Design and implementation of anti-windup controller based on stated feedback H∞ control theory

In the control of an actual plant, there commonly exists a constraint on the control input caused by mechanical constraint on the actuator or in order to protect the plant. This constraint usually exerts an adverse effect on control performance, called windup phenomenon. Anti-windup technique is known as one of the most effective techniques to prevent such windup phenomenon. In this paper, we propose a new design of anti-windup controller based on state feedback H^∞ control theory. This design consists of representation of an anti-windup controller that includes a free parameter, and decision of the free parameter by using state feedback H^∞ control theory. We also discuss the problem on discretization of an anti-windup controller in implementation. In a numerical case study, we demonstrate the performance of the proposed anti-windup controller by computer simulation. © 1998 Scripta Technica, Electr Eng Jpn, 124(1): 33–41, 1998     

Active vibration control of a motor system by using H∞ control theory

This paper considers the vibration control of a motor system which has a motor and a load connected with a flexible shaft. However, this system often generates a shaft torsional vibration. Traditional methods of treating this problem to adjust the PID controller so that the closed-loop frequency response is slower than that of the vibration mode. On the other hand, one method has already been proposed in which the vibration is suppressed by a disturbance observer. This paper proposes a new approach based on H_∞ control theory. For comparison, a PI control system based on classical control theory also is constructed. The results of several experiments show that compared with the PI control system, the H_∞ control system is effective in suppressing the vibration. Further, the H_∞ controller obtained in the study consists of a PI controller and a series compensator that functions as an active vibration controller.     

Output power leveling of wind turbine generator by pitch angle control using H∞ control

Effective utilization of renewable energies such as wind energy is expected instead of the fossil fuels. Wind energy is not constant and windmill output is proportional to the cube of wind speed, which causes fluctuating power of wind turbine generator (WTG). In order to reduce the fluctuating power of WTG, this paper presents an output power leveling technique of WTG by pitch angle control using H_∞ control, and the control input of WTG linear model is separated from the disturbance. The simulation results using actual detailed model for WTG show the effectiveness of the proposed method. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 162(4): 17–24, 2008; Published online in Wiley InterScience ( www.interscience. wiley.com ). DOI 10.1002/eej.20657     

Switching of H∞ controller under constraints and decision of controller state at instance of the controller switching

In real control systems, certain constraints are placed on the input, state, and output values. If such constraints are violated, the system may become unstable, in a worst‐case scenario. One of the promising approaches to solving this problem is to switch the controller according to the state of the closed‐loop system. No useful design strategy for each controller, however, has yet been developed. In addition, the determination of the controller state at the instant of controller switching has not been investigated. First, this paper presents a new design methodology which merges the switching control and H_∞ controller design into one design algorithm. Second, this paper presents a way of determining the controller state at the instant of controller switching. Finally, the proposed method is applied to force control of a one‐DOF manipulator in order to demonstrate the usefulness of the proposed method. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 142(2): 68–75, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10082     

Decentralized load frequency based on H∞ control

This paper presents a decentralized load frequency control (LFC) based on H_∞ optimal control theory with an observer. A few LFC schemes have been proposed based on the optimal control theory, but they have not considered the change of system parameters in operation and the characteristics of load disturbances in a target system. In this paper, H_∞ robust control is introduced to address such problems. Owing to its practical merit, the proposed control scheme is a decentralized LFC. Employing observer theory, the proposed method requires only frequency and tie‐line power deviation in each area. Numerical simulations are shown to demonstrate the effectiveness of the proposed method. H_∞ control was proven to show greater effectiveness of damping disturbance over the conventional optimal control by the design of control systems aimed at restricting the H_∞ norm of its transfer function. In particular, when a decentralized LFC is applied, by reducing the system size, H_∞ norm is easier to dampen; thus H_∞ control is more effective in the decentralized control. Future research topics include the design of H_∞ control system with a weight on frequency response. © 2001 Scripta Technica, Electr Eng Jpn, 136(3): 28–38, 2001     

Two-degrees-of-freedom speed control of resonant mechanical system based on H∞ control theory

In industrial motor drive systems such as those used in industrial plants and robots, a torsional vibration is often generated as a result of the elastic elements present in the torque transmission systems. This vibration makes it difficult to achieve quick speed responses and may result in plant damage. Such systems are simply modeled as two-mass mechanical systems. The H^∞ control theory is applied herein to design a speed controller for the two-mass system. This controller determines closed-loop characteristics, including suppression of torsional vibration, rejection of torque disturbance and robust stability. Moreover, two types of two-degrees-of-freedom control systems, which includes the H^∞ controller, are proposed to improve command response. One is based on the TDOF PI control, in which the PI controller included in the H^∞ controller is rearranged for the TDOF system. Another is based on the model matching feedforward control, in which the prefilter and the feedforward compensator are added to the H^∞ controller. The proposed control system is applied to two types of resonant mechanical systems having different inertia ratio. Several examinations demonstrate that the proposed speed control system is useful for a resonant mechanical system.     

