Model reference adaptive control with adjustable gain for piezoelectric actuator

In this paper a Model Reference Adaptive Control system is presented which is based on qualitative (less precise) models. These qualitative models can represent the underlying physical system accurately even with low order models. Further, multi-valued performance specifications can be expressed explicitly by a qualitative model in the form of a reference model. The Qualitative Model Reference Adaptive Control system utilises a fuzzy qualitative simulation method to represent this reference model. These fuzzy dynamical models are of an analytic form and allow system analysis to be based on fuzzy interval analysis. Therefore, stability of the adaptive loop within Qualitative Model Reference Adaptive Control is based on results of robust parametric stability using interval models.

This paper considers the stability problem of the model reference adaptive control systems by means of the properties of hyperstable systems. A theorem concerning the hyperstability of model reference adaptive control systems is presented. This theorem directly gives a structure of the adaption mechanism. The results presented here include all the results obtained by Butchart, Shackcloth, Parks, Winsor, Roy, and Dressler. The hyperstability approach presented in this paper also allows for other solutions to the adaption mechanism and represents a general method for studying this type of adaptive systems. The results are directly applicable to the design of model reference adaptive control systems and they were verified for some particular cases by analogical simulation.

The efficiency of a separately excited DC motor is improved by controlling both armature current and field current simultaneously. The model reference adaptive control system (MRACS) can be useful for this control problem because parameter values and load disturbance (load torque) of controlled objects vary greatly. Two adaptive control systems for efficiency-optimized speed control are proposed on the basis of MRACS theory and the error system method. These are MRACS based on the current ratio method and on the voltage/current ratio method. In these systems, integral action is introduced into MRACS to cope with the step-load disturbance. Although the parameter variation of the voltage/current ratio MRACS method is large, the number of parameters to be adjusted is small as compared with that in the current ratio MRACS method. For each method, fast transient response and good characteristics are obtained for the parameter changes, step-load disturbance, and step desired signal in simulation studies. Efficiency is considerably improved by these methods at a light-load condition.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In order to obtain better static and dynamic performance of the nonlinear system, in this paper the compound control system which the inner loop adopted direct inverse model control and the outer loop adopted model reference adaptive control was designed. Aiming at the difficulty to building inverse model in the inverse model control system in inner loop, the modeling method of inverse model based on the LS_SVM is proposed. As seen from the simulation results that the actual output signal is in good agreement with the desired output. It is show that the model reference adaptive control system based on LS_SVM inverse model has a good ability to control nonlinear object with high tracking precision, good dynamic performance and better control effect

Model Reference Adaptive Control for Manipulators–A Review

An interactor matrix introduced by Wolovich & Falb (1976) has an important role in the design of model reference adaptive control systems (MRACS) for a class of multi-input multi-output (MIMO) plants. In the early stage of the research, the interactor was supposed to be diagonal matrix and thus there were no unknown parameters (Goodwin et al., 1980). But, there exist many plants which require non-diagonal interactors (Chan & Goodwin, 1982). And the design of MIMO MRACS with non-diagonal interactors had been discussed, where all elements of the interactor are assumed to be known (Elliott & Wolovich, 1982; Goodwin & Long, 1980). However, this assumption is not adequate for adaptive control systems since the parameters of the interactor depend on the unknown parameters of the plant, i.e., the parameter values and the relative degree of each element of the plant must be used to determine the interactor. Furthermore, even we know all of these information, the structure of the interactor is not determined uniquely. In order to remove the assumption, the MRACS design has been proposed where the degree of diagonal elements and the upper bound of the highest degree of the lower triangular interactor matrix are assumed to be known (Elliott & Wolovich, 1984; Dugard et al., 1984). Under these assumptions, off-diagonal elements of the lower triangular interactor are estimated, and the method seemed suitable for adaptive controller design. However, it is not reasonable to assume the diagonal degrees in MRACS since the determination of the degrees depends on the relative degree and parameter values of each element of a transfer matrix of a given plant. From this view point, an interactor in generic sense was considered under the assumption that the relative degrees of all elements of the transfer function matrix are known (Kase & Tamura, 1990; Mutoh & Ortega, 1993). The method covers almost of all classes of MIMO plants having the same numbers of inputs and outputs generally. But there still exist some rare plants. By the way, there exists an idea of the certainty equivalence principle for the indirect MRACS design, i.e., estimate the unknown parameters of a plant first, then design the controllers on-line, using those estimated parameters. However, the design was seemed very difficult especially for MIMO plants, since large amount of calculation is needed to solve so-called Diophantine equation, beside the derivation of the interactor. In other words, there did not exist a suitable method to solve the Diophantine equation or to derive the interactor matrix. In this chapter, an indirect approach to MIMO MRACS will be shown. For

Adaptive control for hybrid dynamical systems with user-defined rate of convergence

This paper presents a novel formulation of the Lyapunov-based ultimate boundedness theorem with explicit specification of transient and ultimate bounds, time to the ultimate bound, and the set of admissible initial conditions. The formulation is tailored to the structure of model reference adaptive control systems accounting for a partitioning of the state vector into a tracking error and a parameter estimation error. It allows for a computation of separate bounds for the single state vector partitions in favor of a single bound on the compound state, consisting of both partitions. This is of great practical importance because tracking error and parameter estimation error are of different magnitudes in general. Regarding model reference adaptive control systems, it is the state of the technology so far that the ultimate boundedness theorem is tailored to the structure of the considered system each time, again and again. It is hence manifest to formulate once a generic version of the theorem, tailored to model reference adaptive control systems, but not to reinvent the wheel for each case.

