Adaptive Variable Structure Control Research Articles

Fuzzy adaptive tracking control of uncertain chaotic system with input perturbance and nonlinearity

In this paper, we investigate the signal tracking problem of the uncertain time-varying delay chaotic system with control input nonlinearity and the fuzzy adaptive variable structure control method is proposed. The fuzzy logic system approximates the nonlinearity of the system. The unknown time-varying delay uncertainties are compensated using an appropriate Lyapunov-Krasovskii functional. The proposed controller can make the tracking errors converge to an adjustable region and all signals of the closed system is bounded. The designed control method can have a certain robustness against the disturbance of the system. Finally, taking the simulations on a multi-scroll chaotic system for example, the effectiveness of the proposed method is illustrated.

Chaos control and generalized projective synchronization of heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive variable structure control

This paper proposes the chaos control and the generalized projective synchronization methods for heavy symmetric gyroscope systems via Gaussian radial basis adaptive variable structure control. Because of the nonlinear terms of the gyroscope system, the system exhibits chaotic motions. Occasionally, the extreme sensitivity to initial states in a system operating in chaotic mode can be very destructive to the system because of unpredictable behavior. In order to improve the performance of a dynamic system or avoid the chaotic phenomena, it is necessary to control a chaotic system with a periodic motion beneficial for working with a particular condition. As chaotic signals are usually broadband and noise like, synchronized chaotic systems can be used as cipher generators for secure communication. This paper presents chaos synchronization of two identical chaotic motions of symmetric gyroscopes. In this paper, the switching surfaces are adopted to ensure the stability of the error dynamics in variable structure control. Using the neural variable structure control technique, control laws are established which guarantees the chaos control and the generalized projective synchronization of unknown gyroscope systems. In the neural variable structure control, Gaussian radial basis functions are utilized to on-line estimate the system dynamic functions. Also, the adaptation laws of the on-line estimator are derived in the sense of Lyapunov function. Thus, the unknown gyro systems can be guaranteed to be asymptotically stable. Also, the proposed method can achieve the control objectives. Numerical simulations are presented to verify the proposed control and synchronization methods. Finally, the effectiveness of the proposed methods is discussed.

Fuzzy adaptive observer-based projective synchronization for nonlinear systems with input nonlinearity

In this paper, a projective synchronization problem of master-slave chaotic systems is investigated. More specifically, a fuzzy adaptive slave chaotic system subject to both sector nonlinearities and dead-zone in the input channel is proposed using only the measurable output of the master system thanks to a suitable observer. The asymptotical projective synchronization between the master and slave systems is achieved by an adequate fuzzy adaptive variable-structure control system. The underlying parameter adaptation design as well as the asymptotical synchronization and stability analysis are carried out using a Lyapunov based approach. The distinctive feature of the control design is that the uncertainties function and the gain reduction tolerances of the dead-zone are no longer required to be known thanks to the parameter adaptation capability of the control system. The proposed synchronization scheme is extended to two classes of the master-slave chaotic systems with time-delays. By using the Lyapunov-Krasovskii approach, some stability conditions relating to these classes are derived. Simulation results are given to show the effectiveness of the proposed projective synchronization scheme.

Supervisory Interval Type-2 TSK Neural Fuzzy Network Control for Linear Microstepping Motor Drives With Uncertainty Observer

This paper proposes a supervisory interval type-2 Tagaki-Sugeno-Kang neural fuzzy network (IT2TSKNFN) control system for precision motion control of linear microstepping motor (LMSM) drives. The IT2TSKNFN incorporates interval type-2 fuzzy sets and TSK fuzzy reasoning into an NFN to handle uncertainties in LMSM drives, including payload variation, external disturbance, and sense noise. Based on the IT2TSKNFN, an uncertainty observer is first introduced to watch compound system uncertainties. Subsequently, an IT2TSKNFN-based controller is developed with robust hybrid control scheme, in which H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> approach and a supervisory controller are embedded to overcome the effects of unstructured uncertainties and reconstruction errors. The supervisory controller combines variable structure control and adaptive IT2TSKNFN control with different weights based on the tracking error. Moreover, projection-type adaptive algorithms that can tune parameters of the IT2TSKNFN online are derived from the Lyapunov synthesis approach; thus, the stability and robustness of the overall control system are guaranteed. Finally, the proposed control algorithms are realized within a TMS320VC33 DSP-based control computer. Simulated and experimental results of an LMSM drive are provided to verify the effectiveness of the proposed IT2TSKNFN control system.

