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∞ Robust Control Design for an Arm Manipulator

This paper deals with the application of the optimal H control design technique to derive a controller for a 3 DOF arm manipulator affected by nonmodeled dynamics, nonlinearities, actuator dynamics and sensor noise. The control objectives were to obtain a robust stable with robust performance controlled system. A family of nonparametric models for a finite number of the arm configurations was obtained. Then, a multivariable nominal model was proposed and derived together with additive nonparametric uncertainty bounds. Weighting functions were used to normalize the H norm of the uncertainty and to act on the command, sensor, and error signals. Finally, a controller was computed by solving the corresponding H optimization problem. The controller was tried on the nominal and worst case configuration models. The results showed robust stability and robust performance of the controlled system.     

Robust control of distillation columns: μ- vs H∞-synthesis

High-purity distillation columns are known to be difficult to control due to their ill-conditioned and non-linear behaviour. Two approaches for the design of robust controllers yielding high performance are presented. For the first approach, first principles are used to develop an uncertainty model describing the nonlinear dynamics within the entire operating range of an industrial distillation column. This structured uncertainty model is used for μ-synthesis. In a second approach which is based on loop shaping ideas, an H_∞-controller is designed. This controller performs as well as the μ-controller. The H_∞-approach offers the advantage that the burden for uncertainty modelling and computation is greatly reduced. However, the GS/T augmentation scheme, which is developed in this paper, must be used for the design of the H_∞-controller to avoid the inversion of the plant in the controller. The paper concludes with a comparison of the H_∞- and μ-synthesis methods.     

Decentralized robust PI controller design for an industrial boiler

This paper presents a new scheme to design decentralized robust PI controllers for uncertain LTI multivariable systems. Sufficient conditions for closed-loop stability and closed-loop diagonal dominance (almost decoupling) of a multivariable system are obtained. Satisfying these conditions and robust performance of the overall system are modeled as local robust performance problems. Then, by appropriately selecting the time constants of the closed-loop isolated subsystems in the IMC (Internal Model Control) strategy, the defined local robust performance problems are solved. To design a decentralized robust PI controller for a real industrial utility boiler, a control oriented nonlinear model for the boiler is identified. The nonlinearity of the system is modeled as uncertainty for a nominal LTI multivariable system. Using the new proposed method, a decentralized PI controller for the uncertain LTI model is designed. The designed controller is applied to the real system. The simulation results show the effectiveness of the proposed methodology.     

On the design of multivariable PID controllers via LMI approach

In this paper, we study the design problem of multivariable PID controllers which guarantee the stability of the closed loop systems, H₂ or H_∞ performance specifications, or maximum output control requirement, respectively. Algorithms based on iterative linear matrix inequality technique are developed to find the feedback gains of PID controllers corresponding to the above mentioned four cases. A numerical example on the design of PID controllers for aircraft is provided to illustrate the effectiveness of the proposed method.     

An Improved Anti‐Windup Bumpless Transfer Structures Design for Controllers Switching

In this paper, an anti‐windup bumpless transfer (AWBT) control structure combined with linear interpolation method is proposed for smooth switching control. By choosing an appropriate scheduling signal, different controllers can be switched smoothly under a unified framework. Meanwhile, some robust specifications including H₂/H_∞ performance, pole placement constraint, and passivity of the closed‐loop system can be preserved through controller switching. Furthermore, for the linear system subject to input saturation, the stability and L₂ gain of the closed‐loop system can be guaranteed. Finally, a cart‐spring pendulum system is simulated to demonstrate the effectiveness of the proposed scheme.     

Delayed-input power system stabilizer using supplementary remote signals

The design of a local H_∞-based power system stabilizer controller, using wide area or global signals as additional measuring information considering time delay, is presented in this paper. The wide area signals are taken from suitable remote network locations where the oscillations are well observable. A long time delay introduced by remote signal transmission and processing in wide area measurement system (WAMS) may harm system stability and degrade system robustness. Three methods for dealing with the effects of time delay are presented in this paper. To provide robust behavior, H_∞ control theory together with an algebraic Riccati equation (ARE) approach has been applied to design the controllers. The effectiveness of the resulting robust H_∞-based PSS controllers is demonstrated through digital simulation studies conducted on a test power system. The simulation results show that the proposed controller contributes significantly to the damping of inter-area oscillations and the enhancement of small-signal stability in the presence of uncertainty in time delay under a wide range of system operating conditions.     

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.     

Robust state feedback synthesis for control of non-square multivariable nonlinear systems

In this paper, a robust nonlinear controller is designed in the Input/Output (I/O) linearization framework, for non-square multivariable nonlinear systems that have more inputs than outputs and are subject to parametric uncertainty. A nonlinear state feedback is synthesized that approximately linearizes the system in an I/O sense by solving a convex optimization problem online. A robust controller is designed for the linear uncertain subsystem using a multi-model H₂/H_∞ synthesis approach to ensure robust stability and performance of non-square multivariable, nonlinear systems. This methodology is illustrated via simulation of a regulation problem in a continuous stirred tank reactor.     

