Wen-Shyong Yu

Fuzzy model based adaptive control for a class of nonlinear systems

A fuzzy model based adaptive control algorithm for a class of continuous-time nonlinear dynamic systems is presented. The fuzzy model consisting of a set of linear fuzzy local models that are combined using a fuzzy inference mechanism is used to model a class of nonlinear systems. Each fuzzy local model represents a linearized model corresponding to the operating point of the controlled nonlinear system. The proposed control algorithm employs the fuzzy controller that is designed by considering the linear state feedback controller corresponding to the fuzzy local model with the maximum weight and the switching-/spl sigma/ modification adaptive controller to adaptively compensate for the plant nonlinearities. Stability robustness of the closed-loop system is analyzed in Lyapunov sense. It is shown, that the proposed control algorithm guarantees global stability of the system with the output of the system approaching the origin if there are no disturbances and uncertainties, converging to the neighborhood of the origin for all realizations of uncertainties and disturbances. The simulation examples for controlling inverted pendulum system are given to illustrate the effectiveness of the proposed method.

Adaptive fuzzy sliding mode control for linear time-varying uncertain systems

In this paper, we propose an adaptive fuzzy sliding mode control scheme (AFSCS) for continuous-time multiple-input-multiple-output (MIMO) linear time-varying uncertain systems. The AFSCS consists of a fuzzy controller with adaptive mechanism to reconstruct the system states using the tracking error and to make the state error reach the equilibrium point in finite time period quickly. The sliding surface is first employed to represent the state error to reach the equilibrium point in a finite time period. Then, an adaptive fuzzy controller using sliding mode is developed to achieve the control performance and the state tracking errors performance quickly. The reaching mode of the uncertain system using the proposed adaptive fuzzy sliding mode controller is guaranteed. Moreover, the chattering around the sliding surface for the proposed adaptive fuzzy sliding mode control can be reduced. A 2-dof parallel robot system will be used to verify the effectiveness of the proposed method.

H∞ Tracking-based adaptive fuzzy-neural control for MIMO uncertain robotic systems with time delays

In this paper, a novel adaptive fuzzy-neural control (AFNC) scheme for multi-input multi-output uncertain robotic systems is proposed for H∞ tracking performance and to suppress the effects caused by multiple time-delayed state uncertainties, unmodeled dynamics, and disturbances. Each delayed uncertainty is assumed to be bounded by an unknown gain. A reference model with the desired amplitude and phase properties is given to construct an error model. A fuzzy-neural (FN) system is used to approximate an unknown controlled system from the strategic manipulation of the model following tracking errors. The proposed AFNC scheme uses two on-line estimations, which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the FN system, simultaneously. Stability and robustness of the AFNC scheme is analyzed in Lyapunov sense. It is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed-loop system with H∞ tracking performance for the overall system without a priori knowledge on the upper bounds of the delayed state uncertainties. The performance of the proposed scheme is evaluated through the simulation results. Simulations are given to show the validity and confirm the performance of the proposed scheme.

H∞ tracking adaptive fuzzy integral sliding mode control for parallel manipulators

Abstract Highly nonlinear coupling phenomenon is an inherently inevitable in parallel manipulators in which limbs/links undergo rotating and sliding with/without fixed base. In this paper, an H ∞ tracking adaptive fuzzy integral sliding mode control scheme is proposed for controlling parallel manipulators with nonlinear unmodeled dynamics, external disturbances, and limb-to-limb couples in which each coupled uncertainty is assumed to be bounded by an unknown gain. The dynamics of the parallel manipulator is formulated as an error dynamics according to a specified reference model; then, a fuzzy model is used to approximate the uncertainties. Two on-line estimation schemes are developed to overcome the uncertainties and identify the gains of the unknown coupled uncertainty bounds from limb-to-limb couples, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear uncertain functions with an on-line update law. By the concept of parallel distributed compensation (PDC), the adaptive fuzzy scheme uses an integral sliding mode control scheme to resolve the system uncertainties, unknown limb-to-limb coupled uncertainties, and the external disturbances such that H ∞ tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB) and the effect on the tracking error can be attenuated to any prescribed level to achieve H ∞ tracking performance. Finally, a numerical example of a planar 2-dof parallel robot system is given to verify the effectiveness of the proposed control scheme.

Robust tracking observer-based adaptive fuzzy control design for uncertain nonlinear MIMO systems with time delayed states

This paper addresses the problem of designing robust observer-based adaptive fuzzy tracking control scheme for a class of MIMO nonlinear systems with plant uncertainties, time delayed uncertainties, and external disturbances. A fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions and an adaptive fuzzy observer is introduced for state estimations. The proposed control law is based on indirect adaptive fuzzy control and uses two on-line estimations. This allows for the simultaneous inclusion of identifying gains of the delayed state uncertainties and training of the weights of the fuzzy system by introducing estimated error vectors. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with online update laws. The adaptive fuzzy tracking control using Variable Structure (VS) control technique is derived based on Lyapunov criterion and the Riccati-inequality to resolve system uncertainties, time delayed uncertainties, and external disturbances. This is done in such a way that all states of the system are bounded and the H ∞ tracking performance is achieved. Finally, a two-connected inverted pendulums on carts system (Liu et al., 2011) [29] is used for simulation purposes and some comparisons are given to illustrate the validity and effectiveness of the proposed method.

