Recently the use of a linear periodic controller has been proposed to solve the model reference adaptive control problem. The resulting controller can handle rapid changes in plant parameters, and it can provide nice ...
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Recently the use of a linear periodic controller has been proposed to solve the model reference adaptive control problem. The resulting controller can handle rapid changes in plant parameters, and it can provide nice transient behavior with arbitrarily good steady-state tracking using a control signal which remains modest in size. However, it also has some undesireable features: i) the proposed sampled-data controller achieves good performance by using a small sampling period, which results in large gains and a correspondingly poor noise tolerance, ii) a rapidly varying control signal is used, which may require a fast actuator, and iii) the closer to optimality that we wish to get, the more complex the controller. In this paper, we completely redesign the control law to significantly alleviate these problems;the new design provides better noise performance, especially when the sign of the high frequency gain is known, uses a smoother and smaller control signal, has a fixed complexity, independent of the desired level of performance, and is more intuitively appealing, in that probing, estimation, and control are now carried out in parallel rather than in series.
A new referencemodeladaptivecontrol scheme is proposed for plants with input delays where the control is formed only from the information about the input and output of the plant. The design procedure is based on th...
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A new referencemodeladaptivecontrol scheme is proposed for plants with input delays where the control is formed only from the information about the input and output of the plant. The design procedure is based on the concept of referencemodel prediction by using the augmented error. The controller contains only filters of minimal complexity and blocks with lumped delay, which is in contrast to the known configurations with distributed delays. A numerical example is presented.
In this study, the problem of model reference adaptive control (MRAC) for switched linear parameter-varying (LPV) systems with parametric uncertainties is investigated. First, a switched LPV controller with the adapti...
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In this study, the problem of model reference adaptive control (MRAC) for switched linear parameter-varying (LPV) systems with parametric uncertainties is investigated. First, a switched LPV controller with the adaptive laws is designed. Then, the proposed LPV controller with the adaptive laws guarantees that all the closed-loop system signals remain bounded under a class of switching signals with average dwell time, and the state tracking error converges to a small ball centred at the origin whose radius can be made arbitrarily small by appropriately choosing the design parameters. Finally, a practical example about MRAC for a turbofan-engine is given to demonstrate the validity of the main results.
In this paper we define a new model reference adaptive control problem which allows a large amount of plant uncertainty. Instead of the usual goal of asymptotic error regulation, here we require that the limit superio...
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In this paper we define a new model reference adaptive control problem which allows a large amount of plant uncertainty. Instead of the usual goal of asymptotic error regulation, here we require that the limit superior of the magnitude of the error be less than a predefined constant times the limit superior of the magnitude of the external reference input. This provides a natural way to incorporate uncertainty which includes nonminimum phase systems.
A model reference adaptive control law is defined for nonlinear distributed parameter systems. The referencemodel is assumed to be governed by a strongly coercive linear operator defined with respect to a Gelfand tri...
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A model reference adaptive control law is defined for nonlinear distributed parameter systems. The referencemodel is assumed to be governed by a strongly coercive linear operator defined with respect to a Gelfand triple of reflexive Banach and Hilbert spaces. The resulting nonlinear closed-loop system is shown to be well posed. The tracking error is shown to converge to zero, and regularity results for the control input and the output are established. With an additional richness, or persistence of excitation assumption, the parameter error is shown to converge to zero as well. A finite-dimensional approximation theory is developed. Examples involving both first- and second-order, parabolic and hyperbolic, and linear and nonlinear systems are discussed, and numerical simulation results are presented.
This paper presents an indirect model reference adaptive control for minimum phase linear systems of arbitrary order with unknown high frequency gain sign. It is proved that the (modified) estimate of the high frequen...
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This paper presents an indirect model reference adaptive control for minimum phase linear systems of arbitrary order with unknown high frequency gain sign. It is proved that the (modified) estimate of the high frequency pin has a uniform positive lower bound. The problem has been solved by using the least squares covariance matrix properties to define an appropriate modification of the parameters estimates.
Introduction: Magnetically controlled shape memory alloy (MSMA) actuators take advantages of their large deformation and high controllability. However, the intricate hysteresis nonlinearity often results in low positi...
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Introduction: Magnetically controlled shape memory alloy (MSMA) actuators take advantages of their large deformation and high controllability. However, the intricate hysteresis nonlinearity often results in low positioning accuracy and slow actuator response. Methods: In this paper, a modified Krasnosel'skii-Pokrovskii model was adopted to describe the complicated hysteresis phenomenon in the MSMA actuators. adaptive recursive algorithm was employed to identify the density parameters of the adopted model. Subsequently, to further eliminate the hysteresis nonlinearity and improve the positioning accuracy, the model reference adaptive control method was proposed to optimize the model and inverse model compensation. Results: The simulation experiments show that the model reference adaptive control adopted in the paper significantly improves the control precision of the actuators, with a maximum tracking error of 0.0072 mm. Conclusions: The results prove that the model reference adaptive control method is efficient to eliminate hysteresis nonlinearity and achieves a higher positioning accuracy of the MSMA actuators.
Based on an extended modelreferencecontrol (MRC) theory developed here, a model reference adaptive control (MRAC) algorithm is proposed for not necessarily minimum phase digital or sampled plants. It is shown that t...
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Based on an extended modelreferencecontrol (MRC) theory developed here, a model reference adaptive control (MRAC) algorithm is proposed for not necessarily minimum phase digital or sampled plants. It is shown that the algorithm is capable of globally stabilizing the plants as well as achieving asymptotical model matching in a suitable sense without making a richness assumption on the reference signal. The only assumptions made on the plant are minimality and known order, and hence the delay in the plant is unknown, and moreever may be larger than the delay in the referencemodel.
The adaptivecontrol of continuous-time linear dynamic systems preceded by an unknown dead-zone in state space form is discussed. A lemma to simplify the error equation between the plant and the matching reference mod...
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The adaptivecontrol of continuous-time linear dynamic systems preceded by an unknown dead-zone in state space form is discussed. A lemma to simplify the error equation between the plant and the matching referencemodel is introduced which allows the development of a robust adaptivecontrol scheme by involving the dead-zone inverse terms. This adaptivecontrol law, ensures global stability of the entire system and achieves the desired tracking precision even when the slopes of the dead-zone are unequal. Simulations performed on a typical linear system illustrate and clarify the validity of this approach.
In this paper, model reference adaptive control of a cantilevered flexible beam with Kelvin-Voigt damping and unknown spatially varying coefficients is investigated. Any mechanically flexible robots/structures are inh...
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In this paper, model reference adaptive control of a cantilevered flexible beam with Kelvin-Voigt damping and unknown spatially varying coefficients is investigated. Any mechanically flexible robots/structures are inherently distributed parameter systems whose dynamics are described by partial, rather than ordinary, differential equations. Adaptation laws are derived by the Lyapunov redesign method on an infinite dimensional Hilbert space. To show the well-posedness of a coupled nonlinear system, combined state error and parameter estimation error equations are constructed as an initial value problem of an infinite dimensional evolution equation in weak form. It is then shown through the Lyapunov redesign approach that the state error actually converges asymptotically to zero. With an additional persistence of excitation assumption, the parameter estimation errors are shown to converge to zero as well.
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