A fuzzy adaptive variable-structure control scheme for uncertain chaotic MIMO systems with sector nonlinearities and dead-zones

In this paper, a fuzzy adaptive variable-structure controller is investigated for a class of uncertain multi-input multi-output (MIMO) chaotic systems with both sector nonlinearities and dead-zones. A suitable adaptive fuzzy system is used to reasonably approximate the uncertain functions. A Lyapunov approach is employed to derive the parameter adaptation laws and prove the boundedness of all signals of the closed-loop system as well as the exponential convergence of the closed-loop errors to an adjustable region. The proposed controller can be applied to the systems with or without sector nonlinearities and/or dead-zones in the input. The effectiveness of the proposed fuzzy adaptive controller is illustrated throughout simulation results.

Stability analysis of a combined direct and variable structure adaptive control

This study presents the proofs of robust stability of a direct adaptive controller with a variable structure (VS) parcel. The control law parameters are adjusted based on a method proposed by Narendra and Boskvic (1990). In this approach, two sets of parameters must be obtained. One set is used to attain the control objective which is, in this case, to track the output of a reference model as closely as possible. The other set is of VS type, which is used to improve performance and robustness. A slight modification of the adaptive law for the VS parameters with proofs of robust stability is proposed here. With this modified law, all mathematical proofs already existing in the literature for robust direct adaptive controllers can be extended to the case under study. The combined controller is applied to a single input single output linear time invariant (SISO LTI) plant with unmodelled dynamics of multiplicative and additive types. It is proven that the combined controller can arbitrarily improve the convergence of the error while keeping the system robustness, if compared to the non-combined case. Simulation results illustrate the efficiency of the proposed control strategy.

Adaptive synchronization of fractional-order chaotic systems via a single driving variable

This letter investigates the synchronization of a class of three-dimensional fractional-order chaotic systems. Based on sliding mode variable structure control theory and adaptive control technique, a single-state adaptive-feedback controller containing a novel fractional integral sliding surface is developed to synchronize a class of fractional-order chaotic systems. The present controller, which only contains a single driving variable, is simple both in design and implementation. Simulation results for three fractional-order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.

Design and stability analysis of a variable structure adaptive backstepping controller

This paper presents the design and stability analysis of a Variable Structure Adaptive Backstepping Controller (VS-ABC) for linear plants with relative degree one, using only input/output measurements. Instead of traditional integral adaptive laws for estimating the plant parameters, switching laws are proposed to increase robustness to parametric uncertainties and disturbances, as well as to improve transient response. Moreover, the controller design is more intuitive when compared with the original adaptive backstepping controller, since the relay amplitudes are related to the plant nominal parameters and their respective uncertainties. Simplified algorithm versions are also presented, named Compact and Relay VS-ABC, which reduce the practical implementation complexity, and encourage applications in industrial environments. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Vector control for induction motor drives based on adaptive variable structure control algorithm

This paper presents a new adaptive robust control for induction motor drives. The proposed control scheme is based on the so-called field oriented control theory that allows to control the induction motor like a separately excited direct current motor drive, where the field flux (produced by the field current) and the armature flux (produced by the armature current) are decoupled. The robust control law is based on the sliding mode control theory, but unlike the traditional sliding mode control schemes, the proposed design incorporates an adaptive switching gain that avoids the need of calculating an upper limit of the system uncertainties. Moreover the proposed control law is smoothed out in order to avoid the high control activity inherent to the switching control laws. The resulting closed loop system is proven to be stable using the Lyapunov stability theory. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Adaptive Variable Structure Control for Uncertain Switched Delay Systems