This study proposes integrating Large Language Models (LLMs) into the adaptation mechanism of Model Reference Adaptive Control (MRAC) systems to improve their performance. MRAC is a widely used method for controlling systems that involve uncertainty and change over time; however, fixed-gain structures cause problems like slow convergence, overshoot, and instability in rapidly changing dynamics. To overcome these limitations, three different MRAC architectures are considered: classical MRAC, low-pass filter-based MRAC, and Error-Feedback (EF) MRAC. In the proposed approach, the GPT-4o-mini model optimizes adaptation gains and error compensation coefficients in real time using current data obtained from the control loop. The methods were tested on a DC motor, a mass–spring–damper system, and a wing rock aircraft model. Simulation results show that LLM-enhanced MRAC architectures not only improve control performance but also provide a flexible and scalable framework for adaptive control design. These findings open new research avenues at the intersection of control theory and natural language processing.

A complex problem of the active structural acoustic control is considered in this paper from the controller design point of view in order to develop a suitable technique for the noise attenuation in a specific domain of a studied active structure – acoustic box attached with piezoelectric actuators and sensors. The model reference adaptive controller is developed based on the information and parameters of the active structure, contained in a state space model obtained through a finite element modeling procedure. The parameters of the reference model were selected based on the investigations of the closed-loop behavior of the control system with an optimal LQ controller in order to meet the requirements of the properly prescribed desired behavior of the controlled system. The model reference adaptive control system for the acoustic box was designed in a discrete-time domain. Model based simulation results show the reduction of the air pressure at a selected point of the actively controlled acoustic box in the presence of considered periodic excitations.

This paper presents a method for fuzzy model reference adaptive control system design for a partially known multi-input multi-output (MIMO) linear dynamic plant. Differential or convolutional equations can describe the plant to be controlled, and the fuzzy controller is assumed to be from the MIMO sector-bounded nonstationary nonlinearities class. The task is to obtain robust adaptive stabilization. Some absolute stability theorems and integral evaluations of the state and control vectors are applied in the MIMO fuzzy adaptive controller design procedure for the first time. A method for automatically obtaining a near-optimal nonlinear dynamic reference model is described. A practical step-by-step procedure of the MIMO adaptive fuzzy controller design is proposed, resulting in highly interpretable MIMO fuzzy control rules based on triangular fuzzy sets and strong triangular fuzzy partition. An example of the fuzzy controller design according to the proposed procedure is given.

The control objectives for Model Reference Adaptive Control Systems (MRAC) are specified in terms of a reference model. The control objectives for Stochastic Self-Tuning Regulators (S-STURE) are specified in terms of an ARMA model. These two types of adaptive control systems share a common characteristic (duality). This duality extends the one existing in the linear case with known parameters between modal control (pole-placement) and minimum variance control. Based on the duality properties, a unified presentation of the two techniques is possible; the S-STURE being interpreted as a stochastic MRAC. The underlying concepts and the structure of these adaptive control systems are described. The available theoretical results concerning the analysis of these systems are briefly reviewed. The primary domain of application of these techniques are indicated. An overview of the unsolved problems concludes the paper.

In most of the studies of model reference adaptive control, it is assumed that an upper bound on the degree of the controlled system is known. It makes the scope of application of model reference adaptive control too restrictive, since the reasonable upper bound on the degree cannot be specified a priori in many cases. In the present paper, we propose a design method of model reference adaptive control systems for nonlinear systems with unknown degrees and with unknown relative degrees 1 or 2. Even if the degree of the controlled system varies, and even if the relative degree also varies between 1 and 2, the structure of the proposed adaptive controller does not change. It is shown that the resulting control system is uniformly bounded, and that the tracking error converges to an arbitrarily small residual region. Finally, several simulation studies also show the effectiveness of the proposed method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

SUMMARY We study the convergence properties of a direct model reference adaptive control system by applying techniques from numerical analysis. In particular, a first-order discrete system coupled to a minimal control synthesis algorithm discretized by the one-step one-stage zero-order-hold sampling is studied. This results in a strongly non-linear dynamic system owing to the adaptive mechanism where stability at steady state, i.e. at the operating point, equates to successful control. This paper focuses on the convergence analysis of the overall dynamical system for understanding accuracy, stability and performance at steadystate. The local stability of the steady state solution is considered by linearizing the system in the neighbourhood of an operating point when the input is a step function. This analysis allows us to specify two gain space domains which define the region of local stability. Moreover, both the accuracy and the frequency-domain analyses give insight into the range of adaptive control weightings that results in optimal performance of the minimal control synthesis algorithm and also highlights a possible approach to a priori selection of the time step and adaptive weighting values. The effectiveness of the proposed analysis is further demonstrated by simulations and experiments on a first-order plant. Copyright # 2006 John Wiley & Sons, Ltd.

In this paper, a design of a signal synthesis adaptive controller for a class of linear time-varying uncertain plants using model reference adaptive control techniques is presented. Following a discussion of the general concept, the design of an adaptive controller for unconstrained and constrained control conditions is given. The small ultimate boundness of the state error is considered as the adaptation criterion, which is shown to be satisfied by a Liapunov type stability theorem. To handle the uncertainties that are associated with the plant dynamics and its environment, a min-max concept is employed in the design of the controller. The signal synthesis adaptive approach presented in this paper does not require as many structural assumptions as do most other adaptive approachers, and this is its principal advantage. The state vectors of the plant and model are assumed to be both accessible. Some simulation results are presented which illustrate the effectiveness of the design given here.