be developed with periodically time-varying control gains. Based on a piecewise time-varying Lyapunov-like function, a sufficient condition of finite-time stability and the relevant time-varying controller are proposed. Considering the finite-time boundedness of the closed-loop periodic system, the L₂-gain criterion with continuous time-varying Lyapunov-like matrix function is studied. A finite-time H_∞ controller is proposed based on the L₂-gain analysis. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed criteria.     

Output-feedback control for sampled-data systems with variable sampling rate

In this paper, we propose design method of controller for sampled-data systems with variable sampling rate. First, we give design method for both H₂ and H_∞ controller. For H₂ control, performance of the system is introduced according to a standard sampled-data setting. A discrete-time H₂ control problem is employed for solving the original problem. Its solvability condition is then established as a parameter-dependent linear matrix inequality. A probabilistic approach is taken for coping with the parameter-dependency. H_∞ controller is designed by almost the same manner. Applying both results, we have design method for multi-objective control.     

Observer-based Non-fragile Mixed Passivity and H∞ Feedback Control for Fuzzy Stochastic Jump System Subject to Quantized Measurements

This paper considers the topic of the observer-based non-fragile mixed passivity and H_∞ state feedback control for time-varying delay and norm-bounded parameter uncertainties fuzzy stochastic Markovian jump system subject to quantized measurements. The aim of this paper is to provide a suitable observer-based non-fragile state feedback controller to enhance stochastic stabilization of the closed-loop system and satisfy mixed passivity and H_∞ performance. By constructing mode-dependent Lyapunov-Krasovskii functional, novel conditions are achieved in virtue of linear matrix inequalities. Two examples including truck-trailer model are given to illustrate the effectiveness of the developed method.

     

New delay-dependent non-fragile H∞ observer-based control for continuous time-delay systems

The problem of the delay-dependent non-fragile H_∞ observer-based control for a class of continuous time-delay systems is investigated in this paper. The additive gain variations under consideration are contained in both the controller gain and obhsiunserver gain. Delay-dependent criteria are derived to guarantee the stability of the non-fragile H_∞ observer-based control system using the Lyapunov functional approach. The controller and observer gains are given from the LMI feasible solutions. Based on the result of this paper, the constraint of matrix equality is not necessary for designing the non-fragile H_∞ observer-based controls. Computer software Matlab can be applied to solve all the proposed results. Finally, a numerical example is illustrated to show the improvement of this paper.     

Sampled-data H ∞ control for networked control systems with digital control inputs

In this article, the problem of sampled-data H _∞ control for networked control systems (NCSs) with digital control inputs is considered, where the physical plant is modelled as a continuous-time one, and the control inputs are discrete-time signals. By exploiting a novel Lyapunov–Krasovskii functional, using the Leibniz–Newton formula and a free-weighting matrix method, sufficient conditions for sampled-data H _∞ performance analysis and H _∞ controller design for such systems are given. Since the obtained conditions of H _∞ controller design are not expressed strictly in term of linear matrix inequalities, the sampled-data H _∞ controller is solved using modified cone complementary linearisation algorithm. In addition, the new sampled-data stability criteria for the NCSs is proved to be less conservative than some existing results. Numerical examples demonstrate the effectiveness of the proposed methods.     

Robust H∞ controller design for dynamic consensus networks

This paper studies an H_∞ suboptimal control problems of consensus networks whereby the weights of network edges are no longer static gains, but instead are dynamic systems, leading to the notion of dynamic consensus networks. We apply model, orthogonal and diagonal transformations to a dynamic consensus network in order to reduce the overall system into N ? 1 independent subsystems. We then establish a generalised methodology for designing a controller for a dynamic consensus network in the presence of external disturbances, focusing especially on using decentralised controllers that achieve consensus in the absence of disturbances and attenuation of disturbances to a prescribed H_∞ performance level. A design example is given to illustrate our results.     

Distributed H_∞ PID Feedback for Improving Consensus Performance of Arbitrary-delayed Multi-agent System

The H∞ proportional-integral-differential(PID) feedback for arbitrary-order delayed multi-agent system is investigated to improve the system performance. The closed-loop multi-input multi-output(MIMO) control framework with the distributed PID controller is firstly described for the multi-agent system in a unified way. Then, by using the matrix theory, the prescribed H∞performance criterion of the multi-agent system is shown to be equivalent to several independent H∞ performance constraints of the single-input single-output(SISO) subsystem with respect to the eigenvalues of the Laplacian matrix. Subsequently, for each subsystem,the set of the PID controllers satisfying the required H∞ performance constraint is analytically characterized based on the extended Hermite-Biehler theorem. Finally, the three-dimensional set of the decentralized H∞ PID control parameters is derived by finding the intersection of the H∞ PID regions for all the decomposed subsystems. The simulation results reveal the effectiveness of the proposed method.     

