Wiener-Hopf design of servo-regulator-type multivariable control systems including feedforward compensation

Frequency-domain design in a quadratic cost setting is treated for a multivariable control system which includes disturbance feedforward, output feedback, and reference-input compensation (i.e. a three-degrees-of-freedom control system). The cost function is taken to account for tracking accuracy, plant saturation and plant sensitivity. The class of all controllers is determined for which the given system is internally asymptotically stable and the quadratic cost function is finite. This controller class is parametrized in terms of arbitrary real rational matrices Z_z Z_u and Z_w which are strictly proper and analytic in Re s ≥ 0. The optimal solution is obtained by setting the Z matrices to zero.     

Static anti‐windup design for a class of nonlinear systems

This paper focuses on the problem of static anti‐windup design for a class of multivariable nonlinear systems subject to actuator saturation. The considered class regards all systems that are rational on the states or that can be conveniently represented by a rational system with algebraic constraints considering some variable changes. More precisely, a method is proposed to compute a static anti‐windup gain which ensures regional stability for the closed‐loop system assuming that a dynamic output feedback controller is previously designed to stabilize the nonlinear system. The results are based on a differential algebraic representation of rational systems. The control saturation effects are taken into account by the application of a generalized sector bound condition. From these elements, LMI‐based conditions are devised to compute an anti‐windup gain with the aim of enlarging the closed‐loop region of attraction. Several numerical examples are provided to illustrate the application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Anti‐windup design of active disturbance rejection control for sampled systems with input delay

A novel anti‐windup design of active disturbance rejection control (ADRC) is proposed for industrial sampled systems with input delay and saturation. By using a generalized predictor to estimate the delay‐free system output, a modified extended state observer is designed to simultaneously estimate the system state and disturbance, which could become an anti‐windup compensator when the input saturation occurs. Accordingly, a feedback controller is analytically designed for disturbance rejection. By proposing the desired closed‐loop transfer function for the set‐point tracking, a prefilter is designed to tune the tracking performance while guaranteeing no steady‐state output tracking error. A sufficient condition for the closed‐loop system stability is established with proof for practical application subject to the input delay variation. Illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control design.     

Modern Wiener--Hopf design of optimal controllers Part I: The single-input-output case

An analytical feedback design technique is presented here for single-input-output processes which are characterized by their rational transfer functions. The design procedure accounts for the topological structure of the feedback system ensuring asymptotic stability for the closed-loop configuration. The plant or process being controlled can be unstable and/or nonminimum phase. The treatment of feedback sensor noise, disturbance inputs, and process saturation is another major contribution of this work. The cornerstone in the development is the selection of a performance index based on sound engineering considerations. It is these considerations, in fact, which ensure the existence of an optimal compensator for the system and make the performance index a natural one for the problem at hand.     

An approach to multivariable system identification

Two prototype identifiable structures are presented which make possible the identification via an equation-error model reference adaptive system of linear plants with rational transfer function matrices. The structures include as specialisations many of the particular structures presented hitherto in the literature. Convergence properties are also discussed, and several modes of convergence are distinguished: model output to plant output, model transfer function matrix to plant transfer function matrix, and model parameters to plant parameters. Conditions are presented for exponentially fast convergence in the absence of noise.     

Reduced order controller design for discrete time systems

Robust discrete control system design techniques and model reduction are discussed. A new linear quadratic guussian/loop transfer recovery procedure for discrete time systems is presented. In this technique, a full-state feedback or an output injection feedback is designed which has the desired loop shape, and then recovered by a realizable linear quadratic gaussian controller. To do this, results that show the effects of the weighting matrices (noise intensities) on linear quadratic regulator (Kalman-Bucy filter) return difference and inverse-return difference arc derived and a procedure to recover the linear quadratic regulator loop transfer function is described. The complexity of the resulting controller is then reduced without causing closed-loop instability. Two methods for model reduction are considered. The first is the discrete balanced realization and the second is P frequency weighting technique where it is possible to vary the approximation accuracy with frequency. The controller design and reduction techniques are illustrated by designing a reduced order controller for an 8th order lumped inertia flexible mechanical system.     

A time-domain approach to z-domain model identification

A time-domain parameter-optimization approach to discrete linear-model identification is presented, z-domain transfer functions are sought with outputs closely matching corresponding outputs of observed systems. Optimal transfer-function coefficients are determined through the minimization of mean-square output error. The general technique developed is applied to problems in model reduction and identification in the presence of measurement noise.     

