MRAC-Based Adaptive Feedback Linearization Control Method for Continuous-Time Nonlinear Systems with Uncertain Parameters

The precise position control for electro-hydraulic servo system (EHSS) is a key technical problem for modern industry control. This paper presents a model reference adaptive control (MRAC) strategy combining fractional order calculus theory and neural network to solve the high nonlinearity and parameter uncertainties in the EHSS. The reference model in the MRAC strategy is a fractional second-order model and the controller with adaptive law is designed by a Wiener recurrent neural network (WRNN). Simulations indicate the validity and superiority of the proposed fractional MRAC strategy.

The problem of feedback linearization (FL) of continuous and discrete nonlinear MIMO systems is considered. The idea of FL method consists in converting the original nonlinear system into a linear one by means of feedback. Then, the methods of control theory for linear systems are used for system design. A widespread approach to FL design is based on the method of normal form, that uses a nonsingular transformation of system state variables z = T(x). In order to obtain a normal form of the nonlinear system in the neighbor of a some point, it is necessary to determine a special function - the system virtual output, for which a relative degree (in the case of single input) or a vector relative degree (in the case of multiple input) is determined. Applicability of the normal form method for FL is provided by the conditions of controllability and involutivity for the considered nonlinear system, which are not always true. Moreover, when developing a linearizing control law, the main difficulty lies in the transition from transformed variables z to state variables x of the original system. In this paper, we propose another approach, based on representing the original nonlinear system into a state-dependent coefficient form and applying the canonical similarity transformation z = T(x)x, that allow getting the system to canonical form, that considerably simplifies the FL problem. Such similarity transformation allow accomplishing linearization of system without determining of the virtual system output. Another advantage of the proposed method is that the technique of the transition from the transformed variables z to the state variables x of the original system is simpler. The results are illustrated by examples for continuous and discrete nonlinear systems.

One of the most common methods of synthesis of the nonlinear control systems is the method of a feedback linearization (FL). The idea of this method consists in conversion of the original nonlinear system into a linear one by means of a state feedback and coordinate transformation. Then, the methods of control theory for the linear systems are used for the system design. If the original nonlinear system cannot be linearized exactly by the state feedback, the method of the approximate feedback linearization (AFL) is used. The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system (not of the entire system). In this paper, the author proposes a method of an approximate feedback linearization control of the nonlinear singularly perturbed (SP) systems. The proposed method is based on a decomposition of the original SP system and construction of AFL control in the form of composite FL controls for the slow and fast subsystems. In general, a nonlinear SP system cannot be easily separated into slow and fast subsystems, because the conditions of Tikhonov theorem are not complied. In order to overcome this, the author proposes to perform the feedback linearization method at first for the system's part, which describes the fast state variables. Thus, a fast control is chosen, so that the conditions of Tikhonov theorem would be met. Then, using a standard singular perturbation technique, we obtain a slow subsystem. Further the problem of FL control for a slow subsystem is solved. The resulting AFL control is obtained in the form of a composite control. Application of the proposed approach is illustrated with two examples.

Partial-state feedback multivariable MRAC and reduced-order designs

On the hybrid MRAC-PID control: A comparison study

This paper addresses the problem of sensor uncertainty compensation for model reference adaptive control (MRAC) of multivariable systems. Two output feedback based MRAC schemes are developed for MIMO plants with known and unknown plant dynamics. The sensor uncertainty is modeled as parametrizable uncertain functions and a compensator is constructed to adaptively cancel the effects of sensor uncertainties, to generate an adaptive estimate of the plant output. The estimated system output is used for the feedback control law. For systems with unknown plant dynamics, a new feedback controller structure is developed, so that uncertainties of both plant and sensor measurements can be effectively compensated by adaptation. Simulation results are presented to show that the proposed MRAC scheme for unknown plant dynamics can significantly improve the tracking performance despite the sensor uncertainties.

This paper investigates the use of neural networks (NNs) in conventional model reference adaptive control (MRAC) to control a nonlinear magnetic levitation system. In the conventional MRAC scheme, the controller is designed to realize plant output convergence to a reference model output based on a plant which is linear. This scheme is effectively for controlling linear plants with unknown parameters. However, using MRAC to control the nonlinear magnetic levitation system in real time is a difficult control problem. In this paper, we incorporate a NN in MRAC to overcome the problem. The control input is given by the sum of the output of the adaptive controller and the output of the NN. The NN is used to compensate the nonlinearity of the plant that is not taken into consideration in the conventional MRAC. From experiment results, it has been shown that the plant output can converge to the reference model output after using NN in MRAC.