Robust H∞ dynamic output feedback control for spacecraft rendezvous with poles and input constraint

This paper is concerned with the output feedback control problem for spacecraft rendezvous subject to target angular velocity uncertainty and controller uncertainty, external disturbance and input constraint. A general full-order dynamic output feedback (DOF) controller is proposed. As a stepping-stone, the H_∞ performance requirement, poles and input constraint are analysed separately via linear matrix inequalities (LMIs). Then, with the obtained results, the controller design problem is cast into a convex problem subject to a set of LMI constraints through a critical change of controller variables. Furthermore, when the system states are all available, a reduced sufficient condition of the non-fragile state feedback controller is given. Compared with existing results, the designed controller has overcome the disadvantage of strictly proper DOF controller, where the initial value of the control input is zero. Besides, the constraint on poles placement is relaxed. A numerical simulation is performed to verify the effectiveness of the proposed method.     

Optimally robust H∞ polynomial fuzzy controller design using quantum-inspired evolutionary algorithm

This paper proposes an optimally robust H_∞ polynomial fuzzy controller design using quantum-inspired evolutionary algorithm (QEA) for continuous/discrete time polynomial fuzzy systems with model uncertainties and external disturbances. To improve control performance, QEA is adopted to evolve optimal control gains with a fitness function that is defined by performance requirements. The stability and robustness of the control system are then guaranteed by the proposed robust H_∞ stability conditions, which are formed by the sum of squares (SOS) method. By using the principle of copositivity, novel relaxed SOS-based stability conditions are derived to reduce the conservativeness of solving SOS-based stability conditions, while the feasible solution space is broadened. Four numerical examples demonstrate the effectiveness of the proposed approaches.     

Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics

This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H_∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H_∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.     

A genetic-multivariable fractional order PID control to multi-input multi-output processes

A multivariable fractional order PID controller is designed and to get suitable coefficients for the controller, a genetic algorithm with a new topology to generate a new population is proposed. The three parts of the genetic algorithm such as reproduction, mutation, and crossover are employed and some variations in the methods are fulfilled so that a better performance is gained. The genetic algorithm is applied to design FOPID controllers for a multivariable process and the results are compared with the responses of a H_∞ based multivariable FOPID controller. The simulation responses show that in all cases, the genetic-multivariable FOPID controller has suitable performance, and the output of the system has a smaller error. Also, in the proposed method, variations in one output have a smaller effect on another output which is shown the ability of the proposed method to overcome the interaction in the multivariable processes.     

Design of finite-time H∞ controller for uncertain nonlinear systems and its application

This paper studies the problem of finite-time H _∞ control for strict feedback nonlinear systems with external disturbance. The finite-time stability theory, H _∞ control method, backstepping technique, together with adding a power integrator tool are combined to design a finite-time H _∞ state feedback controller. The obtained controller can make the closed-loop system finite-time convergent, and the influence of the external disturbance is attenuated to a given degree. Two numerical examples are presented to show the effectiveness and feasibility of the proposed method. Meanwhile, the proposed method is also applied to robot manipulators.     

Receding horizon H∞ control problems for sampled-data systems§

In this article, the receding horizon H_∞ control problems for sampled-data systems are considered. Since sampled-data systems can be rewritten as equivalent jump systems, the receding horizon H_∞ control problems for time-varying jump systems are considered first and the design methods of a state feedback receding horizon H_∞ controller and an output feedback receding horizon H_∞ controller are given. Then the obtained results are applied to sampled-data systems and the design methods of a state feedback receding horizon H_∞ controller and an output feedback receding horizon H_∞ controller are given. Two numerical examples are given to illustrate the theory.     

Sparse structured non-fragile H ∞ controller design for linear systems

This paper presents a study on the problem of designing non-fragile H _∞ controllers with sparse structures for linear continuous-time systems. A new algorithm is proposed to define and further design sparse structured controllers. Firstly, sparse structures are specified from a given fully parameterized H _∞ controller. Then, a three-step design procedure for non-fragile dynamic output feedback H _∞ controllers with the sparse structures is provided. The resulting designs guarantee that the closed-loop system is asymptotically stable and the H _∞ performance from the disturbance to the regulated output is less than a prescribed level. A numerical example is given to illustrate the design methods.