Robust control of electrically-stimulated muscle using polynomial H∞ design

The work is concerned with the design and experimental evaluation of robust feedback systems for the control of ankle moments generated by the electrical stimulation of the human calf muscle. This is an important part of the problem of designing feedback controllers for stabilising the upright posture of people with spinal cord injuries while they stand. Robust controllers are designed using the polynomial approach to mixed sensitivity H_∞ feedback design. The approach was found to give a convenient and transparent way to design for performance. Moreover, the method gives a useful indicator of the robustness properties of a given design. This is highly useful for experimental controller “tuning”.     

H ∞ robust controller for self-tuning control applications Part 1. Controller design

The design of H _∞ controllers for scalar self-tuning control applications is considered. The conventional cost function employed in H _∞ design involves the sum of weighted sensitivity and complementary sensitivity terms and leads to a control law which may be too difficult to calculate on-line. The cost function defined here allows both such terms to be costed, but is constructed so that the control law calculation is much simplified.     

Robust fuzzy controller design of nonlinear dynamic systems based on H ∞ optimal criterion

A new design method of fuzzy controllers to achieve H X optimal performance for a class of uncertain nonlinear systems is presented. The dynamic behaviour of a product-sum-type fuzzy controller is analysed and the result reveals that this type of fuzzy controller behaves approximately like a state feedback controller with non-constant feedback gains which are dependent on input signals. Based on the H X control design technique, a systematic analysis and design of the fuzzy controller is presented for guaranteeing the stability or even the performance. Even though the bound of the plant nonlinearity is unknown, the influence of the nonlinear term on the system error is attenuated to a prescribed level by the proposed fuzzy controller. Finally, the fuzzy controller is applied to the Duffing forced oscillation system, which confirms the validity of the controller.     

Relaxed stability condition and state feedback H ∞ controller design for T-S fuzzy systems

In this paper, a fuzzy Lyapunov approach is presented for stability analysis and state feedback H _∞ controller design for T-S fuzzy systems. A new stability condition is obtained by relaxing the ones derived in previous papers. Then, a set of LMI-based sufficient conditions which can guarantee the existence of state feedback H _∞ controller for T-S fuzzy systems is proposed. In comparison with the existing literature, the proposed approach not only provides more relaxed stability conditions but also ensures better H _∞ performance. The effectiveness of the proposed approach is shown through two numerical examples. Recommended by Editor Young-Hoon Joo. Xiao-Heng Chang received the B.E. and M.S. degrees from Liaoning Technical University, China, in 1998 and 2004, respectively, and the Ph.D. degree from Northeastern University, China, in 2007. He is currently a Lecturer in the School of Information Science and Engineering, Bohai University, China. His research interests include fuzzy control and robust control as well as their applications. Guang-Hong Yang received the B.S. and M.S. degrees in Northeast University of Technology, China, in 1983 and 1986, respectively, and the Ph.D. degree in Control Engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, nonfragile control systems design, and robust control. Dr. Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS), and an Associate Editor of the Conference Editorial Board of the IEEE Control Systems Society.     

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.     

Two-stage H ∞ optimization approach to multirate controller design

A two-stage H _?? optimization methodology is presented for designing multirate controllers achieving comparable H _?? closed-loop performance with that of an optimal fast rate design at a reduced real-time computational load. In the first stage, a fast rate controller is designed by solving an H _?? optimal control problem formulated to address the design specifications; then the fast rate controller is decomposed into low frequency and high frequency parts. In the second stage, the high frequency part of the controller is retained and the low frequency part is redesigned at the slow rate using lifting and H _?? optimization. In the proposed approach, potential problems of aliasing due to the multirate nature of the controller are addressed by taking into consideration closed-loop performance.     

Covariance matrix adaptation evolution strategy based design of fixed structure robust H∞ loop shaping controller

This paper proposes the application of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) in fixed structure H_∞ loop shaping controller design. Integral Time Absolute Error (ITAE) performance requirement is incorporated as a constraint with an objective of maximization of stability margin in the fixed structure H_∞ loop shaping controller design problem. Pneumatic servo system, separating tower process and F18 fighter aircraft system are considered as test systems. The CMA-ES designed fixed structure H_∞ loop-shaping controller is compared with the traditional H_∞ loop shaping controller, non-smooth optimization and Heuristic Kalman Algorithm (HKA) based fixed structure H_∞ loop shaping controllers in terms of stability margin. 20% perturbation in the nominal plant is used to validate the robustness of the CMA-ES designed H_∞ loop shaping controller. The effect of Finite Word Length (FWL) is considered to show the implementation difficulties of controller in digital processors. Simulation results demonstrated that CMA-ES based fixed structure H_∞ loop shaping controller is suitable for real time implementation with good robust stability and performance.     

H∞ optimal design of robust observer against disturbances

This paper considers the robust observer design problem for linear dynamic systems subject to the interference of external disturbances. For such systems, the state estimate from the conventional Luenberger is normally biased with respect to the true system state. To remedy this situation, this paper proposes a new structure for robust observers. With this new structure, the robust observer design problem is skillfully transformed into the well-known disturbance rejection control problem. The H_∞ optimal control design technique can then be applied to shape the proposed robust observer in the frequency domain. The proposed robust observer is a joint state and disturbance observer, which simultaneously estimates both the system state and unknown disturbances, and can be applied to non-minimum-phase systems.     

