Traditional Model Reference Adaptive Control Research Articles

Singularity-free adaptive control of discrete-time linear systems without prior knowledge of the high-frequency gain

This paper proposes a new output feedback model reference adaptive control (MRAC) method for discrete-time linear time-invariant systems with arbitrary relative degrees. The proposed method does not require any prior knowledge of the high-frequency gain represented by kp, thereby completely eliminating the common design condition in the traditional discrete-time MRAC framework: the sign of kp is known, as well as an upper bound on |kp|. Specifically, an output feedback adaptive control law is developed, which incorporates a time-varying gain function to effectively address the singularity issue. The developed adaptive control law leads to the derivation of a linear estimation error equation for the closed-loop system. Consequently, a gradient algorithm based parameter update law is directly formulated by utilizing the estimation error and some other available signals without requiring any prior knowledge of kp. In comparison to the traditional MRAC and Nussbaum function-based methods, it does not necessitate any additional design conditions or involve any transient performance issues, while still ensuring closed-loop stability and asymptotic output tracking for any given bounded reference signal. The simulation study showcases the design procedure and evaluates the efficacy of the proposed control method.

Design and Implementation of MRAC & MRAC-PID Feedback for Turntable

The paper explains a control method for turntable by feedback a PID controller with the traditional model reference adaptive controller (MRAC) based on the MIT rule. The traditional MRAC is designed for a first-order system with the adjustment of a two-variable parameter. However, the majority of plants, including turntable, are second-order systems. Traditional MRAC tracking performance for second-order systems is unsatisfactory. The control law for the second order system along with extension from the first to the second order of MRAC is derived. The modified MRAC i.e., MRAC-PID controller is designed for the application of turntable. It enhanced the system’s dynamic performance. To assess the performance of the proposed controller, MATLAB/Simulink software was used. The article incorporates a detailed analysis and comparison of PID, MRAC as well as MRAC-PID controllers based on the MIT rule for the turntable system. The robustness of the proposed controller is validated by introducing uncertainties in two aspects i.e., mistuning of the controller gains and turntable system dynamics change. The probabilistic design assessment for the mistuning is carried out through levels of uncertainty in controller gain. It is observed that PID and MRAC would track the reference model but modified MRAC has better performance in terms of tracking accuracy, adaptability, and rapidity. Several performance indexes such as integral absolute error (IAE), integral time absolute error (ITAE), and integral square error (ISE) were employed to justify the proposed controller superiority.

Yaw-Rate-Tracking-Based Automated Vehicle Path Following: An MRAC Methodology With a Closed-Loop Reference Model

Abstract Concerning automated vehicles, various path-following controllers have been designed by the model reference adaptive control (MRAC) approach. Through appropriate Lyapunov redesigns, asymptotical stability and signal boundedness are ensured for the path-tracking control loops. However, transient behaviors of the closed-loop responses are seldom considered in the context of MRAC synthesis. To bridge the foregoing gap, a closed-loop-reference-model-based MRAC, which yields an improved transient performance compared with a traditional MRAC, is exploited to synthesize a vehicular path-following control law. Besides, an infinitely differentiable projection operator is complemented to the control parameters’ adaptation schemes for estimation speed-up and robustness enhancement. Hardware-in-the-loop experiments are used to evaluate the proposed method and to demonstrate its improvement over some conventional MRAC designs.

Performance Evaluation of Stewart-Gough Flight Simulator Based on L1 Adaptive Control

In the design of the six degrees of freedom (6-DOF) flight simulation system, the unmodeled dynamic, transient performance and steady-state performance of the system are generally concerned. Considering that the model of flight simulation system is highly nonlinear and requires high response speed and high stability, this paper applies L1 adaptive controller to the control of flight simulation platform. The controller has a low-pass filter in feedback loop to avoid high frequencies in the control signals, and the required transient performance can be enhanced by increasing the adaptive gain, which can improve the transient, stability, and smoothness of the flight simulator platform. The performance of the L1 adaptive controller is obtained by comparison with the traditional model reference adaptive controller (MRAC). In addition to maintaining the good transient response of MRAC, the L1 adaptive controller improves the stability of the system. The output amplitude of the actuator is reduced by 39.95%, which effectively reduces the performance requirements of the actuator. Some additional experimental evaluations are carried out to show the performance of the controller.

