Sliding Mode Control with Adaptive Fuzzy Compensation for Uncertain Nonlinear System

Tuning of a pH process is a challenging problem due to the strong on-line non-linearity and extreme sensitivity to disturbances of the process. Hence, a nonlinear control strategy based on sliding mode, which is a standard approach to tackle the parametric and modeling uncertainties of a nonlinear system, is chosen for tuning a pH process. Fuzzy Sliding Mode Control (FSMC) as a robust and intelligent nonlinear control technique is proposed to control processes with severe nonlinearity and unknown models. The proportional and integral constants are adjusted by new tuning rule of fuzzy to adapt with the extreme condition of process. Sliding mode control is introduced into classical model free Fuzzy Logic Control(FLC) for discrete time nonlinear systems with uncertainty to design a novel fuzzy sliding mode control to meet the requirement of necessary and sufficient reaching conditions of tuning a pH process. The simulation results show that the proposed controller outperforms the classical fuzzy logic controller in stability, convergence and robustness. Here Sliding Fuzzy logic control for obtaining the optimal design of the pH process is explained. The performance of the algorithm in obtaining the optimal tuning values has been analyzed in pH process through computer simulation.

To eliminate the effect of the uncertain disturbances and improve the control accuracy of spacecraft Attitude Control System, a nonlinear control algorithm named nonsingular terminal sliding-mode feedback controller is proposed in this work, which is mainly made up of nonsingular terminal sliding-mode controller and sliding-mode feedback controller. In the first place, nonsingular terminal sliding-mode controller is designed, which guarantees global asymptotic convergence of the attitude in the presence of the uncertain perturbations from the space. Despite that, it is the influence of the uncertain disturbances that hinder the control accuracy. Then, in order to promote the control accuracy, the sliding-mode feedback controller based on the principle of minimum sliding-mode error is proposed, which is used to compensate the control errors of the nonsingular terminal sliding-mode controller caused by the uncertainties. Hence, the determination principle of the weighting matrix in sliding-mode feedback controller is discussed, and the algorithm structure of the sliding-mode feedback controller is also analyzed, which provides the theoretical basis for the sliding-mode feedback controller. By contrast, an adaptive fuzzy algorithm is designed and introduced into the nonsingular terminal sliding-mode controller to improve the control accuracy, which named the nonsingular terminal fuzzy sliding-mode controller. Last but not the least, several numerical examples are presented to demonstrate the efficacy of the proposed nonsingular terminal sliding-mode feedback controller. Simulation results confirm that the control accuracy of the nonsingular terminal sliding-mode feedback controller is higher than the nonsingular terminal sliding-mode controller and the same as nonsingular terminal fuzzy sliding-mode controller. Not only is the calculation of the nonsingular terminal fuzzy sliding-mode feedback controller smaller than nonsingular terminal fuzzy sliding-mode controller, the adjusted parameters are also fewer than nonsingular terminal fuzzy sliding-mode controller obviously. The numerical results clearly indicate that the proposed nonsingular terminal sliding-mode feedback controller based on the principle of minimum sliding-mode error can compensate control errors accurately and quickly; therefore, it can reduce the effect of the uncertainties from the space indirectly.

This paper demonstrates a fuzzy sliding mode control (FSMC) scheme for a static reactive power (VAR) compensator (SVC) to improve the damping of a synchronous generator. A robust sliding regime is derived to guarantee the stability of the FSMC with parameter uncertainties. Two types of FSMC-fuzzy switching gain compensation and fuzzy control signal compensation, are recommended to regulate the reactive power of the SVC. A synchronous generator system with the proposed FSMC-SVC has been studied and its dynamic responses are simulated. And the results show that the suggested FSMC possesses the advantages of fuzzy control and sliding mode control, e.g., insensitivity to parameter variations and load disturbances. The dynamic performance of the synchronous machine system can be improved dramatically over a wide range of operating condition. In these control schemes, the reducing switches control are adopted for simplification. >

