Model Reference Adaptive Controllers and Stochastic Self-Tuning Regulators—A Unified Approach

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

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>

A New Approach to the Design of an Adaptive Control System

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.

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.

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.

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>

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 objective of this research is to provide a method for design of control systems when the plant involved is highly variable in both structure and parameter values. This typifies many manufacturing processes, which in general are highly sensitive to intrinsic properties of the infeed material, have poorly understood or controlled boundary conditions, and often have highly non-linear characteristics. In addition, the disturbances most frequent in a manufacturing process are best characterized as parameter changes rather than state variable changes. The choice of a parameter adaptive control paradigm is obvious since it has the property of optimizing system response characteristics in the face of wide plant parameter variations. Model Reference Adaptive Systems (MRAS) enjoy an ease of performance specification, and again seem applicable; however, there is a restriction within current theory that the plant be characterized in its structure well enough to have a reference model of identical order. This restriction implies a static plant structure and more a priori information than is often present. During this contract the basic design characteristics of certain MRAS have been studied and problems with reduced order models identified, such as noise and input magnitude sensitivity and instability caused by high frequency learning signals. This has lead to certain solutions and resulting guidelines for design. This is then followed by design studies for a position servomechanism (which serves as the foundation of many automated manufacturing processes). This study expanded the domain from MRAS to self-tuning controllers (STC) and found that both can deal with reduced order models if the initial parameter values are not too distant from the actual values. However, the STC appears to be the more robust. 12 refs., 56 figs.

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.

Model Reference Adaptive Control for Manipulators–A Review

This study proposes a new frequency selective learning adaptive control approach for model reference adaptive control systems to improve their adaptation performance without depending on high learning rates. It is developed by inspiration from the philosophies of the Q ‐modification and concurrent learning approaches and retains the key advantages of both. The philosophy of this proposed approach is that the known part of the plant dynamics passes through multiple filters. By constraint of the governing dynamic equations, this result equals an expression containing the unknown parameters in a filtered version, which is used for augmentation of the update law. The use of multiple filters aims at increasing the rank of the update law based on online instantaneous information and for a sufficient number of filters at different bandwidths, exponential stability can be achieved in the presence of the structured matched uncertainty. Moreover, it can cope with a sudden change of the system configuration. As a result, it leads to an efficient adaptive control approach. Furthermore, a challenging roll control problem of an aircraft demonstrates the usefulness of this proposed approach.

An adaptive control system with good following characteristics is designed for the electro-hydraulic servo system which are strongly coupled and seriously nonlinear. The model of position servo system on air rudder is discussed with the uncertain system equivalent to the one with parametric variable double input and single output to establish a Popov-MRAC (Model Reference Adaptive Control) system. The simulation results show that the Popov MRAC system has good following characteristics, precision and robustness.

SummaryIn this study, we present a reinforcement learning (RL)‐based flight control system design method to improve the transient response performance of a closed‐loop reference model (CRM) adaptive control system. The methodology, known as RL‐CRM, relies on the generation of a dynamic adaption strategy by implementing RL on the variable factor in the feedback path gain matrix of the reference model. An actor‐critic RL agent is designed using the performance‐driven reward functions and tracking error observations from the environment. In the training phase, a deep deterministic policy gradient algorithm is utilized to learn the time‐varying adaptation strategy of the design parameter in the reference model feedback gain matrix. The proposed control structure provides the possibility to learn numerous adaptation strategies across a wide range of flight and vehicle conditions instead of being driven by high‐fidelity simulators or flight testing and real flight operations. The performance of the proposed system was evaluated on an identified and verified mathematical model of an agile quadrotor platform. Monte‐Carlo simulations and worst case analysis were also performed over a benchmark helicopter example model. In comparison to the classical model reference adaptive control and CRM‐adaptive control system designs, the proposed RL‐CRM adaptive flight control system design improves the transient response performance on all associated metrics and provides the capability to operate over a wide range of parametric uncertainties.

In a model reference adaptive control system, the plant is assumed to be unknown in advance, then it is a difficult task to choose an adequate reference model such that the perfect model matching condition (i.e. the unstable plant zeros must be the zeros of the reference model) is assured in every adaptive step. In thepaper, based on the theory of the minimum H∞-norm, an adaptive controller obtained by minimising the H∞-norm of the error transfer function between the closed-loop system and the reference model is developed, andit always guarantees the stability of a closed-loop system, regardless of whether or not the controlled plant is unstable or nonminimum phase.