Robust control for an uncertain LCL resonant ICPT system using LMI method

Frequency drift has considerable adverse effects on the inductively coupled power transfer (ICPT) system such as decrease of transmission power and distance, EMC interference, system detuning and performance deterioration, and deviated operation from system design requirements endangering the stability so that robust control of ICPT system remains an open applied research problem. This article presents a relevant uncertain model for the LCL resonant ICPT system first via the generalized state-space averaging and the LFT methods, and then a solution to H_∞ controller synthesis by making use of the LMI method. The control design is first tested by computer simulation and thereafter verified by means of physical experiments. The results show that by applying the proposed H_∞ synthesis controller the overall system has achieved both predetermined robustness with respect to the norm-bounded load and frequency uncertainties and dynamically tracking the voltage references according to the actual power demands.     

Robust H∞ control for uncertain discrete stochastic time-delay systems

This paper deals with the problems of robust stabilization and robust H_∞ control for discrete stochastic systems with time-varying delays and time-varying norm-bounded parameter uncertainties. For the robust stabilization problem, attention is focused on the design of a state feedback controller which ensures robust stochastic stability of the closed-loop system for all admissible uncertainties, while for the robust H_∞ control problem, a state feedback controller is designed such that, in addition to the requirement of the robust stochastic stability, a prescribed H_∞ performance level is also required to be satisfied. A linear matrix inequality (LMI) approach is developed to solve these problems, and delay-dependent conditions for the solvability are obtained. It is shown that the desired state feedback controller can be constructed by solving certain LMIs. An example is provided to demonstrate the effectiveness of the proposed approach.     

Decentralized multivariable voltage and speed regulator for large-scale power systems with guarantee of stability and transient performance

This paper presents a novel procedure for the design of decentralized regulators for large power systems with a formal proof of ‘global’ stability. The distinctive feature of the solution is that both voltage and rotor speed dynamics are regulated simultaneously contrary to most of the solutions proposed so far in the literature. First, the traditional multimachine power system algebraic-differential equations are reformatted into suitable state equations, more appropriate for modern control tools. Secondly, a voltage and speed controller based on this model is proposed. The design consists of first cancelling some of the dynamical model non-linearities using non-linear excitation and valve input. The resulting subsystems are stabilized by auxiliary controls with linear and non-linear components. The non-linear component, which uses local signals to dominate those with interconnections, is derived from a stability criterion involving the Lyapunov function of the entire power system. The gains of the linear component are computed from the solution of an algebraic Riccati equation similar to the one involved in the full information H _∞ problem. These gains guarantee that effects of interconnection signals on voltage and speed dynamics are considerably reduced. The benefit of the proposed scheme is that the voltage regulation characteristic ensures a good post-fault voltage profile which helps improve rotor oscillations damping. Simulation results on a realistic power system confirm that the system stability is considerably improved in presence of severe contingencies.     

H ∞ Control for uncertain system with time-delay and nonlinear external disturbance via adaptive control method

This paper considers the H _∞ control problem for the uncertain time delay system with nonlinear external disturbance. Given a system containing nonlinear external disturbance, our purpose is to design a robust controller such that the uncertain system is asymptotically stable with a generalized H _∞ disturbance attenuation level ρ. In this paper we propose a new approach to design the controller for the uncertain system which is composed of a linear controller and an adaptive controller. The problem is solved by introducing a switching function and using the idea of formulation. Based on Lyapunov stability theory, new sufficient conditions are obtained in terms of linear matrix inequalities. The effectiveness and advantages of the proposed controller design are shown via a numerical example.     

H ∞ robust control of DC-AC interfaced microsource in microgrids

This paper focuses on the direct current-alternating current (DC-AC) interfaced microsource based H∞ robust control strategies in microgrids. It presents detail of a DC-AC interfaced microsource model which is connected to the power grid through a controllable switch. A double loop current-regulated voltage control scheme for the DC-AC interface is designed. In the case of the load disturbance and the model uncertainties, the inner voltage and current loop are produced based on the H∞ robust control strategies. The outer power loop uses the droop characteristic controller. Finally, the scheme is simulated using the Matlab/Simulink. The simulation results demonstrate that DC-AC interfaced microsource system can supply high quality power. Also, the proposed control scheme can make the system switch smoothly between the isolated mode and grid-connected mode.     

