This paper concerns the application of neuro-fuzzy approach in order to perform the responses of the speed regulation and reduce the chattering phenomenon introduced by sliding mode control. So first, we conceived a sliding mode controller of the induction motor. A new approach is applied to the cascade structure is presented. For this purpose, a new decoupled and reduced model is first proposed. Then, a set of simple surfaces and associated control laws are synthesized. However, as the magnitude of the piecewise smooth function depends closely on the upper bound of uncertainties, which include parameter variations and external disturbances, we propose a new form of this piecewise smooth control function with a threshold which ensure a significant reduction of the chattering but could not eliminate it. To overcome such a limitation of this control, adaptive neuro fuzzy inference controllers (ANFIS) are designed. Simulation results reveal some very interesting features.
Fault tolerant control for uncertain systems with time varying state-delay is studied in this paper. Based on sliding mode controller design, a fault tolerant control method is proposed. By means of the feasibility of some linear matrix inequalities (LMIs), delay dependent sufficient condition is derived for the existence of a linear sliding surface which guarantees quadratic stability of the reduced-order equivalent system restricted to the sliding surface. A reaching motion controller, which can be seen as a fault tolerant controller, can retain the stability of the closed loop system in the present of uncertainties, disturbances and actuator fault is designed. A numerical simulation shows the effectiveness of the approach.
This paper is devoted to design H∞ sliding mode controller for continuous-time Markov jump systems with interval time-varying delays and general transition probabilities. An integral sliding surface is constructed and its reachability is guaranteed via a sliding mode control law. Meanwhile, a linearisation strategy is applied to treat the nonlinearity induced by general transition probabilities. Using a separation method based on Finsler lemma to eliminate the coupling among Lyapunov variables and controller parameters, sufficient conditions for asymptotically stochastic stability of sliding mode dynamics are formulated in terms of linear matrix inequalities. Finally, a single-link robot arm system is simulated to demonstrate the effectiveness of the proposed method.
The aim of this paper consists in using one of the emergent techniques which proves its capability of improving performances of several systems, called "neuro-fuzzy", in order to reduce the chattering phenomenon and also to perform the control obtained with fuzzy sliding mode control. In fact, after determining the decoupled model of the motor, a set of simple surfaces and associated a smooth control function with a threshold have been synthesized. However, the magnitude of this control function depends closely on the upper bound of uncertainties, which include parameter variations and external disturbances, and this generates chattering. Usually, the upper bound of uncertainties is difficult to be known before motor operation, so a fuzzy sliding mode controller is investigated to solve this difficulty and in which a simple fuzzy inference mechanism is used to reduce the chattering phenomenon by simple adjustments. In order to optimize the control performances and ensure a significant reduction of chattering compare with ones obtained in the previous fuzzy sliding mode, we propose in this paper to use adaptive predictive neural approach to regulate the speed of the motor. The neural control algorithm is provided with the predicted system output which is the speed variable via a recursive on line identification of the overall system which is based on a static feed forward linear network with one hidden layer. The predicted data are passed to a numerical optimization algorithm which attempts to minimize a quadratic performance criterion to compute the suitable control signal.
In this paper the design of a time varying switching plane for the sliding mode control of the third order system subject to the velocity and acceleration constraints is considered. Initially the plane passes through the system representative point in the error state space and then it moves with a constant velocity to the origin of the space. Having reached the origin the plane stops and remains motionless. The plane parameters (determining angles of inclination and the velocity of its motion) are selected to ensure the minimum integral absolute error without violating velocity and acceleration constraints. The optimal parameters of the plane for the system subject to the acceleration constraint are derived analytically, and it is strictly proved that when both the system velocity and acceleration are limited, the optimal parameters can be easily found using any standard numerical procedure for solving nonlinear equations. The equation to be solved is derived and the starting points for the numerical procedure are given.
The rotary inverted pendulum (RIP) system is one of the fundamental, nonlinear, unstable and interesting benchmark systems in the field of control theory. In this paper, two nonlinear control strategies, namely hierarchical sliding mode control (HSMC) and decoupled sliding mode control (DSMC), are discussed to address the stabilization problem of the RIP system. We introduced HSMC with state-dependent switching gain for stabilization of the RIP system. Numerical simulations are performed to analyze the performance of the hierarchical sliding mode controllers with the decoupled sliding mode controller and the controller obtained from the pole placement technique. We proposed HSMC with state-dependent switching gain as it shows better performance as compared to HSMC with constant switching gain, DSMC, and the state feedback controller based on pole placement technique. The stability analysis of proposed HSMC is also discussed by using Lyapunov stability theory.
In this work, an alternative for sliding surface design based on linear and bilinear matrix inequalities is proposed. The methodology applies for reduced and integral sliding mode control, both continuous- and discrete-time; it takes advantage of the Finsler's lemma to provide a greater degree of freedom than existing approaches for sliding subspace design. The sliding surfaces thus constructed are systematically found via convex optimization techniques, which are efficiently implemented in commercially available software. Examples are provided to illustrate the effectiveness of the proposed approach.