Design of Fuzzy Sliding Mode Controller for the Ball and Plate System
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Date
2011-07
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Addis Ababa University
Abstract
The Ball and Plate system is a non-linear, multivariable and under-actuated system which provides a suitable experimental platform for control algorithm development and investigation of both stabilization and trajectory tracking control of unstable systems.
Sliding mode control, as one of the tools available to design robust controllers, is introduced in the outer loop of a double-loop feedback configuration. Since the robustness of sliding mode control is obtained at the cost of infinite switching of the control input, undesirable phenomenon known as chattering will be a concern in practical implementations. To this end, Fuzzy Logic is used to tune the gain of the switching control component based on the distance of the system trajectory from the sliding surface. Genetic algorithm is implemented to determine the parameters of the fuzzy system in an optimal manner.
Linear algebraic method is used to design an inner loop angle controller from a set of Diophantine equations. An implementable zero-position error transfer function is selected from tabulated results of analog computer simulations of Integral of Time Multiplied Absolute Error (ITAE) optimal systems. Specifications for the desired settling time and limitation in the actuator voltage are used as constraints to obtain the coefficients of the overall transfer function.
The mathematical model of the Ball and Plate system, solved from Euler-Lagrange Equations of Motion, is investigated by realizing the designed controllers using Simulink ® and Real-Time Windows Target™ rapid prototyping software. The 3-D model of the system designed using V•Realm™ Builder based on the standards of Virtual Reality Modeling Language (VRML) is interfaced with the Simulink ® model via Simulink® 3D Animation™ product.
Simulation results show that the ball could be stabilized anywhere on the plate in 3.5 seconds and it could also track a circular trajectory of 0.4m radius at 0.8 rad/s in 10 seconds without significant chattering.
Key Words: Fuzzy Sliding Mode Control, Variable Structure Control, Linear Algebraic Method, Ball and Plate control, VRML, Simulink® 3D Animation™/MATLAB®
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Keywords
Fuzzy Sliding Mode Control ; Variable Structure Control ;Linear Algebraic Method ; Ball and Plate control ; VRML ; Simulink