PSO Optimization of the Controller Parameters for an Inherently Unstable Attraction Type Levitation System

Abstract

Abstract-Optimization of the controller parameters with a comparative analysis approach for a double I core actuator based inherently unstable DC attraction type levitation system (DCALS) is presented here since the classically designed controllers play a very critical role for suspension in air with no visible means of support. Here the proposed system suspends a cylindrical rod under two I core actuators to achieve pitching control of the suspended rod with single degree of freedom movement control, which is a useful application in precision instrumentation. Proposed controllers which are typically employable for suspension purpose are the classically designed controllers such as Lead or, Lead-Lag or, PID for a nominal operating air-gap (10 mm) have been optimized utilizing particle swarm optimization and a comparative analysis of the transient performances has been produced at nominal as well as off-nominal operating air-gaps (low and high). Optimization algorithms are implemented inside the MATLAB software environment. The particle swarm optimization algorithm is found to be more competent in finding optimal results. Keyword-Optimization, DC attraction type levitation system (DCALS), particle swarm optimization (PSO), transient performance. I. INTRODUCTION DC attraction type levitation system (DCALS) is inherently unstable and strongly non-linear in nature ([1], [2]). A DCALS may be linearised for an operating air-gap and the linearised system can be stabilized using conventional classical controllers. Two I core actuator based magnetic levitation system has been proposed to suspend one cylindrical rod in air. To achieve stable suspension of the rod, linearised modeling of the system has been developed at different operating air-gaps and accordingly some conventional classical controllers (Lead, Lead-Lag, PID, PI plus Lead) have been implemented. Resulting controllers have been tuned by extremely tedious and time consuming 'trial and error' process on the 's'-plane utilizing root-locus design concept. Here, the Ziegler-Nichols tuning rule for PID controller tuning, failed straight away since the plant has one zero in the RHS of 's'-plane. It has been found that these controllers provide satisfactory performance in the neighborhood of operating point and performance degradation occurs as the operating point is changed. It becomes difficult for the controllers to maintain stability if there is wide variation of operating air-gap. Due to the inherent nonlinear nature of the system, the uncertainty in the nominal linearised model increases as one move away from the nominal operating point. As a result, the controller becomes practically invalid for large variations of the operating air-gap. But from implementation point of view there is an urgent need to enhance the capability of the controller so that the prototype can stably levitate over a large air-gap variation. One possible solution that is mostly reported in the literature is the design of a non-linear controller by considering the non-linear model of the...