Intelligent mixed H2/H∞ adaptive tracking control system design using self-organizing recurrent fuzzy-wavelet-neural-network for uncertain two-axis motion control system

In this paper, an intelligent adaptive tracking control system (IATCS) based on the mixed H₂/H_∞ approach under uncertain plant parameters and external disturbances for achieving high precision performance of a two-axis motion control system is proposed. The two-axis motion control system is an X–Y table driven by two permanent-magnet linear synchronous motors (PMLSMs) servo drives. The proposed control scheme incorporates a mixed H₂/H_∞ controller, a self-organizing recurrent fuzzy-wavelet-neural-network controller (SORFWNNC) and a robust controller. The combinations of these control methods would insure the stability, robustness, optimality, overcome the uncertainties, and performance properties of the two-axis motion control system. The SORFWNNC is used as the main tracking controller to adaptively estimate an unknown nonlinear dynamic function that includes the lumped parameter uncertainties, external disturbances, cross-coupled interference and frictional force. Moreover, the structure and the parameter learning phases of the SORFWNNC are performed concurrently and online. Furthermore, a robust controller is designed to deal with the uncertainties, including the approximation error, optimal parameter vectors and higher order terms in Taylor series. Besides, the mixed H₂/H_∞ controller is designed such that the quadratic cost function is minimized and the worst case effect of the unknown nonlinear dynamic function on the tracking error must be attenuated below a desired attenuation level. The mixed H₂/H_∞ control design has the advantage of both H₂ optimal control performance and H_∞ robust control performance. The sufficient conditions are developed for the adaptive mixed H₂/H_∞ tracking problem in terms of a pair of coupled algebraic equations instead of coupled nonlinear differential equations. The coupled algebraic equations can be solved analytically. The online adaptive control laws are derived based on Lyapunov theorem and the mixed H₂/H_∞ tracking performance so that the stability of the proposed IATCS can be guaranteed. Furthermore, the control algorithms are implemented in a DSP-based control computer. From the experimental results, the motions at X-axis and Y-axis are controlled separately, and the dynamic behaviors of the proposed IATCS can achieve favorable tracking performance and are robust to parameter uncertainties.     

On nonlinear H ∞ sliding mode control for a class of nonlinear cascade systems

In this work two main robust control strategies, the sliding mode control (SMC) and nonlinear H ^∞ control, are integrated to function in a complementary manner for tracking control tasks. The SMC handles matched L ^∞[0,∞) type system uncertainties with known bounding functions. H ^∞ control deals with unmatched disturbances of L ₂[0,∞) type where the upper-bound knowledge is not available. The new control method is designed for a class of nonlinear uncertain systems with two cascade subsystems. Nonlinear H ^∞ control is applied to the first subsystem in the presence of unmatched disturbances. Through solving a Hamilton-Jacoby inequality, the nonlinear H ^∞ control law for the first subsystem well defines a nonlinear switching surface. By virtue of nonlinear H ^∞ control, the resulting sliding manifold in the sliding phase possesses the desired L ₂ gain property and to a certain extend the optimality. Associated with the new switching surface, the SMC is applied to the second subsystem to accomplish the tracking task, and ensure the L ₂ gain robustness in the reaching phase. Two illustrative examples are given to show the effectiveness of the proposed robust control scheme.     

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.     

Finite-time fault-tolerant control for flutter of wing

In this paper, we use the radial basis function neural network and the finite-time H_∞ adaptive fault-tolerant control technique to deal with the flutter problem of wings with propulsion system, which is affected by input saturation, time delay, time-varying parameter uncertainties and external disturbances. Then sensor and actuator faults are both considered in the control design. The theory content of this article includes the trajectory optimization, modeling of wing flutter and fault-tolerant controller design. The stability of the finite-time H_∞ adaptive fault-tolerant controller is theoretically proved. Finally, simulation results are given to demonstrate the effectiveness of the scheme.     

Application Of H2/H∞ Technique To Aircraft Landing Control

The paper describes the automatic control of an aircraft in the longitudinal plane during landing, taking into account sensor errors and disturbances. Aircraft auto‐landing is achieved by combining H₂ and H_∞ control techniques, thereby obtaining a robust H₂/H_∞ controller. It provides good precision tracking and robust stability with respect to the uncertainties caused by different disturbances and noise‐type signals. The weights of the H₂ and H_∞ control techniques within the robust H₂/H_∞ controller are adjusted so that the aircraft accurately tracks the desired trajectory during the two main stages of the landing process. The theoretical results are validated by numerical simulations for the landing of a Boeing; the results are very good (Federal Aviation Administration accuracy requirements for Category III are met) and prove the robustness of the new auto‐landing system even in the presence of disturbances and sensor errors.     

Robust control of multistage printing systems

Printing errors (e.g. doubling) in multistage printing machines are mainly caused by web tension fluctuations, which arise from excessive rotation non-synchronization errors among the driven rollers in different stages (units). Therefore, the critical task in printing quality control is to attenuate web tension variations. In this paper, a robust H_∞ control strategy is proposed to attenuate tension fluctuations when the system is subject to disturbances and variations in speed or other operating conditions. Three system robustness properties are analyzed by using structured singular value analysis (μ-analysis). A systematic investigation is taken to analyze the impacts of different parameter variations on system robustness, with a purpose of providing a reference for achieving robust stability in a multistage printing system. The effectiveness of the proposed robust H_∞ controller is evaluated by both simulation and experimental tests.     

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.     

