Performance criteria and tuning of fractional-order cascade control system
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Ó Indian Academy of Sciences Sadhana(0123456789().,-volV)FT3 ](0123456789().,-volV)
Performance criteria and tuning of fractional-order cascade control system SOMNATH GARAI1, PRIYOBROTO BASU2,* , ASHOKE SUTRADHAR1 and ANINDITA SENGUPTA1 1
Department of Electrical Engineering, Indian Institute of Engineering Science and Technology, Shibpur, Kolkata, India 2 Department of Instrumentation and Control Engineering, Calcutta Institute of Engineering and Management, Kolkata, India e-mail: [email protected]; [email protected]; [email protected]; [email protected] MS received 5 May 2020; accepted 5 July 2020 Abstract. Industrial process control systems suffer from the overshoot problem. Designing the controller plant models by conventional Proportional Integral Derivative (PID) may increase the rise time, settling time and overshoot. Cascade control is a remedial measure undertaken to overcome these problems. In this paper, we present a new cascade model using fractional-order PIDs. The fractional-order cascade controller can be expressed by fractional-order differential equations. Different laws proposed in the field of fractional calculus form the theoretical part in evaluating the equations and designing the controllers. The new structure gives improved responses for the first-order and second-order systems with time delay. Better simulation results are obtained by introducing Smith predictor in primary and secondary loops. Detailed analyses have been done on the stability, performance criteria and disturbance rejection. The usefulness of this proposed cascade structure and its superiority over normal cascade are illustrated with examples. Keywords. Cascade control; fractional-order PID controllers; model mismatch; robust; Smith predictor; stability analysis.
1. Introduction Proportional-Integral-Derivative (PID) controllers, being easier to implement and understand, are widely utilized in industries. However, advances in the field of fractional calculus enhance designing of fractional-order PID (FOPID) controllers. The advantage is that in FOPID we have five tuning factors, i.e. proportional gain (Kp), integral gain (Ki), derivative gain (Kd), lambda (k) and mu (l), to get better performance than in classical PID controllers [1]. To tune the FOPID, one of the tuning methods is by the PSO algorithm as established in [2] and [3]. To tune fractional-order PI (FOPI) controllers, relay auto-tuning method is established in [4]. This method is appropriate when the process model is unable to be decided precisely. Stability boundary locus method can be applied to design FOPIk by satisfying the required Gain Margin (GM) and Phase Margin (PM) of the system [5]. A new tuning rule is
*For correspondence
illustrated in [6], where a new set of Optimal FractionalOrder Proportional Integral (OFOPI) tuning rules are proposed. Composition of DE and Smith predictor methods gives efficient control of time delay processes [7]. A new method is represented to reduce the overshoot and increase robustness by cascading
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