PID CONTROLLER DESIGN FOR INTERVAL TYPE SYSTEMS USING STABILITY BOUNDARY LOCUS

Abstract

By the end of the last century, control has become an inescapable but mostly unseen element of the present world. Examples ranges from common household products, for example, air-conditioners, hot water heaters etc. to large scale systems like aircraft, chemical plants, and manufacturing industries. Over the last few decades, proportionalintegral- derivative (PID) and its variant controllers have been predominantly used in the industrial processes because of their design simplicity and ease in implementation. There are a handful of techniques available in the literature for the tuning of PID controllers. Generally, these techniques fall under the three categories namely, heuristic tuning, rule-based tuning, and model-based tuning techniques. The trial-and-error method is an example of heuristic tuning. Rule-based tuning methods are Ziegler-Nichols, Cohen-Coon, Chiens-Hrones-Reswick (C-H-R), Kappa-Tau, and Lambda methods. The internal model control (IMC) and stability boundary locus (SBL) belong to the modelbased PID tuning techniques. In this thesis, SBL technique of PID controller design has been implemented for load frequency control (LFC) problem of interconnected power systems and microgrid secondary frequency control. Further, the SBL-based PID controllers are designed to control the azimuth and pitch angles of a two-rotor aerodynamical system (TRAS) and for the control of a gimbal. The major advantages of SBL approach over other techniques are: • The SBL technique does not need parameters sweeping i.e., it does not require to test multiple data-points by the implementation of an algorithm many times with different parameter sets. • The SBL technique does not require linear programming to figure out a group of inequalities. • Apart from the system stabilization, the SBL methodology can be used for pole shifting that ensures a desired response settling time. Firstly, PID controllers are designed for LFC problem of a four-area power system using SBL approach to satisfy the requirement of specific gain margin and specific phase ix margin. For thiswork, linear power system model has been considered consisting of nonreheated, reheated, and hydro turbines. Then, SBL technique of PID controller design is employed for interval single area power system having specific gain margin and specific phase margin in the presence of communication delay. In this work, PID controllers are designed for single area power system having non-reheated thermal turbine with droop characteristics (NRTD) and then for single area power system having reheated thermal turbine with droop characteristics (RTD). The proposed approach is then validated on a realistic interval IEEE 39-busNewEngland test system with communication delay, GDB and GRC. Afterwards, parametric uncertainty margin (PUM) has been computed for a PI-controlled perturbed LFC system using Kharitonov’s theorem and SBL approach. Then, fractional order PID (FOPID) controllers for linear systems are synthesized in the presence of communication time delay, parametric uncertainties, and physical nonlinearities using SBL approach and big bang-big crunch (BB-BC) optimization. Further, FOPID controllers are designed for secondary frequency control of an islanded Microgrid in the presence of communication time delay using SBL methodology. Further, robust PID controllers are designed for the laboratory model of twin-rotor helicopter known as two rotor aero-dynamical system (TRAS) in the presence of communication time delay. The proposed control design approach for nonlinear TRAS is based on Stability Boundary Locus (SBL) technique of PID tuning. Then, line-of-sight (LOS) rate of a single-axis gimbal loop has been stabilized using a robust PID controller in the presence of time delay. The PID controller parameters are obtained by using SBL approach such that the overall gimbal stabilization loop will have desired specific gain margin and phase margin. Therefore, in this thesis, an attempt has been made to design PID controllers for linear, interval, and nonlinear systems in the presence of various system constraints, specific gain margin and phase margin, and communication time delay using the SBL approach. The generalized formulae are also developed for the computation of PUM for perturbed systems using SBL and Kharitonov’s theorem.