Generally, the greatest difficulty encountered when designing a fuzzy sliding mode controller (FSMC) or an adaptive fuzzy sliding mode controller (AFSMC) capable of rapidly and efficiently controlling complex and nonlinear systems is how to select the most appropriate initial values for the parameter vector. In this paper, we describe a method of stability analysis for a GA‐based reference adaptive fuzzy sliding model controller capable of handling these types of problems for a nonlinear system. First, we approximate and describe an uncertain and nonlinear plant for the tracking of a reference trajectory via a fuzzy model incorporating fuzzy logic control rules. Next, the initial values of the consequent parameter vector are decided via a genetic algorithm. After this, an adaptive fuzzy sliding model controller, designed to simultaneously stabilize and control the system, is derived. The stability of the nonlinear system is ensured by the derivation of the stability criterion based upon Lyapunov′s direct method. Finally, an example, a numerical simulation, is provided to demonstrate the control methodology.

In this paper, a magnetorheological (MR) mount with fuzzy sliding mode controller (FSMC) is studied for vibration suppression when the system is subject to base excitations. In recent years, magnetorheological fluids are becoming a popular material in the field of the semi-active control. However, the dynamic equation of an MR mount is highly nonlinear and it is difficult to identify. FSMC provides a simple method to achieve vibration attenuation of the nonlinear system with uncertain disturbances. This method is capable of handling the chattering problem of sliding mode control effectively and the fuzzy control rules are obtained by using the Lyapunov stability theory. The numerical simulations using one-dimension and two-dimension FSMC show effectiveness of the proposed controller for vibration suppression. Further, the well-known skyhook control scheme and an adaptive sliding mode controller are also included in the simulation for comparison with the proposed FSMC..

In this paper, decoupled neural fuzzy sliding-mode control design method for highly nonlinear systems is proposed. The decoupled control method provides a simple way to achieve asymptotic stability for a class of fourth-order nonlinear system into two second-order subsystems by a separate control objective expressed in terms of a sliding surface for each subsystems. Using the proposed method the second subsystem is successfully incorporated into the first one via a two-level decoupling strategy. In the controller design method, reaching mode and sliding mode control of sliding mode control is approximated based on neural network control and fuzzy logic control method respectively. Two simulation results of a cart-pole and ball-beam systems are shown to demonstrate the effectiveness of the proposed method.

The system of Pb-211 robot waist is a nonlinear hydraulic servo control system. It is very difficult to achieve speedy response without overshoot by the PID control algorithm for the system control. To improve the performance of the system, a new controller is designed with a fuzzy sliding-mode control algorithm, which makes use of the merits both the fuzzy control and the sliding-mode control algorithm. The simulation results show that the new controller is effective, which can achieve high speediness and steady accuracy without overshoot. The fuzzy sliding-mode control has obvious advantage compared the traditional PID algorithm, and it has strong robust too.

Due to the under-actuated feature, the reference signals using the combination of the system outputs, whose number is larger than that of reference signal, are designed so that the number of control inputs and sliding surfaces is the same, and that the uncontrollable mode is indirectly controlled. Under the uncertain environment, the sliding-mode under-actuated control (SMUC) with the satisfaction of suitable condition is designed to asymptotically track the reference signal. Otherwise, a bounded tracking result is obtained for the mild condition. In this situation, an on-line fuzzy modeling for the uncertainty is employed to design a fuzzy model-based sliding-mode under-actuated control (FSMUC) to improve the system performance; e.g., the bounded tracking result of SMUC becomes an asymptotical tracking. The proposed hybrid fuzzy sliding-mode under-actuated control (HFSMUC) combining SMUC and FSMUC with a transition can be applied to a class of generalized, under-actuated and uncertain nonlinear systems, e.g., the trajectory tracking control of a differential mobile robot (DMR). Finally, the simulations of the HFSMUC system are presented to confirm the efficiency and effectiveness of the proposed control.