A Real-Time Parameter Estimation Method by Using Disturbance Observer-Based Control

Abstract The robust tracking control and accurate real-time uncertainty estimation performances by using disturbance observer-based model reference adaptive control (DOBMRAC) are proposed in this article. An example of coefficient of friction estimation system is studied to demonstrate the proposed method. First, the uncertainty adaptation law in the traditional model reference adaptive control (MRAC) was usually assumed that the uncertainty is a constant or slowly variable. The adaptation law of MRAC could not deal with the time-varying uncertainties. Therefore, a time-varying uncertainty adaptation law by disturbance observer (DOB) is designed to accurately estimate the time-varying uncertainty. Then, a Lyapunov candidate function is implemented to integrate DOB and MRAC as DOBMRAC to perform robust tracking control and accurate real-time uncertainty estimation, simultaneously. The coefficients of friction estimation system are performed to verify robust tracking control and accurate real-time estimation performance by using DOBMRAC. From the simulation results, the proposed DOBMRAC and MRAC are compared, and the proposed method shows well robust tracking control performance and real-time estimation ability. The proposed DOBMRAC has the advantages of rapid convergence responses, robust tracking control, and accurate real-time uncertainty estimation, simultaneously.

MRAC for unknown discrete-time nonlinear systems based on supervised neural dynamic programming

This paper investigates the model reference adaptive control (MRAC) problem for unknown nonlinear discrete-time systems, which is how to guarantee adaptation to the variable reference input and robustness to perturbation. A supervised neural dynamic programming (SNDP) approach is developed to solve this MRAC problem, which includes a learning mode and a control mode. In the learning mode, a data-based adaptive critic learning algorithm is proposed, which guarantees that the controlled objective adaptively tracks the reference model on behavior. Such an algorithm also ensures flexible switching from the learning mode to the control mode under which the robustness of the closed-loop control systems is further improved. By employing a newly defined mode scheduler that regulates the learning mode and the control mode, the adaptation and the robustness of the systems are both achieved by the developed SNDP approach. Its uniformly ultimately bounded property is proved by using Lyapunov method. Simulation results verify that the developed SNDP approach ensures the adaptation to the variable reference input, and has superiority over some traditional MRAC methods in improving the robustness.

Multi-model robust adaptive control of tall buildings

Model reference adaptive control (MRAC) strategies are gaining an increasing interest by researchers working in the area of structural control mainly for their capacity of compensating for large uncertainties, faults and time varying disturbances in linear and nonlinear plants. In this paper a modification of the standard MRAC algorithm is proposed which adopts multiple reference models (M-MRAC). The motivation of the proposed scheme is that flexible buildings subjected to multiple hazards, like wind and earthquake, require different damping levels to avoid the occurrence of different limit states. A M-MRAC scheme that uses two reference models is adopted. The first reference model, with small structural damping, is active in the presence of low level excitation like moderate wind loading, while the second reference model, with a higher damping, is activated when a suitable response-dependent signal exceeds a defined threshold in the presence of severe seismic loading. Analyses on a tall building subjected to wind and earthquake show the capacity of the M-MRAC in tracking the reference system and in mitigating the structural response. Comparison with traditional MRAC highlights that the main advantage of M-MRAC is the reduction of the control force, at the expense of a slight reduction of control effectiveness.

Adaptive Flight-Control Design Using Neural-Network-Aided Optimal Nonlinear Dynamic Inversion

A neural-network-aided nonlinear dynamic inversion-based hybrid technique of model reference adaptive control flight-control system design is presented in this paper. Here, the gains of the nonlinear dynamic inversion-based flight-control system are dynamically selected in such a manner that the resulting controller mimics a single network, adaptive control, optimal nonlinear controller for state regulation. Traditional model reference adaptive control methods use a linearized reference model, and the presented control design method employs a nonlinear reference model to compute the nonlinear dynamic inversion gains. This innovation of designing the gain elements after synthesizing the single network adaptive controller maintains the advantages that an optimal controller offers, yet it retains a simple closed-form control expression in state feedback form, which can easily be modified for tracking problems without demanding any a priori knowledge of the reference signals. The strength of the technique is demonstrated by considering the longitudinal motion of a nonlinear aircraft system. An extended single network adaptive control/nonlinear dynamic inversion adaptive control design architecture is also presented, which adapts online to three failure conditions, namely, a thrust failure, an elevator failure, and an inaccuracy in the estimation of . Simulation results demonstrate that the presented adaptive flight controller generates a near-optimal response when compared to a traditional nonlinear dynamic inversion controller.

