A robust adaptive pole‐placement controller without strictly positive real condition

This paper considers the adaptive pole‐placement control problem for system (1) with unmodelled dynamics η_n dominated by a small constant ε multiplied by a quantity independent of ε but tending to infinity as the past input, output, and noise grow. Using bounded external excitation and randomly varying truncation techniques, we give a design method of adaptive pole‐placement controller. It is shown that the closed‐loop system is globally stable, the estimation error for the parameter contained in the modelled part is of order ε, and the closed‐loop system under the adaptive pole‐placement control law is suboptimal in the sense of $$\mathop{\lim\sup}\limits_{{n\to\infty }}{1\over n}\mathop{\sum}\limits_{i=0}^n{\left({A^{*}(z)y_{n}‐L(z)C(z)w_{n}‐B(z)R(z)y_{n}^{*}}\right)^{2}{\leq}O({\varepsilon}^{2})+\gamma^{2}\mathop{\sum}\limits_{j=1}^q{b_{j}^{2}}}$$\nopagenumbers\end while the SPR condition used usually in other papers is replaced by a stability condition. Copyright © 2001 John Wiley & Sons, Ltd.     

An adaptive tracking problem for a family of retarded time-delay plants

Most of the existing switching control techniques are developed specifically for finite-dimensional linear time-invariant (LTI) systems. In many practical applications, however, it is essential to take time delay into consideration in the modelling as the control system can be highly sensitive to delay. In this paper, a multi-model switching control algorithm is proposed for retarded time-delay systems. It is assumed that the plant is represented by a family of known multi-input multi-output, observable, LTI models with multiple delays in the states, and that corresponding to each model in the known family, there exists a high-performance finite-dimensional LTI controller. In addition, it is supposed that a bound on the magnitude of the external inputs and disturbances is available. It is then shown that the proposed switching controller can stabilize the uncertain system, and that under some mild conditions, output tracking can be achieved in the given problem setting. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive control of siso plants with unmodelled dynamics

In this paper we pursue a twofold aim. First we want to simplify the complexity of the classical Monopoli's scheme, the so-called ‘Augmented error signal control scheme’. Then we also wish to cope with the realistic situation in which the presence of unmodelled dynamics has to be taken into account. This latter problem has been faced in the literature by suitably modifying the adaptation mechanism in order to avoid undesired phenomena as well as to obtain an attractive stability region for the state trajectories starting from any point in a predefined initial condition set. In our case the necessity of introducing any sort of modification in the adaptation mechanism is completely avoided, but we still obtain asymptotic stability of the output error signal.     

Robustness of VS-MRAC with respect to unmodelled dynamics and external disturbances

A variable structure model reference adaptive controller (VS-MRAC) using only input and output measurements was recently proposed and shown to be globally asymptotically stable with superior transient behaviour and disturbance rejection properties. In this paper a singular perturbation approach is used in order to establish the robustness of the controller in the presence of unmodelled dynamics (parasitics) and disturbances. We develop a new Lyapunov-based technique to analyse the overall system and show that for sufficiently small parasitics the system remains stable and the output error is small in some sense.     

Lyapunov‐stable discrete‐time model reference adaptive control

Discrete‐time model reference adaptive control (MRAC) is considered with both least squares and projection algorithm parameter identification. For both cases complete Lyapunov proofs are given for stability and convergence. The results extend the approach of Johansson (Int. J. Control 1989; 50 (3):859–869) to include Lyapunov stability for MRAC when the normalized projection algorithm is used for parameter identification. Copyright © 2005 John Wiley & Sons, Ltd.     

Generation of adaptive gait patterns for quadruped robot with CPG network including motor dynamic model

This paper describes the generation of adaptive gait patterns using new Central Pattern Generators (CPGs) including motor dynamic models for a quadruped robot under various environments. The CPGs act as the flexible oscillators of the joints and adjust joint angles to required values. The CPGs are interconnected with each other and sets of their coupling parameters are adjusted by a genetic algorithm so that the quadruped robot can realize stable and adequate gait patterns. Generation of gait patterns results in the formation of the CPG networks suitable for the formation of not only a straight walking pattern but also of rotating gait patterns. Experimental results demonstrate that the proposed CPG networks are effective for the automatic adjustment of the adaptive gait patterns for the tested quadruped robot under various environments. Furthermore, the target tracking control based on image processing is achieved by combining the general gait patterns. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 155(1): 35–43, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20225     

Minimum switching control for adaptive tracking

The switching adaptive control method has been used for quite a few years to solve the adaptive stabilization and model reference adaptive control problems. However, a serious problem with the switching control method is that the number of ‘candidate’ controllers can potentially be very large, especially for multi‐input–multi‐output systems. In this paper, we consider a class of minimum‐phase multi‐input–multi‐output plants with some mild compactness assumptions. Given any polynomial reference input, we provide a switching control law which guarantees exponentially stability of the closed‐loop system with exponential tracking performance. The main contribution of the paper is that we give the minimum number of candidate controllers required for switching. In particular, the number is equal to 2 for single‐input–single‐output plants (one for each sign of the high‐frequency gain), and is equal to 2^m for m‐input–m‐output plants. That is, the number is independent of the degree and the relative degree of the plant. Copyright © 2006 John Wiley & Sons, Ltd.     

Dynamical adaptive synchronization

The notions of dynamical synchronization and adaptive dynamical synchronization problems are introduced. The algorithm solving adaptive synchronization problem for a subclass of Lurie systems with exciting input is proposed. The performance and potentialities of proposed solutions are demonstrated by two examples related to formation control and self‐organization of swarm systems. Copyright © 2006 John Wiley & Sons, Ltd.     

A novel robust current control approach using adaptive line enhancer for three‐phase current‐source active power filter

An effective system control method is presented for applying a three‐phase current‐source PWM converter with a deadbeat controller to active power filters (APFs). In the shunt‐type configuration, the APF is controlled such that the current drawn by the APF from the utility is equal to the current harmonics and reactive current required for the load. To attain the time‐optimal response of the APF supply current, a two‐dimensional deadbeat control scheme is applied to APF current control. Furthermore, in order to cancel both the delay in the two‐dimensional deadbeat control scheme and the delay in DSP control strategy, an Adaptive Line Enhancer (ALE) is introduced in order to predict the desired value three sampling periods ahead. ALE has another function of bringing robustness to the deadbeat control system. Due to the ALE, settling time is made short in a transient state. On the other hand, total harmonic distortion (THD) of source currents can be minimized compared to the case where ideal identification of the controlled system can be made. The experimental results obtained from the DSP‐based APF are also reported. The compensating ability of this APF is very high in accuracy and responsiveness although the modulation frequency is rather low. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(1): 50–61, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20014     

Bioprocess applications of model-based estimation techniques

The last decade has seen the development of a number of approaches for estimating those variables which are difficult to measure on-line in industrial process situations. Whilst a range of techniques is available, a common element is the use of process knowledge in the form of a system model. In the case of bioprocess systems, although a large range of models has been presented in the literature, their use in estimation schemes on an industrial scale has been limited. A number of reasons can be identified for their low level of utilisation. Of particular significance is the uncertainty which exists in quantifying system performance and the process-model mismatch which inevitably results. The level of ‘pre-defined model’ uncertainty, together with the knowledge gained during the course of the fermentation, serves to dictate estimator structure. The paper considers a range of estimation strategies and contrasts, through industrial applications, their performance characteristics and utility.