Energy-based robust controller design for flexible spacecraft

This paper presents a class of non-model2based position controllers for a kind of flexible spacecraft. With the controllers, one can achieve not only the closed-loop stability of the original distributed parameter system, but also the asymptotic stability of the truncated system, which is obtained through representing the deflection of the appendage by an arbitrary finite number of flexible modes. The system dynamics are not explicitly involved in the controller design and stability proof. Instead, only a very basic system energy rehtionship of the flexible spacecraft is utilized. The controllers possess several remarkable advantages over the traditional model-based ones. Numerical simulations are carried out on a kind of spacecraft with one flexible appendage and satisfactory results are obtained.     

Robust H ∞ filter design for affine fuzzy systems

This paper investigates the problem of robust H _∞ filtering for nonlinear systems, which are described by affine fuzzy parts with norm-bounded uncertainties. The system outputs have been chosen as premise variables, which can guarantee the plant and the filter always switch to the same region. By using a piecewise Lyapunov function and adding slack matrix variables, a fuzzy-basis-dependent H _∞ filter design method is obtained in the formulation of linear matrix inequalities (LMIs), which can be efficiently solved numerically. Compared with the existing results, the proposed method needs less LMI constraints and leads to less conservatism. Finally, numerical examples illustrate the effectiveness of the new results.     

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.     

H ∞ approach to T-S fuzzy controller for limiting reconstruction errors

In this article, the reconstruction error between a real system to be controlled and its Takagi–Sugeno (T-S) fuzzy model is considered in the context of control system design. Accordingly, we propose an H _∞ approach to an adaptive controller that consists of two parts: one is obtained by solving certain linear matrix inequalities (fixed part) and the other is acquired using a fuzzy approximator in which the related parameters are tuned by an adaptive law (variable part). The proposed controller can guarantee a convergent and uniformly bounded control state while maintaining the stability of all the signals involved.     

Delay-dependent robust H ∞ control for uncertain fuzzy Markovian jump systems

This paper is concerned with the problem of delay-dependent robust H _∞ control for uncertain fuzzy Markovian jump systems with time delays. The purpose is to design a mode-dependent state-feedback fuzzy controller such that the closed-loop system is robustly stochastically stable and satisfies an H _∞ performance level. By introducing slack matrix variables, a delay-dependent sufficient condition for the solvability of the problem is proposed in terms of linear matrix inequalities. An illustrative example is finally given to show the applicability and effectiveness of the proposed method. Recommended by Editorial Board member Young Soo Suh under the direction of Editor Jae Weon Choi. This work is supported by the National Science Foundation for Distinguished Young Scholars of P. R. China under Grant 60625303, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20060288021, and the Natural Science Foundation of Jiangsu Province under Grant BK2008047. Yashun Zhang received the B.S. and M.S. degrees in Control Science and Control Engineering from Hefei University of Science and Technology in 2003 and 2006. He is currently a Ph.D. student in Control Science and Control Engineering, Nanjing University of Science and Technology. His research interests include fuzzy control, sliding mode control and nonlinear control. Shengyuan Xu received the Ph.D. degree in Control Science and Control Engineering from Nanjing University of Science and Technology in 1999. His research interests include robust filtering and control, singular systems, time-delay systems and nonlinear systems. Jihui Zhang is a Professor in the School of Automation Engineering of Qingdao University, China. His main areas of interest are discrete event dynamic systems, production planning and control, and operations research.     

Comment on ‘H∞robust controller for self-tuning control applications’

Grimble and Fairbairn's recently published results on H^∞ robust self-tuning control are discussed. It is pointed out that further explanation about the system model is needed, and the identified system model should be revised. Grimble (1987 a, b) and Fairbairn and Grimble (1990) give a new approach to designing self-tuning controllers for SISO discrete-time stochastic systems. There are some points that call for further discussion.     

Robust H∞ performance using lifted polynomial parameter-dependent Lyapunov functions

This paper investigates the robust H _∞ performance of time-invariant linear uncertain systems where the uncertainty is in polytopic domains. Robust H _∞ is checked by constructing a quadratic parameter-dependent Lyapunov function. The matrix associated with this quadratic Lyapunov function is a polynomial function of the uncertain parameters, expressed as a particular polynomial matrix involving κ powers of the dynamic matrix of the system and one symmetric matrix to be determined. The degree of this polynomial matrix function is arbitrary. Finsler's Lemma is used to lift the obtained stability conditions into a larger space in which sufficient stability tests can be developed in the form of linear matrix inequalities. As κ increases, less conservative H _∞ evaluations are obtained. Both continuous and discrete-time systems are investigated. Numerical examples illustrate the method and compare the present results with similar works in the literature.     

Robust flight control system design using H∞ loop-shaping and recessive trait crossover genetic algorithm

A proposed approach to robust controller design is introduced. This approach combines the recessive trait crossover genetic algorithm with the loop-shaping design procedure using H_∞ synthesis. The requirements, design and simulation of a flight control system for precision tracking task are considered. The proposed method is applied to design a control system for the F-16 fighter aircraft model. The flight simulations reveal that the desired performance objectives are achieved and that the controller provides acceptable performance in spite of modeling errors and plant parameter variations.     

Fractional fixed-structure H∞ controller design using Augmented Lagrangian Particle Swarm Optimization with Fractional Order Velocity

The optimization of a fixed-structure controller is in general computationally intractable, posing a challenge to control system engineers. This paper introduces a novel technique for designing such control techniques by formulating it as a nonlinear non-convex constrained problem. A novel PSO algorithm, namely the Augmented Lagrangian Particle Swarm Optimization with Fractional Order Velocity (ALPSOFV), is proposed for improving the convergence rate. The structure of the controller is selectable and, therefore, the Fractional Order Proportional Integral Derivative (FOPID) algorithm is chosen in the scope of the study. The results for three test examples show the good performance of the ALPSOFV.