Abstract
In this paper, a simple method for finding the stability region of feedback control system with One Non-Integer Plus Time Delay (NIOPTD-I) plant and fractional order Proportional Integral Derivative (FOPID) controller is presented. Analytical expressions for finding the asymptotic stability regions in (X, Y, Z) space are derived using D-partition method. Stability regions are obtained for various fractional orders of P\(I^{\lambda }D{^\mu }\) controller in the range of (0, 2). Fractional order parameters are chosen such that larger stability region in positive direction than integer order parameters is obtained. Controller tuning parameters are chosen from the obtained stability region. The use of proposed FOPID controller for the NIOPTD-I plant increases the stability region and also the degree of freedom increases from three to five in comparison to FOPI controller. Knowledge of these stability regions makes design of controller easier. Effectiveness of the proposed method is illustrated with examples, which shows better control performance.
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