H∞ control approach to a magnetic levitation system by 4-point attraction with nonlinear characteristics

An H_∞ control system design for a magnetic levitation system by 4 points attraction is presented. In the levitation system, a vehicle which runs as the secondary in a reluctance-type linear motor is levitated by four pairs of attraction forces and guided by two pairs of attraction forces. Because it has contactlessness, in the field of semiconductor products, its application is favorable for ultraclean environments in microscopic processing. In the control system design, the influence of both disturbances and uncertainties in the model is considered. The main disturbances stem from the position sensors. The uncertainties are divided into electromagnetic and mechanical ones: the former are due to the gain change in the current amplifier, the influence of leakage flux and linearization error in the magnetic circuit, and the latter are due to the changes of the mass and the moment of inertia of the vehicle. Therefore, the designed controller is indispensable to guarantee robustness of this system for both stability and performance. The controller design is based on the standard H_∞-optimal control problem. As the novel features in this paper, the low sensitivity and the robust stability for this system design is obtained. Further, there are two-poles on jω-axis in the controlled model, and an integrator is included in the controller so that equivalently there are three poles on the jω-axis in the model. Finally, several experiments, comparisons and simulations are carried out to verify the low sensitivity and robustness of the designed control system.     

Fully parameterized fixed‐order controller design for H∞ loop shaping method using frequency responses—extension to MIMO systems

Robust control is often applied to systems with uncertainties and disturbances. Above all, the H∞ loop shaping method is known to achieve good control performance and robustness. In this method, the final controller consists of weighting functions and a stabilizing controller. The stabilizing controller is derived for the shaped plant to suppress the H∞ norm of the transfer matrix consisting of a sensitivity function, a complementary sensitivity function, and so on. In addition, the stabilizing controller improves robust stability margin while keeping gain characteristic of the shaped plant if weighting functions are suitable. As a result, the closed‐loop system is well‐balanced between good tracking and robustness. However, a final controller tends to be high‐order. For this problem, reduction techniques are often applied to the final controller. In this case, performance and stability is not always adequately evaluated due to errors by the controller reduction. This paper proposes a fully parameterized fixed‐order controller design method using frequency responses of the plant. We formulate a design problem for multi‐input–multi‐output systems as an optimization problem. Therefore, we can directly design a low‐order controller from frequency responses using the iterative LMI optimization. Accordingly, we can avoid to deteriorate the evaluation of performance and stability.     

Output‐feedback H∞ quadratic tracking control of linear systems using reinforcement learning

This paper presents an online learning algorithm based on integral reinforcement learning (IRL) to design an output‐feedback (OPFB) H_∞ tracking controller for partially unknown linear continuous‐time systems. Although reinforcement learning techniques have been successfully applied to find optimal state‐feedback controllers, in most control applications, it is not practical to measure the full system states. Therefore, it is desired to design OPFB controllers. To this end, a general bounded L₂ ‐gain tracking problem with a discounted performance function is used for the OPFB H_∞ tracking. A tracking game algebraic Riccati equation is then developed that gives a Nash equilibrium solution to the associated min‐max optimization problem. An IRL algorithm is then developed to solve the game algebraic Riccati equation online without requiring complete knowledge of the system dynamics. The proposed IRL‐based algorithm solves an IRL Bellman equation in each iteration online in real time to evaluate an OPFB policy and updates the OPFB gain using the information given by the evaluated policy. An adaptive observer is used to provide the knowledge of the full states for the IRL Bellman equation during learning. However, the observer is not needed after the learning process is finished. A simulation example is provided to verify the convergence of the proposed algorithm to a suboptimal OPFB solution and the performance of the proposed method.     

电力系统励磁控制机端电压的迭代学习补偿

为提高电力系统稳定性而采取的励磁控制需要有较强的维持机端电压的能力,通过对实际输出波形幅值的检测,将设定幅值与检测幅值的偏差及其偏差变化率作为学习控制器的输入,进行补偿控制,提高实验结果的准确性,基于单机无穷大系统将开闭环迭代学习控制规律与常规PID控制规律进行了比较,仿真结果表明励磁控制迭代学习补偿器具有精度高、快速性好的特点。     

An H∞ approach to linear iterative learning control design

A new design methodology for iterative learning control systems is developed. It is based on the convergence condition for systems operating on an infinite time interval which is of the H_∞ type. The principal idea of the design technique is to design a learning controller such that the speed of convergence is maximized, with a compromise to robustness. The issue of finite versus infinite trial lengths is addressed, as well as limitations on the best achievable rate of convergence due to structural properties of the plant.     

