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.     

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.     

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     

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.     

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     

Stabilization control for multimachine system using decentralized H∞ excitation controller realizing terminal voltage control and damping control

In this paper, to achieve both damping of power system oscillation and terminal voltage control simultaneously on a multimachine power system, we propose a decentralized H_∞ excitation controller. In the proposed method, H_∞ control via the Normalized Coprime Factorization approach is used to achieve the proposed design idea. By the Normalized Coprime Factorization approach, the weighting function in H_∞ control design is simplified, and output feedback controllers that take into account the realities and constraints of the power systems are designed. The proposed controller is subjected to model reduction of H_∞ controllers, and is transformed to a discrete system to perform digital control by computer systems in consideration of application to a real system. We verify that the proposed excitation controller can achieve both damping of power system oscillation and terminal voltage control by computer simulations of a multimachine power system. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 147(1): 33–41, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10254     

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.     

Inertial fluctuation-insensitive robust control of a robot manipulator based on a combination of an inertial torque computation filter and H∞ control

This paper describes a new type of robust control of robot manipulators, which guarantees robust stability against fluctuation of the inertial matrix. In this control, the inertial matrix is calculated as the computed torque from the Newton-Euler formulation. As a result, the cutoff frequency of the sensitivity function can be set much higher than in conventional control systems such as disturbance observer-based decentralized robust control systems. © 1998 Scripta Technica. Electr Eng Jpn, 122(2): 38–47, 1998     

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.     

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.     

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     

Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties

In this paper, the problem of robust H_∞ filtering for switched linear discrete‐time systems with polytopic uncertainties is investigated. Based on the mode‐switching idea and parameter‐dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H_∞ performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H_∞ noise‐attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

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     

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.     

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     

Neural‐network‐based finite‐time H∞ control for extended Markov jump nonlinear systems

This paper presents a neural‐network‐based finite‐time H_∞ control design technique for a class of extended Markov jump nonlinear systems. The considered stochastic character is described by a Markov process, but with only partially known transition jump rates. The sufficient conditions for the existence of the desired controller are derived in terms of linear matrix inequalities such that the closed‐loop system trajectory stays within a prescribed bound in a fixed time interval and has a guaranteed H_∞ noise attenuation performance for all admissible uncertainties and approximation errors of the neural networks. A numerical example is used to illustrate the effectiveness of the developed theoretic results. Copyright © 2009 John Wiley & Sons, Ltd.     

Target tracking with unknown noise statistics based on intelligent H∞ particle filter

In this paper, the target tracking based on the H∞ unscented particle filter and the particle swarm optimization is proposed. The proposed algorithm combines unscented particle filter and H∞ filter to estimate the target state. Furthermore, to prevent the particle degeneracy and impoverishment, particle swarm optimization is adapted to optimize particles. The proposed method has the common advantageous feature that it does not need to know the noise statistics. The performance of the proposed algorithm is shown through Monte Carlo runs and its performance is compared with that of other methods.     

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.