Fuzzy Sliding Mode Control of a Magnetic Ball Suspension System

However, feedback linearization control does not guarantee robustness in the presence of modeling errors. In [3], ∞ H control and sliding mode control was proposed. ∞ H control is a computation expensive method that presents good disturbance attenuation performance. In [4], sliding mode control and PID controller was discussed. In [5], the PID controller was discussed. The PID controller is a simple method for operating point linearization. However, the PID controller has good performance only within a small operating range. In [6], Fuzzy learning control was proposed. The learning control is a computation expensive method. In [7], adaptive robust nonlinear controller learning was proposed that is also a computationally expensive. In [8], an evolutionary programming based fuzzy sliding mode control was proposed. The evolution computation [13,14] is also a computationally expensive in tuning the neural network controller structure and parameters. In [9], an improved force model-identification method was proposed. In [10], an integral variable controller with grey prediction was proposed to reduce the chattering and steady state error. This paper presents an adaptive fuzzy estimator sliding mode position control design for robust stabilization and disturbance rejection for a magnetic ball suspension system (MBSS). In general, the conventional sliding mode control design assumes that the upper boundary of the parameter variations and external disturbances is known and the sign function is used. It causes high frequency chattering and high gain phenomenon. In this paper, we propose a novel adaptive fuzzy estimator sliding mode control for the MBSS to avoid the high gain and reduce the chattering magnitude. The parameter variation and external disturbance estimator is designed to estimate the unknown lumped uncertainty values in real-time. This is different from the conventional fuzzy sliding mode control which estimates the unknown upper boundary uncertainty. This method utilizes a Lyapunov function candidate to guarantee convergence and asymptotically track the MBSS position commands. We employ experiments to validate the proposed method. Sliding mode control [15,16] has attracted a great deal of attention in recent years because it is proven as a powerful tool for nonlinear robust control design. It is an effective and robust technology for rejecting parameter variations and external disturbances. It has been applied in robot control, motor control and many control fields [3,10,12, 15-22]. The uncertainties, parameter variations and/or disturbances can be rejected for variable structure control when the upper boundary of the system lumped uncertainty is known. The system uncertainty boundaries are difficult to obtain in practical applications. In real applications, uncertainty boundaries can easily exceed the assumed magnitude range, under which the sliding mode can not be used. Using high gain control to improve disturbance rejection has been proposed [18]. A control system using a large constant gain is simple to implement. However, it produces unnecessary deviations from the switching manifold and causes large chattering in the control systems. Serious chattering can reduce by using the boundary layer which the signum function is replaced by the saturation function. However, it produces steady state errors. Hence, in recent years, some researchers [10,20-23] have proposed methods to find the uncertain upper boundaries and eliminate the steady state error in which the signum function is replaced by the saturation function. Their major concept estimates