Anti-sway tracking control of tower cranes with delayed uncertainty using a robust adaptive fuzzy control

Tower cranes are very complex mechanical systems and have been the subject of research investigations to reduce the swaying of the payload for several decades. Inherently, the dynamical model of the tower cranes is highly nonlinear and classified as underactuated. Also, the actuators are far from the payload which makes the system non-colocated. It is proposed here to use an H ∞ based adaptive fuzzy control technique to control the swaying motion of a tower crane. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating the dynamics of the tower crane with an online update law. The proposed robust control law for payload positioning is based on a variable structure (VS) adaptive fuzzy control scheme. The adaptive fuzzy control technique fuses a VS scheme and it is derived based on a Lyapunov criterion and the Riccati-inequality. The control design overcomes modeling inaccuracies, such as drag and friction losses, effect of time delays from backlash, as well as parameter uncertainties and compensate for the effect of the external disturbances on tracking error such that all the states of the system are uniformly ultimately bounded (UUB). Therefore, the H ∞ tracking performance can be achieved such that the payload swing is reduced to as small as possible when the payload is moved from point to point. Simulations show that the proposed control scheme is effective in reducing payload swing in the presence of uncertainties, time delays, and external disturbances.

Interval type-2 fuzzy adaptive tracking control design for PMDC motor with the sector dead-zones

We propose IT2FAC scheme to reduce the sector dead-zone nonlinearities.This scheme integrates variable structure to achieve the H ∞ tracking performance.This scheme uses the Lyapunov criterion to ensure the boundedness of all states.This scheme exhibits faster tracking responses for the PMDC motor systems. This paper deals with the permanent magnet DC motor system with sector dead-zones and external disturbances via interval type-2 fuzzy adaptive tracking control scheme to achieve H ∞ tracking performance. The type-2 fuzzy dynamic model is used to approximate the motor dynamics without constructing sector dead-zone inverse, where the parameters of the fuzzy model are obtained both from the fuzzy inference and online update laws. Based on the Lyapunov criterion and Riccati-inequality, the control scheme is derived to stabilize the closed-loop system such that all states of the system are guaranteed to be bounded and H ∞ tracking performance is achieved due to uncertainties, dead-zone nonlinearities, and external disturbances. The advantage of the proposed control scheme is that it can better handle the vagueness or uncertainties inherent in linguistic words using fuzzy set membership functions with adaptation capability by linear analytical results instead of estimating non-linear system functions as the system parameters are unknown. Finally, the simulations of the PMDC motor system with sector dead-zone nonlinearities are used to illustrate the effectiveness of the proposed control scheme and the performance comparisons with the three-dimensional autonomous R o ? ssler system (Wang and Chua, 2008) are used to validate the H ∞ tracking performance of the PMDC motor system.

Continuous-time indirect adaptive control of the electrohydraulic servo systems

A continuous-time robust indirect adaptive control (IAC) algorithm with a self-excitation capability is proposed for position control of an electrohydraulic servo system subject to parametric uncertainties and load disturbances. In this algorithm, a gradient least squares dead zone estimation is used to identify the plant parameters and then a linear pole-placement controller is designed using the estimate. By a coprimeness verification procedure, the proposed algorithm facilitates the establishment of the adaptive pole-placement control of the closed-loop system by using an additional nonlinear feedback signal implemented for supplying the system with sufficiently rich signals. An analysis shows this algorithm can guarantee parameter estimation convergence and system stability based on the certainty equivalence principle. The performance of the proposed algorithm is evaluated through both the simulation results and the experimental studies. Simulations and experiments are conducted to see how well the proposed algorithm compares with two existing control schemes in controlling the same process. The results show that the IAC scheme confirms the analysis and has considerable robustness subject to parametric uncertainties and load disturbances and has better performance than the other two controllers.

Model reference fuzzy adaptive control for uncertain dynamical systems with time delays

This paper investigates a model reference fuzzy adaptive control (MRFAC) scheme for uncertain dynamical systems with known structures but unknown parameters which are dependent on known variables, multiple delayed state uncertainties, and disturbances. Each delayed uncertainty is assumed to be bounded by an unknown gain. A fuzzy basis function expansion (FBFE) is used to represent the unknown parameters of the controlled system from the strategic manipulation of the model following tracking errors. The proposed MRFAC scheme uses two on-line estimations, which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the FBFE simultaneously. Stability and robustness of the MRFAC scheme is analyzed in the sense of Lyapunov. It is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed-loop system with the model following tracking errors uniformly ultimately bounded in the presence of plant parameter uncertainties, delayed state uncertainties, and external disturbances. The theoretical results are evaluated through a gyroscopic system with a single actuating input.

An Observer-Based Indirect Adaptive Fuzzy Control for Rolling Cart Systems

Rolling cart system is a highly nonlinear phenomenon in which links undergo tipping and rolling with no fixed base. This in turn requires that the system running states be predicted correctly. This paper makes a full analysis of the rolling cart states by applying observer-based adaptive tracking control scheme based on fuzzy system and variable structure system (VSS) with system uncertainties, multiple time delayed state uncertainties, and external disturbances. A fuzzy modeling is used to approximate the dynamics of the rolling cart. The observer-based fuzzy adaptive control scheme is developed to override the nonlinearities, time delays, and external disturbances such that the H∞ tracking performance is achieved. The advantage of employing adaptive fuzzy system is that we can utilize the linguistic information by setting the membership functions of fuzzy logical system and the adaptation parameters to estimate the model uncertainties directly for using linear analytical results instead of estimating nonlinear system functions. Based on Lyapunov criterion and Riccati-inequality, some sufficient conditions are derived so that all states of the system are uniformly ultimately bounded and the effect of the external disturbances on the tracking error can be attenuated to any prescribed level to achieve H∞ tracking performance. Finally, a numerical example of a two-links rolling cart is given to illustrate the effectiveness of the proposed control scheme.