Input dependent Nyquist plot for limit cycle prediction and its suppression using fractional order controllers

Abstract

In practical systems having separable hard nonlinearities, sustained oscillation is detected at the steady state response due to the presence of stable limit cycles. An optimization problem is proposed to tune the fractional order controller parameters for system with multiple-nonlinearity to suppress the limit cycle magnitude in addition to meet the desired closed loop specifications. To extend the applicability of the existing Nyquist plot for predicting this limit cycle, an input dependent Nyquist plot is proposed in this paper. A servo system with backlash and relay nonlinearities is considered as a case study for limit cycle prediction with obtained fractional order controllers using an input dependent Nyquist plot. The predicted limit cycle information is compared with optimization results, input dependent root locus and are validated through closed loop simulations. Further, the robustness of the designed controllers are tested under system parameter uncertainty, disturbance and measurement noise conditions.

Heuristic algorithms based optimal tuning of FOLQI controller for quadruple tank process under disturbance conditions

“…(i) FO-PID controller for magnetic levitation system providing better performance in terms of IAE, ISE, ITAE and control effort compared to integer order PID controller, 24 (ii) FO-PI/FO-PD controllers providing better suppression of limit cycle over conventional PID controller for servo plant with separable non-linearity, [25][26][27] (iii) unified controller parameter expressions of FO controllers are derived for universal plant having complex coefficient plus fractional complex order derivative with dead time to meet desired frequency domain specifications, 28 (iv) FO adaptive controller gives better performance in terms of control effort than classical controllers for variable time delay process system, 29 (v) FO-PI along with conventional feedforward controller design using classical frequency domain approach for level control system provide better performance than conventional controllers along with feedforward controller in terms of settling time, overshoot and level tracking, 30 (vi) FO-Sliding Mode Controller (SMC) provides better performance characteristics like finite time convergence and reduced chattering effect in the presence of parameter uncertainties compared to conventional SMC 31 and (vii) dual mode adaptive FO-PI with feedforward controller resulting better performance than decentralised PI, Quantitative Feedback Therory (QFT) and SMC controller in terms of settling time, overshoot and ISE. 10 On the other hand, controller parameters are tuned using various meta-heuristic algorithms by formulating objective function with constraints.…”