This paper focuses on the problem of model reference fuzzy sliding mode control for a class of strict-feedback systems with mismatched uncertainties and unknown dead-zone. The original nonlinear system dynamics can be transformed into an equivalent system by means of the concept of Lie derivative. Fuzzy logical systems are used to approximate the unknown nonlinear functions and the unknown upper bounds of uncertainties. Some adaptive laws as a parameter estimation approach are used to reduce the modeling error. By virtue of Lyapunov stability theorem and the theory of sliding mode control, the proposed model reference adaptive fuzzy sliding mode controller can guarantee the stability of the whole closed-loop systems and obtains good tracking performance. Simulation results show the efficacy of the proposed method.

Adaptive TSK fuzzy sliding mode control design for switched reluctance motor DTC drive systems with torque sensorless strategy

Addressing the challenges of significant speed overshoot, stability issues, and system oscillations associated with the sliding mode control (SMC) strategy in maximum power point tracking (MPPT) for permanent magnet synchronous wind power systems, this paper introduces a fuzzy sliding mode control (FSMC) method employing an innovative exponential convergence law. By incorporating a velocity adjustment function into the traditional exponential convergence law, a novel convergence law was designed to mitigate oscillations during the sliding phase and expedite the convergence rate. Additionally, a fuzzy controller was developed to implement a fuzzy adaptive SMC strategy, optimizing the MPPT for permanent magnet synchronous wind power generation systems. Simulation results indicated that this approach offered a faster response and superior interference rejection capabilities, compared to conventional and modified SMC strategies. The improved FSMC strategy demonstrated a swift, dynamic response and excellent steady-state performance, improving the efficiency of MPPT, thus confirming the effectiveness of the proposed method.

This paper deals with an optimal design of decoupling-variable structure fuzzy controller for induction motor. It can avoid the randomness of choice of the parameters of a variable structure controller. According to the principle of fuzzy logic control and sliding mode control, the theory of this new fuzzy sliding mode control is presented and a mathematical description for induction motor is given. The sliding mode control is used to achieve robust performance against parameter variations and external disturbances. A fuzzy control law is applied to reduce or overcome the system chattering owing to sliding mode control. The simulant experiment curves and results are given.

An effective method, adaptive fuzzy sliding-mode (SM) PI Control to design full-bridge inverter is proposed in this paper. For practical applications, sliding mode control (SMC) with chattering phenomenon is a large hindrance. The modified model of the PI controller is built by the plant extension scheme, in order to relieve the chattering. Also, the fuzzy logic is applied to find the appropriate parameter values of the PI controller, and can adapt to plant parameter variations and external load disturbances. The proposed method has been realized for the actual full-bridge inverters controlled by DSP and CPLD. Simulation and experimental results of the closed-loop system show that the proposed method yields system performance improvement, such as low total harmonic distortion (THD), fast dynamic response, reduced steady-state error, and reduced chattering.

Aiming at the path tracking problem of AUV (autonomous underwater vehicle) in the process of docking, a fuzzy sliding mode control algorithm based on RBF (radial basis function) neural network is proposed. Firstly, the sliding mode control is used to track the trajectory, the fuzzy control is used to continuously correct the parameters of the exponential reaching rate in the sliding mode control to alleviate the shaking problem. Then the RBF neural network is used to compensate uncertainty in the AUV motion model and the external unknown interference. Finally, the stability of the control system is proved by Lyapunov stability theory. The simulation result shows that the designed control algorithm can track the trajectory of AUV effectively. By comparing tracking effects with traditional sliding mode control and fuzzy sliding mode control, it is proved that the proposed control method has faster tracking speed, better stability and better tracking performance.

The doubly-fed induction generators (DFIGs) are highly complex systems with nonlinearity and uncertainty. Therefore, employing robust intelligent control is required to improve the system performance. This paper takes advantage of combining the sliding mode control (SMC) and fuzzy control. The proposed controller, known as fuzzy sliding mode control (FSMC), can reduce the fluctuation produced by the pulse with a modulation converter and accelerate the trajectory to the sliding surface. The closed-loop system stability is also guaranteed in this work. The results simulation shows good performance and robustness of the proposed controller.