Distributed model reference adaptive containment control of heterogeneous multi-agent systems with unknown uncertainties and directed topologies

This paper proposed three control schemes using model reference adaptive control (MRAC) and RBF neural network(RBFNN). Through comparision, it proposed a MRAC scheme with RBFNN compensator for speed control of high precision servo systems. The MRAC scheme is used to give better solutions with online adaptation and guarantee the stablity of the system. In the feedback channel, the parameter <i>K_p</i> makes it easier to design the system poles. By using a PI controller before <i>K_p</i>, the dynamic performance of the system is improved. As a speed compensate controller, the RBFNN is designed parallel with the model reference control. The RBFNN controller is able to online learn the unknown model dynamics, parameter variation and disturbance of the system. Thus, it is feasible to preserve favorable model-following characteristics under various conditions. The effectiveness of the proposed control scheme is demonstrated by simulation. It is found that the proposed scheme can reduce the plant's sensitivity to parameter variation and disturbance. High precision performance is obtained when given constant and sine wave disturbance at the same time.

The idea of improving the transient behaviour in model reference adaptive control by using the estimation error to modify the underlying controller structure has attracted attention in the literature. In this note, we show that the modifications proposed so far can in fact all be derived as linear feedbacks from the tracking error. Consequently, the improved performance obtained with these schemes is solely due to a nonadaptive high gain feedback. >

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It is shown how to change the primary control structure of a model reference adaptive control (MRAC) scheme from the usual minimum settling time-type algorithm to a ripple-free response control (RFRC) scheme. RFRC does not try to compensate process zeros, avoiding ringing effects (like intersampling ripple). The main issue in the derivation of the RFRC-MRAC scheme is the establishment of a stable adaptive law which guarantees a ripple-free behavior if the error signal tends to zero. In the original MRAC scheme, the error signal consisted of the desired error plus a transient term which tends to zero when adaptation proceeds. In this MRAC scheme, the error consists of a filtered form of the desired RFRC error. Hence, if the error used in the adaption tends to zero, the RFRC behavior is achieved. The scheme avoids ringing effects and can control nonminimum-phase processes. The cost of these advantages is a slowing down of the process response by a number of samples equal to the order of the numerator polynomial. Simulations confirm the RFRC-like characteristics, and practical results on a water level system show the usability of the method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Develops an indirect adaptive controller using feedback linearization (IACFL). IACFL addresses the problem of designing a robust controller for a nonlinear system with observable nonlinear functions and state variables. IACFL consists of strictly positive real (STR)-Lyapunov synthesis algorithm, Input state feedback linearization (ISFL) algorithm, and model reference adaptive controller (MRAC). IACFL provides that, when estimated parameters of the nonlinear system are given in ISFL repeatedly, the output of nonlinear system can follow that of a stable reference linear model.

This paper presents a method of designing optimal dynamic compensator for a class of typical chemical reaction process-CSTR systems. Firstly, the model of nonlinear CSTR system is provided, Secondly, by using feedback linearization method, the nonlinear system is converted into a linear system, then according to the LQR theory, the methods of designing dynamic compensator is designed, and we analyze the asymptotic stability of the optimal regulator which has been compensated. At last, the simulation results show the effectiveness of the method.

This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed (SP) system using approximate feedback linearization (AFL) method. The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system. According to AFL approach, we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately. The resulting AFL control is constructed in the form of asymptotic composition (composite control). Standard procedure for the composite control design consists of the following steps: 1) system decomposition, 2) solution of control problem for fast subsystem, 3) solution of control problem for slow subsystem, 4) construction of the resulting control in the form of the composition of slow and fast controls. The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system. To overcome this, we propose to change the sequence of the design procedure: 1) solving the control problem for fast state variables part, 2) system decomposition, 3) solving the control problem for slow state variables part, 4) construction of the resulting composite control. By this way, fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable. The application of the proposed approach is illustrated through several examples.