Controllers Design via Given Oscillation Index: Parametric Uncertainty and Power-Bounded External Disturbances

The problem is considered of output controllers design for linear multivariable systems with deviating in prescribed bounds physical parameters of the plant, and subjected to the influence of unknown polyharmonic external disturbances, limited only in power. The controller is built so that to provide the prescribed bounds of mean-square values of controlled variables in addition to the robust stability of the closed-loop system. The problem solution is reduced to the H_∞-optimization procedure produced in some specific way. The solution of the well-known “benchmark” problem is considered.     

Delay-dependent robust stabilization and H ∞ control for uncertain stochastic T-S fuzzy systems with discrete interval and distributed time-varying delays

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno (T-S) fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities (LMIs) and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.     

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.     

A receding–horizon approach to the nonlinear H∞ control problem

The receding–horizon (RH) methodology is extended to the design of a robust controller of H_∞ type for nonlinear systems. Using the nonlinear analogue of the Fake H_∞ algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input–output map of the closed-loop system obtained with the RH control law has a bounded L₂-gain. Robustness properties of the nonlinear H_∞ control law in face of dynamic input uncertainty are considered.     

Robust tracking control design for uncertain robotic systems with persistent bounded disturbances

In this study, a robust nonlinear L_∞‐gain tracking control design for uncertain robotic systems is proposed under persistent bounded disturbances. The design objective is that the peak of the tracking error in time domain must be as small as possible under persistent bounded disturbances. Since the nonlinear L_∞ ‐gain optimal tracking control cannot be solved directly, the nonlinear L_∞ ‐gain optimal tracking problem is transformed into a nonlinear L_∞ ‐gain tracking problem by given a prescribed disturbance attenuation level for the L_∞ ‐gain tracking performance. To guarantee that the L_∞ ‐gain tracking performance can be achieved for the uncertain robotic systems, a sliding‐mode scheme is introduced to eliminate the effect of the parameter uncertainties. By virtue of the skew‐symmetric property of the robotic systems, sufficient conditions are developed for solving the robust L_∞ ‐gain tracking control problems in terms of an algebraic equation instead of a differential equation. The proposed method is simple and the algebraic equation can be solved analytically. Therefore, the proposed robust L_∞ ‐gain tracking control scheme is suitable for practical control design of uncertain robotic systems. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

L2–L∞ fuzzy control for Markov jump systems with neutral time-delays

The L₂–L_∞ fuzzy control problem is considered for nonlinear stochastic Markov jump systems with neutral time-delays. By means of Takagi–Sugeno fuzzy models, the fuzzy controller systems and the overall closed-loop fuzzy dynamics are constructed. A sufficient condition is firstly established on the stochastic stability using stochastic Lyapunov–Krasovskii functional. Then in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of mode-dependent state feedback L₂–L_∞ fuzzy controller are presented and proved respectively for constant and time varying case. Finally, the design problems are formulated as optimization algorithms. Simulation results are exploited to illustrate the effectiveness of the developed techniques.     

Control of large model mismatch systems using multiple models

H _∞ control is an effective approach to handle model uncertainties. However, when modeling mismatch is large, it tends to be challenging to meet the desired requirements of both stability and performance by only using a single H _∞ controller. This study presents a switching method to enhance the robust stability and performance of H _∞ control by dividing the range of dynamics into multiple uncertain models. The candidate robust controllers are designed by solving a set of linear matrix inequalities for each uncertain model. A structural scheduling logic that selects the most proper controller into closed-loop is proposed. The selected controller can ensure bounded exponentially weighted H _∞ norm of the closed-loop switching systems. This work analyses their robust stability and disturbance attenuation performance via a linear fractional transformation by using the small gain theorem. The effectiveness of this method is validated with a fist-order inertial system with pure time delay.     

Sliding mode control of drum water level in an industrial boiler unit with time varying parameters: A comparison with H∞-robust control approach

In steam power-plants, to prevent over-heating of drum components or flooding of steam lines, perfect control of drum water level is of great importance. But during the operation, disturbances affecting water level, model uncertainties and parameter mismatch due to variant operating conditions lead to the variation of model parameters. In this paper, under transient conditions and in the presence of model uncertainties, two control strategies are implemented to achieve desired tracking of drum water level: robust sliding mode and H_∞ control. Two transfer functions between drum water level (output variable); feed-water and steam mass rates (input variables) are considered. For the dynamic system with time varying characteristic and parametric uncertainties, a sliding mode controller is developed and an optimal H_∞ controller is designed based on μ-synthesis with DK-iteration algorithm. For different desired commands of drum water level (including a sequence of steps and ramps-steps); it is observed that both control strategies guarantee robust stability and performance of the system without actuators saturation (control signals are bounded). However, using the sliding mode controller leads to the more smooth and rapid time responses of drum water level with less oscillatory behaviour of control efforts (and consequently less energy consumption). In addition, for tracking objectives in short command times, sliding mode controller performs more appropriately.