Experimental Validation of Bayesian Nonparametric Adaptive Control Using Gaussian Processes

Many current model reference adaptive control methods employ parametric adaptive elements in which the number of parameters are fixed a priori and the hyperparameters, such as the bandwidth, are predefined, often through expert judgment. As an alternative to these methods, a nonparametric model using Gaussian processes was recently proposed. Using Gaussian processes, it is possible to maintain constant coverage over the operating domain by adaptively selecting new kernel locations as well as adapt hyperparameters in an online setting to improve model prediction. In this work, the first extensive experimental flight results are presented using Gaussian process/model reference adaptive control. Experimental results show that Gaussian process/model reference adaptive control outperforms traditional model reference adaptive control methods that use radial basis function neural networks in terms of tracking error as well as transient behavior on trajectory following using a quadrotor. Results show an improvement of a factor of two to three over preexisting state-of-the-art methods. Additionally, many model reference adaptive control frameworks treat the adaptive element as being known exactly, and they do not incorporate certainty of the prior model into the control policy. In this paper, the notion of a Bayesian scaling factor is introduced that scales the adaptive element in order to incorporate the uncertainty of the prior model and current model confidence. The stability and convergence of using the Bayesian scaling factor in a closed loop is proven.

Identifier-tracking model reference adaptive control

Model reference adaptive control is a major design method for controlling plants with uncertain parameters. The primary objective of this paper is to develop a new design approach for a differentiator-free model reference adaptive control of a single-input single-output linear time-invariant plant. The proposed method, called the “Identifier-tracking model reference adaptive control”, uses a stacked identifier structure that is new to the field of adaptive control. The goal is to make the output of the plant asymptotically track the output of the first identifier, and then driving the output of the first identifier to track that of the second identifier, and so forth, up to the qth identifier where q is the relative degree of the plant. Lastly, the output of the qth identifier is forced to converge to that of the reference model. Simulation results show the superiority of the proposed method over the traditional model reference adaptive control with augmented error in terms of the transient response. Since the resulting control systems are non-linear and time-varying, the stability analysis of the overall system plays a central role in developing the theory.

A robust MRAC using variable structure design for multivariable plants

It is well known that undesirable transient responses and tracking performances have been frequently observed in traditional model reference adaptive control (MRAC) problems, especially for multivariable plants with unmodeled dynamics and output disturbances. In this paper, a new robust model reference adaptive control using variable structure design (VSD) is proposed to investigate the solution. Based on a definition of generalized relative degree (GRD) for multivariable plants, the general case for plants with arbitrary GRD is completely solved. It is shown that, even when the uncertainties are presnet, global stability and robustness of the closed-loop control system are achieved. Furthermore, without any persistence of excitation, the tracking errors will, at least asymptotically, converge to zero for GRD-one plants and to a small residual set for plants with any higher GRD. With a suitable choice of initial control parameters, the tracking errors can even be driven to zero in finite time for GRD-one plants and to a small residual set exponentially for plants with any higher GRD.

A new robust model reference control with improved performance for a class of multivariable unknown plants

AbstractMotivated by recent works on parametrization of multivariable plants for model reference adaptive control (MRAC), a new robust model reference control (MRC) scheme for a class of multivariable unknown plants is presented. The salient feature of this control scheme is the improved performance of the output‐tracking property, which is hardly attainable by the traditional MRAC schemes. The controller here is devised using the concept of variable structure design which prevails in the robust control context. It is shown by a Lyapunov approach that without any persistent excitation the global stability of the overall system is achieved and the tracking errors will converge to a residual set. The size of that set can be directly related to the size of unmodelled dynamics and output disturbances explicitly as long as a set of control parameters is chosen properly (large).