A technique for the identification of linear systems

An iterative technique is proposed to identify a linear system from samples of its input and output in the presence of noise by minimizing the mean-square error between system and model outputs. The model chosen has a transfer function which is a ratio of polynomials in z^-1. Although the regression equations for the optimal set of coefficients are highly nonlinear and intractable, it is shown that the problem can be reduced to the repeated solution of a related linear problem. Computer simulation of a number of typical discrete systems is used to demonstrate the considerable improvement over the Kalman estimate which can be obtained in a few iterations. The procedure is found to be effective at signal-to-noise ratios less than unity, and with as few as 200 samples of the input and output records.     

Robust adaptive tracking control for a class of mechanical systems with unknown disturbances under actuator saturation

A robust adaptive tracking control scheme is presented for a class of multiple‐input and multiple‐output mechanical systems with unknown disturbances under actuator saturation. The unknown disturbances are expressed as the outputs of a linear exogenous system with unknown coefficient matrices. An adaptive disturbance observer is constructed for the online disturbance estimation. An actuator saturation compensator is introduced to attenuate the adverse effects of actuator saturation. The adaptive backstepping method is then applied to design the robust adaptive tracking control law. It is proved that the designed control law makes the system outputs track the desired trajectories and guarantees the global uniform ultimate stability of the closed‐loop control system. Simulations on a two‐link robotic manipulator verify the effectiveness of the proposed control scheme.     

具有输入饱和的近空间飞行器鲁棒控制

针对近空间飞行器这一类存在外部扰动,输入饱和和参数不确定的多输入多输出线性系统,提出了一种基于干扰观测器的抗饱和鲁棒控制方案.将干扰观测器与抗饱和控制技术相结合,从而消除系统存在的未知外部扰动、输入饱和和不确定性对系统控制的影响.首先,设计干扰观测器对线性外部系统产生的未知扰动进行估计.然后根据干扰观测器输出,通过超前抗饱和方法设计抗饱和补偿器,并将其加入到鲁棒控制器的设计中,保证闭环系统存在输入饱和、未知外部扰动和参数不确定情况下的稳定性.为便于设计,干扰观测器、抗饱和补偿器和控制器设计矩阵均通过求解线性矩阵不等式得到.最后,将提出的鲁棒抗饱和控制方法应用于近空间飞行器,仿真结果验证了该控制方案的有效性.     

Parametrizations of linear dynamical systems: Canonical forms and identifiability

We consider the problem of what parametrizations of linear dynamical systems are appropriate for identification (i.e., so that the identification problem has a unique solution, and all systems of a particular class can be represented). Canonical forms for controllable linear systems under similarity transformation are considered and it is shown that their use in identification may cause numerical difficulties, and an alternate approach is proposed which avoids these difficulties. Then it is assumed that the system matrices are parametrized by some unknown parameters from a priori system knowledge. The identiability of such an arbitrary parametrization is then considered in several situations. Assuming that the system transfer function can be identified asymptotically, conditions are derived for local and global identifiability. Finally, conditions for identifiability from the output spectral density are given for a system driven by unobserved white noise.     

Plant rational transfer approximation from input-output data

A rational transfer function model of the plant is generally desirable in feedback system design, when only plan input and output data are available over finite, sometimes incomplete, time intervals. This is especially so in a recent exact design technique for highly uncertain time-varying and non-linear plants. Here, the plants are replaced rigorously by an equivalent linear time-invariant plant set. Existing numerical techniques were found inadequate, especially in the high-frequency range, which is important in the design of feedback systems with large plant uncertainty. A technique was developed with excellent results, even for noisy data, unstable and non-minimum phase plants and severely truncated time intervals. The transfer function is calculated directly, without derivation of the input, output signal transforms. The operations involve repeated integrations of the data. Numerous examples are included.     

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein–Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.     

Positive real control of two-dimensional systems: Roesser models and linear repetitive processes

This paper considers the problem of positive real control for two-dimensional (2-D) discrete systems described by the Roesser model and also discrete linear repetitive processes, which are another distinct sub-class of 2-D linear systems of both systems theoretic and applications interest. The purpose of this paper is to design a dynamic output feedback controller such that the resulting closed-loop system is asymptotically stable and the closed-loop system transfer function from the disturbance to the controlled output is extended strictly positive real. We first establish a version of positive realness for 2-D discrete systems described by the Roesser state space model, then a sufficient condition for the existence of the desired output feedback controllers is obtained in terms of four LMIs. When these LMIs are feasible, an explicit parameterization of the desired output feedback controllers is given. We then apply a similar approach to discrete linear repetitive processes represented in their equivalent 1-D state-space form. Finally, we provide numerical examples to demonstrate the applicability of the approach.     

