Two Stage Fractional Order Control Approach to Design an Optimal Controller for A Small Size Rotor Having Internal Dissipation

A Conformal Mapping Based Fractional Order Approach for Sub-optimal Tuning of PID Controllers with Guaranteed Dominant Pole Placement

Abstract: A novel conformal mapping based fractional order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PIλDμ) controller have been approximated in this paper vis-a-vis a LQR tuned conventional integer order PID controller, to achieve equivalent integer order PID control system. This approach eases the implementation of analog/digital realization of a FOPID controller with its integer order counterpart along with the advantages of fractional order controller preserved. It is shown here in the paper that decrease in the integro-differential operators of the FOPID/PIλDμ controller pushes the open loop zeros of the equivalent PID controller towards greater damping regions which gives a trajectory of the controller zeros and dominant closed loop poles. This trajectory is termed as “M-curve”. This phenomena is used to design a two-stage tuning algorithm which reduces the existing PID controller’s effort in a significant manner compared to that with a single stage LQR based pole placement method at a desired closed loop damping and frequency.

Active stabilization of rotors with circulating forces due to spinning dissipation

Abstract: Destabilizing effects due to rotating dampers in gyrating or spinning systems govern their dynamic behavior very prominently. Tippe-tops and gyro-pendulums exhibit their seemingly counter intuitive behavior due to such dissipations. Rotors at speeds higher than certain threshold values become unstable due to rotating damping forces generated by dissipation in rotor material, couplings or due to friction in splines and tool tips. There are several techniques by which one may stabilize such rotors. Although the current methods in practice are quite effective for large or medium size rotors but these may not be suitable for small, mini or micro rotor systems. This paper proposes a class of alternative techniques to stabilize rotors any size through implementation of strategies developed here, however the selection of actuating mechanism would depend on the size of the rotor. In this paper the size of the rotor that may be actuated by piezo-electrical type actuators are considered. Thus may be called small si...

Inverse optimal control formulation for guaranteed dominant pole placement with PI/PID controllers

Abstract: This paper presents an analytical approach of guaranteed dominant pole placement tuning for PID controllers to handle second order systems. Analytical expression of PID controller gains are reported in terms of the system's open loop characteristics and desired closed loop damping ratio, natural frequency and relative dominance of pole placement. Inverse optimal control formulation has been done, considering that the PID controller gains are equivalent to optimal state feedback gains of a quadratic regulator and a brief comparison of the achievable cost of control for various specified open loop and closed loop conditions are reported. The idea has been extended for pole placement tuning of PI controllers as well to handle first order systems along with discussion about the corresponding inverse optimality.