This paper describes design and implementation of a control philosophy for simultaneous stabilization and performance improvement of an electromagnetic levitation system. An electromagnetic levitation system is an inherently unstable and strongly nonlinear system. To determine the overall closed loop stability for such a system, cascade lead‐lag compensation has mostly been reported [1,2]. However, a single lead controller can not satisfy both stability and performance for such unstable systems [3]. Performance enhancement to satisfy the conflicting requirements of fast response with almost zero overshoot and zero steady state error has been successfully achieved by using a two loop controller configuration. The lead controller in the inner loop is designed to ensure stability while the outer loop PI controller is designed for performance enhancement. This approach decouples the twin requirements of stabilization (by the inner loop) and performance achievement (by the outer PI loop). The outermost PI controller has been designed using the ‘Approximate Model Matching’ technique [4]. The proposed control strategy has been implemented and the experimentation has been demonstrated successfully. Different experimental results have been included for verification.
A new two-stage method is proposed for the model-matching fractional-order (FO) controller (FOC) design for the single-input single-output (SISO) / multiple-input multiple-output (MIMO) linear systems. A streamlined procedure for the selection of reference model M(s), based on a linear quadratic regulator (LQR) with integral action (LQRI) is presented. Since the proposed M(s) is designed using the optimal control theory, the designed output-feedback closed-loop system can be termed as a suboptimal one. Formulation of M(s) incorporates the time-domain characteristics, and the optimal interaction desired to be present in the designed closed-loop system. The developed controller design procedure also works with a user-specified M(s). In the first stage of the controller design, a higher-order controller K(s) which makes the closed-loop system exactly equal to the M(s) is obtained. In the second stage, K(s) is approximated to a FOC or an integer-order (IO) controller (IOC) C(s) with the aim of matching a certain number of approximate generalized time moments (AGTMs) and/or approximate generalized Markov parameters (AGMPs) of K(s) to those of C(s) at a set of frequency points in the s-plane. The simulation and experimental validation of the proposed approach are performed by the design and implementation of the controller for an IO MIMO plant with time-delays. The controller design algorithm is also illustrated based on the user-defined reference model for a FO MIMO plant with time-delays taken from the literature. The obtained results show that the FOC results in better performance compared with its IO counterpart.INDEX TERMS AGTM and AGMP matching, fractional-order controller, MIMO, model-matching, reference model.
The brief deals with a new algorithm for designing Proportional-Integral (PI) and ProportionalIntegral Derivative (PID) Controllers for system with parametric uncertainty. The parameters of the controller are obtained by the frequency response matching of the actual and the desired closed-loop characteristics at two different frequency points. The desired closed-loop reference model can be chosen from the design requirements and the process dynamics. The method gives two set of linear algebraic equations, solution of which gives the controller parameters. The proposed method is also used for controller design of parametric uncertain system with dead time. The technique is demonstrated with two numerical examples and a good set-point response is achieved. Simulation results are obtained using MATLAB software.
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