Adaptive System Identification in the Short-Time Fourier Transform Domain Using Cross-Multiplicative Transfer Function Approximation

In this paper, we introduce cross-multiplicative transfer function (CMTF) approximation for modeling linear systems in the short-time Fourier transform (STFT) domain. We assume that the transfer function can be represented by cross-multiplicative terms between distinct subbands. We investigate the influence of cross-terms on a system identifier implemented in the STFT domain and derive analytical relations between the noise level, data length, and number of cross-multiplicative terms, which are useful for system identification. As more data becomes available or as the noise level decreases, additional cross-terms should be considered and estimated to attain the minimal mean-square error (mse). A substantial improvement in performance is then achieved over the conventional multiplicative transfer function (MTF) approximation. Furthermore, we derive explicit expressions for the transient and steady-state mse performances obtained by adaptively estimating the cross-terms. As more cross-terms are estimated, a lower steady-state mse is achieved, but the algorithm then suffers from slower convergence. Experimental results validate the theoretical derivations and demonstrate the effectiveness of the proposed approach as applied to acoustic echo cancellation.     

H/sub /spl infin// filtering for singular systems

This note considers the H/sub /spl infin// filtering problem for linear continuous singular systems. The purpose is the design of a linear filter such that the resulting error system is regular, impulse-free and stable while the closed-loop transfer function from the disturbance to the filtering error output satisfies a prescribed H/sub /spl infin//-norm bound constraint. Without decomposing the original system matrices, a necessary and sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is given. Finally, an illustrative example is presented to demonstrate the applicability of the proposed approach.     

NN-Based Adaptive Tracking Control of Uncertain Nonlinear Systems Disturbed by Unknown Covariance Noise

A class of uncertain nonlinear systems that are additionally driven by unknown covariance noise is considered. Based on the backstepping technique, adaptive neural control schemes are developed to solve the output tracking control problem of such systems. As it is proven by stability analysis, the proposed controller guarantees that all the error variables are bounded with desired probability in a compact set while the tracking error is mean-square semiglobally uniformly ultimately bounded (M-SGUUB). The tracking performance and the effectiveness of the proposed design are evaluated by simulation results.     

Adaptive dynamic surface control using disturbance observer for nonlinear systems with input saturation and output constraints

An adaptive dynamic surface control (DSC) approach using fuzzy approximation and nonlinear disturbance observer (NDO) for uncertain nonlinear systems in the presence of input saturation, output constraint and unknown external disturbances is proposed in this paper. The issue of input saturation is addressed by introducing a lower bound assumption on the approximation function of saturation. The output constraint is handled by introducing an appropriate barried Lyapunov function. The nonlinear disturbance observer (NDO) is employed to estimate the unknown unmatched disturbances. It is manifested that the ultimately bounded convergence of all the variables in the closed-loop system is guaranteed and the tracking error can be made farely small by tuning the design parameters. Finally, two simulation examples illustrate the effectiveness and feasibility of the proposed approach.     

Subspace model identification under load disturbance with unknown transient and periodic dynamics

To overcome the influence from load disturbance with unknown transient and periodic dynamics, as often encountered when performing identification tests in engineering applications, a bias-eliminated subspace model identification method is proposed to realize consistent estimation, which can be used for both open- and closed-loop systems. By decomposing the output response into disturbed and undisturbed components, an oblique projection is subtly introduced to eliminate the disturbance and noise impact so as to obtain unbiased estimation on the deterministic system state matrices, while the disturbance response dynamics could be estimated. In particular, a specific algorithm based on minimizing the output prediction error is given to find out the disturbance period if exists, such that the disturbance effect can be eliminated by the above projection regardless of the disturbance waveform and magnitude. A shift-invariant approach is then given to retrieve the deterministic state matrices. Consistent estimation on the deterministic system matrices is analyzed with a proof. A benmark example from the literature and an industrial injection molding process are used to demonstrate the effectiveness and merit of the proposed method.     

Adaptive output rejection of unmatched input disturbances

To adaptively reject the effect of certain unmatched input disturbances on the output of a linear time-invariant system, a transfer function matching condition is needed. A lemma which presents a novel basic property of linear systems is derived to characterize system conditions for such transfer function matching. An adaptive disturbance rejection control scheme is developed for such systems with uncertain dynamics parameters and disturbance parameters. This adaptive control technique is applicable to control of systems with actuator failures whose failure values, failure time instants, and failure patterns are unknown. A solution is presented to this adaptive actuator failure compensation problem, which ensures closed-loop stability and asymptotic output tracking, in the presence of any up to m−1 uncertain failures of the total m actuators. Desired adaptive system performance is verified by simulation results.