This paper investigates the robust H∞ control problem for a class of uncertain switched delay systems with parameter uncertainties, unknown nonlinear perturbations, and external disturbance. Based on the multiple Lyapunov functions method, a sufficient condition for the solvability of the robust H∞ control problem is derived by employing a hysteresis switching law and variable structure controllers. When the upper bounds of the nonlinear perturbations are unknown, an adaptive variable structure control strategy is developed. The use of the adaptive technique is to adapt the unknown upper bounds of the nonlinear disturbances so that the objective of asymptotic stabilization with an H∞-norm bound is achieved under the hysteresis switching law. A numerical example illustrates the effectiveness of the proposed design methods.

A variable structure adaptive fuzzy logic stabiliser for a two-area load frequency control problem

This paper presents a variable structure adaptive fuzzy logic control approach for designing a decentralised controller for load frequency control of interconnected power areas. The proposed variable structure adaptive fuzzy logic load frequency controller (AFLFC) is designed to improve the dynamic performance of the frequency and tie-line power flow under a sudden load change in the power areas. The AFLFC provides a stabilising signal to work in conjunction with the original integral controller. The effect of generation rate constraint (GRC) for both areas has been considered in the controller design. Time-domain simulations are performed to demonstrate the effectiveness of the proposed AFLFC. The simulation results show that the proposed AFLFC provides good damping and reduces the overshoot of the different area frequency deviations and also reduces the interchanged tie power.

Simple adaptive variable structure control for unknown chaotic systems

This paper proposes two novel adaptive variable structure tracking controllers for a large class of chaotic systems with unknown dynamics in presence of both external disturbances and input nonlinearities. The pros and cons of each proposed methodology is also represented. In order to eliminate the chattering effect in the former controlled system, two corresponding fuzzy adaptive controllers are presented. Besides, synchronization of two non-identical uncertain chaotic systems is investigated using our proposed methods in both full and reduced-order forms. It can be seen that not only our proposed control schemes can be applied to a wide class of uncertain chaotic systems but also it is simple to implement in practical application. Finally, the proposed methods are applied to some famous chaotic systems to verify the effectiveness of the proposed methods.

Adaptive variable structure control of MIMO nonlinear systems with time-varying delays and unknown dead-zones

In this paper, adaptive variable structure neural control is presented for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with state time-varying delays and unknown nonlinear dead-zones. The unknown time-varying delay uncertainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear function outside the deadband without necessarily constructing a dead-zone inverse as an added contribution. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. In addition, a modified adaptive control algorithm is given in order to avoid the high-frequency chattering phenomenon. Simulation results demonstrate the effectiveness of the approach.

Design of adaptive variable structure controllers for T–S fuzzy time‐delay systems

AbstractIn this paper, the adaptive variable structure control problem is presented for Takagi–Sugeno (T–S) fuzzy time‐delay systems with uncertainties and external disturbances. The fuzzy sliding surfaces for the T–S fuzzy time‐delay system are proposed by using a Lyapunov function, and we design the adaptive variable structure controllers such that the global T–S fuzzy time‐delay system confined on the fuzzy sliding surfaces is asymptotically stable. One example is given to illustrate the effectiveness of our proposed methods. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Adaptive Statistic Tracking Control Based on Two-Step Neural Networks With Time Delays

This paper presents a new type of control framework for dynamical stochastic systems, called statistic tracking control (STC). The system considered is general and non-Gaussian and the tracking objective is the statistical information of a given target probability density function (pdf), rather than a deterministic signal. The control aims at making the statistical information of the output pdfs to follow those of a target pdf. For such a control framework, a variable structure adaptive tracking control strategy is first established using two-step neural network models. Following the B-spline neural network approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. The dynamic neural network (DNN) is employed to identify the unknown nonlinear dynamics between the control input and the weights related to the integrated function. To achieve the required control objective, an adaptive controller based on the proposed DNN is developed so as to track a reference trajectory. Stability analysis for both the identification and tracking errors is developed via the use of Lyapunov stability criterion. Simulations are given to demonstrate the efficiency of the proposed approach.