Multidimensional system of cascaded control of plasma form and current in tokamak with channel decoupling and <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript>-controller

Consideration was given to the development and numerical modeling of the multidimensional cascaded system with H _∞-controller in the external cascade for control of the plasma form and current in tokamak. For controller design, the problem of mixed sensitivity was solved by selecting the weight functions in the composite matrix of the performance criterion. The internal loop was intended for decoupling the current control channels in the magnetic coils of the tokamak poloidal fields and following the given scenario currents. Linearized models obtained from the nonlinear plasma-physical DINA code by linearizing the ITER scenario at different points were used to design the controllers. The robust stability margin was estimated in the frequency domain using singular numbers of the matrix transfer functions of the closed-loop control system. The designed cascaded system was modeled in the DINA code.     

A new approach to robust and non-fragile H∞ control for uncertain fuzzy systems

This paper investigates the robust H_∞ control and non-fragile control problems for Takagi-Sugeno (T-S) fuzzy systems with linear fractional parametric uncertainties. The robust H_∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H_∞ performance of the resulting closed-loop system is ensured. And the non-fragile H_∞ control problem is to design a state feedback controller with parameter uncertainties. Based on the linear matrix inequality (LMI) approach, new sufficient conditions for the solvability of the two problems are obtained. It is shown that the desired state feedback fuzzy controller can be constructed by solving a set of LMIs. Numerical examples are also provided to demonstrate the effectiveness of the proposed design method.     

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.     

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 nonlinear ship course‐keeping control by H∞ I/O linearization and μ‐synthesis

In this paper, the H_∞ input/output (I/O) linearization formulation is applied to design an inner‐loop nonlinear controller for a nonlinear ship course‐keeping control problem. Due to the ship motion dynamics are non‐minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H_∞ I/O linearization is proposed to obtain a nonlinear H_∞ controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a μ‐synthesis method is employed to design an outer‐loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed‐loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd.     

Stabilizing composite control for a class of linear systems modeled by singularly perturbed Ito differential equations

In this paper, the problem of robust H_∞ control is investigated for sampled-data systems with probabilistic sampling. The parameter uncertainties are time-varying norm-bounded and appear in both the state and input matrices. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input delay approach, the probabilistic sampling system is transformed into a continuous time-delay system with stochastic parameters in the system matrices. By linear matrix inequality (LMI) approach, sufficient conditions are obtained, which guarantee the robust mean-square exponential stability of the system with an H_∞ performance. Moreover, an H_∞ controller design procedure is then proposed. An illustrative example is included to demonstrate the effectiveness of the proposed techniques.     

APPLICATION OF H∞ CONTROL AND CLOSED LOOP IDENTIFICATION TO A MAGNETIC LEVITATION SYSTEM

A systematic procedure for modeling and robust control of a multivariable magnetic levitation system is described. Our previous study revealed that an observer-based LQ controller can stabilize the system, but generates spillovers in the presence of an impulse disturbance. To solve this problem, we apply an H_∞ control to suppress the spillovers caused by unmodeled dynamics which we estimate using closed loop identification. First, an exactly linearized model is obtained to compensate for nonlinearities in the system, followed by estimation of the unmodeled dynamics using closed loop identification. Second, this information is used to design a two degree of freedom H_∞ servo system for suppressing the spillover while tracking a step reference input. Finally, the desired robust performance of the resulting servo system is confirmed theoretically by γ-analysis and also experimentally.     

一种可保证瞬态特性的改进的鲁棒模型参考自适应控制

针对典型的鲁棒模型参考自适应控制中瞬态性能无法得到保障的问题, 提出一种改进的鲁棒模型参考自适应控制器. 该控制器在标准的鲁棒自适应控制中加入??_∞ 补偿器, 以抑制闭环自适应系统中参数估计误差和不确定扰动对系统输出跟踪性能造成的不利影响. 理论分析和仿真验证表明, 所提出的控制器不但保留了典型鲁棒模型参考自适应控制的理想特性, 并且通过设计适当的??∞ 补偿器使得闭环系统的瞬态性得到了较大的改善, 其改善的程度依赖于??∞ 补偿器性能指标的大小.

     

Robust H∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching

This paper is concerned with the problems of robust stochastic stabilization and robust H_∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching. The parameter uncertainties are time‐varying norm‐bounded. For the robust stochastic stabilization problem, the purpose is the design of a state feedback controller which ensures the robust stochastic stability of the closed‐loop system irrespective of all admissible parameter uncertainties; while for the robust H_∞ control problem, in addition to the robust stochastic stability requirement, a prescribed level of disturbance attenuation is required to be achieved. Sufficient conditions for the solvability of these problems are obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, explicit expressions of the desired state feedback controllers are also given. An illustrative example is provided to show the effectiveness of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.