A Novel Hybrid (PID + MRAC) Adaptive Controller for an Air Levitation System
Keywords:
adaptive controller, air levitation system, HMRAC, Lyapunov functionAbstract
The air levitation system belongs to a class of systems with fast dynamics and low damping. Such characteristics make the plant intrinsically unstable and respond in a non-linear form. Thus, it is prohibitive to use classic control techniques, such as the PID (Proportional-Integral-Derivative) controller, to track the position of the sphere. The control system must be able to compensate the non-linearities, high oscillation and reject disturbances. Thus, this research proposes to create a new approach for the hybrid controller (PID + MRAC) present in the literature. The topological character of the proposed MRAC (Model Reference Adaptive Controller) consists of three parts: a feedforward controller, a derivative portion and an ordinary feedback. The feedforward portion has the purpose of rejecting undesirable disturbances. The derivative portion increases the stability of the system and the ordinary feedback makes the error null in steady state. Due to the convergence time of the adjustment parameters, MRAC performs poorly during reference changes and in the rejection of disturbances. Thus, it is common practice to use the MRAC with the PID controller. In its methodological aspect, the control law was created from Lyapunov's theory, with the purpose of ensuring asymptotic stability for the system. As a result, the proposed controller (Hybrid-MRAC or H-MRAC) showed better results than a literature reference (A-PID), in terms of mean absolute (MAE), mean square (MSE) and root mean square (RMSE) errors. In MAE simulations it was 51,25% lower on average, MSE was 51,65% and RMSE 31,40%. In the experiments, the MAE was on average 19,72% lower, the MSE 42,92% and the RMSE 18,58%.
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