NN-based output feedback adaptive variable structure control for a class of non-affine nonlinear systems: A nonseparation principle design

Based on non-separation principle design and the application of Implicit Function Theorem, Mean Value Theorem, neural network parametrization and a simple linear observer, a new adaptive variable structure output feedback control is addressed for a class of non-affine nonlinear systems. In the presented scheme, many restrictive conditions, such as Lipschitz assumption, SPR (strictly positive realness) condition and contracting assumption are not required with the help of neural network parametrization. One of the main purposes of this work is to find out the relationships between the design parameters for observer and controller, and how to choose these design parameters in non-separation principle way. Semi-globally uniformly ultimate boundedness for the steady-state and transient performance is provided, and simulations verify the effectiveness of the proposed scheme.

Adaptive variable structure control for chaos suppression of unified chaotic systems

This paper investigates the chaos suppression problem for a class of unified chaotic systems subject to uncertainties and control input with dead-zone nonlinearity. Using the variable structure control technique, a robust adaptive control law is established to suppress chaos in a class of unified chaotic systems even with unknown uncertainties and dead-zone nonlinearity in input. In particular, a switching surface is newly proposed to simplify the task of ensuring the stability of the closed-loop system in the sliding mode. Numerical results validate the effectiveness of the proposed adaptive control scheme.

Adaptive variable structure controller for spacecraft vibration reduction

A hybrid control scheme to vibration reduction of flexible spacecraft is presented by using a variable structure technique for attitude control and piezoelectric materials for active vibration suppression. The attitude controller consists of a linear feedback term and a discontinuous feedback ones. An adaptive version of the proposed attitude controller is also achieved through releasing the limitation of knowing the bounds of the lumped perturbations in advance. An additional independent control system acting on the flexible parts can be designed for further vibration suppression. Simulation results have shown the theoretical and practical merit of this approach.

Adaptive Variable Structure Control of Aircraft withan Unknown High-Frequency Gain Matrix

This paper presents nonlinear adaptive and sliding-mode flight control systems for the roll-coupled maneuvers of aircraft. It is assumed that the parameters of the aircraft, as well as its high-frequency gain matrix, are unknown. Based on a backstepping design approach, nonlinear control laws (an adaptive variable structure control law and an adaptive control law) for the trajectory control of the roll angle, angle of attack, and sideslip angle using the aileron, elevator, and rudder are derived. The decomposition of the high-frequency gain matrix is used for the derivation of singularity-free flight control laws. An additional advantage of the control laws lies in the choice of design parameters of matrix decomposition for shaping the response characteristics. In the closed-loop system, the roll angle, angle of attack, and sideslip angle trajectories asymptotically follow the reference output trajectories. Simulation results are presented that show that in the closed-loop system, simultaneous longitudinal and lateral maneuvers are precisely performed in spite of the uncertainties in the aircraft parameters using each control system.

A Model Reference Adaptive Variable Structure Controller for Reconfigurable Flight Control Systems

This paper presents a new design of reconfigurable flight controller, applying both variable structure control and model reference adaptive control. In case of control effectors failures, aircraft model will vary, and unknown disturbances will affect the characteristics of controller. To study this problem, a model reference adaptive variable structure control law is designed, which composes a model-following adaptive control part and a variable structure control part. According to the model matching condition, an update scheme is used in the adaptive control part to eliminate system errors caused by model mismatch. With an adaptive sliding-mode gain the variable structure control part can deal with uncertain bounded disturbances of flight system. An aircraft example with stabilsator failure is presented to demonstrate the feasibility of the proposed reconfigurable control law. Simulation results show the control law is effective for reconfigurable flight control systems.