High‐bandwidth design of hard disk control system using H∞ control with feedback‐type uncertainty

In hard disk drives, it is important to enlarge the control bandwidth in order to shorten the track pitch for larger data capacity. However, it is difficult for the H_∞ control method to increase the control bandwidth if the mechanical resonance modes have uncertainty. This is because the robustness of the H_∞ control method is assured by the small‐gain theorem for additive or multiplicative perturbation and the control bandwidth is limited by the uncertainty. In this study, we propose an H_∞ control method for high‐bandwidth design by introducing a new uncertainty model with a feedforward and a feedback path in order to reduce the conservatism of robust design. The effectiveness is shown by numerical simulations. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 173(4): 54–62, 2010; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21025     

Central suboptimal H∞ filter design for nonlinear polynomial systems

This paper presents the central finite‐dimensional H_∞ filter for nonlinear polynomial systems, which is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H_∞ filtering problem to the corresponding optimal H₂ filtering problem, using the technique proposed in (IEEE Trans. Automat. Control 1989; 34 :831–847). The paper presents the central suboptimal H_∞ filter for the general case of nonlinear polynomial systems based on the optimal H₂ filter given in (Int. J. Robust Nonlinear Control 2006; 16 :287–298). The central suboptimal H_∞ filter is also derived in a closed finite‐dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H_∞ filter available for the corresponding linearized system. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust learning controller design for MIMO stochastic discrete‐time systems: An H∞‐based approach

This paper is devoted to designing iterative learning control (ILC) for multiple‐input multiple‐output discrete‐time systems that are subject to random disturbances varying from iteration to iteration. Using the super‐vector approach to ILC, statistical expressions are presented for both expectation and variance of the tracking error, and time‐domain conditions are developed to ensure their asymptotic stability and monotonic convergence. It shows that time‐domain conditions can be tied together with an H_∞‐based condition in the frequency domain by considering the properties of block Toeplitz matrices. This makes it possible to apply the linear matrix inequality technique to describe the convergence conditions and to obtain formulas for the control law design. Furthermore, the H_∞‐based approach is shown applicable to ILC design regardless of the system relative degree, which can also be used to address issues of model uncertainty. For a class of systems with a relative degree of one, simulation tests are provided to illustrate the effectiveness of the H_∞‐based approach to robust ILC design. Copyright © 2011 John Wiley & Sons, Ltd.     

H∞ filtering for continuous‐time singular systems with time‐varying delay

This paper focuses on H_∞ filter design for continuous‐time singular systems with time‐varying delay. A delay‐dependent H_∞ performance analysis result is first established for error systems via a novel estimation method. By combining a well‐known inequality with a delay partition technique, the upper bound of the derivative of the Lyapunov functional is estimated more tightly and expressed as a convex combination with respect to the reciprocal of the delay rather than the delay. Based on the derived H_∞ performance analysis results, a regular and impulse‐free H_∞ filter is designed in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Quantized H∞ filtering for state‐delayed systems with finite frequency specifications

This paper presents a novel design approach for the finite frequency (FF) H_∞ filtering problem for discrete‐time state‐delayed systems with quantized measurements. The system state and output are assumed affected by FF external noises. Attention is focused on the design of a stable filter that guarantees the stability and a prescribed ?₂ gain performance level for the filtering error system in the FF domain of input noises. Sufficient conditions for the solvability of this problem are developed by choosing an appropriate Lyapunov‐Krasovskii functional based on the delay partitioning technique and using the FF ?₂ gain definition combined with the generalized S‐procedure. Then, by means of Finsler's lemma, the derived conditions are linearized and additional slack variables are further introduced to more flexible result. Final filter design conditions are consequently established in terms of linear matrix inequalities in three different frequency ranges, ie, low‐, middle‐ and high‐frequency range. Finally, a simulation example is presented to illustrate the effectiveness and the merits of the proposed approach.     

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

This paper considers the problem of adaptive robust H_∞ state feedback control for linear uncertain systems with time‐varying delay. The uncertainties are assumed to be time varying, unknown, but bounded. A new adaptive robust H_∞ controller is presented, whose gains are updating automatically according to the online estimates of uncertain parameters. By combining an indirect adaptive control method and a linear matrix inequality method, sufficient conditions with less conservativeness than those of the corresponding controller with fixed gains are given to guarantee robust asymptotic stability and H_∞ performance of the closed‐loop systems. A numerical example and its simulation results are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust weighted H∞ filtering for networked systems with intermittent measurements of multiple sensors

In this paper, we investigate the robust weighted H_∞ filtering problem for networked systems with intermittent measurements under the discrete‐time framework. Multiple outputs of the plant are measured by separate sensors, each of which has a specific failure rate. Network‐induced delay, packet dropouts and network‐induced disorder phenomena are all incorporated in the modeling of the network link. The resulting closed‐loop system involves both delayed noise and non‐delayed noise. In order to make full use of the delayed information, we define a weighted H_∞ performance index. Sufficient delay‐dependent and parameter‐dependent conditions for the existence of the filter and the solvability of the addressed problem are given via a set of linear matrix inequalities. Two simulation examples are presented to illustrate the relationship between the minimal performance level and the weighting factor, which show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.