Analysis and control of nonlinear phenomena in electrical drives

Abstract

Electrical motors are key to the growth of any modern society. In order to ensure optimal utilisation of the motors, the shaft speed and armature current must be controlled. Currently, the most efficient way of achieving both speed and current control in electrical motors is through power electronic switching, thus making the system both nonlinear and time varying. The combination of electric motors and control electronics is referred to as electric drives. Due to the inherent nonlinear nature of electrical drives, the system is prone to complex dynamical phenomena including bifurcations, chaos, co-existing attractors and fractal basin boundaries. The types of nonlinear phenomena that occur in some of the more common electrical drive systems, namely permanent magnet dc (PMDC) drives, series connected dc (SCDC) drives and switched reluctance motor (SRM) drives, are considered for analysis in this project. The nominal steady state behaviour of these drives is a periodic orbit with a mean value close to the reference value. But as some system parameters are being varied, the nominal orbit of the system referred to as the period-1 orbit, may lose its stability leading to the birth of new attracting orbit that is periodic, quasi-periodic or chaotic in nature. The most common technique for performing stability analysis of a periodic orbit is the Poincaré map approach, which has been successfully applied in DC-DC converters. This method involves reducing the continuous time dynamical system into a discrete time nonlinear iterative map and the periodic orbit into a fixed point. The stability of the periodic orbit then depends on the eigenvalue of the Jacobian matrix of the map evaluated at the fixed point. However, for some power electronic based system the nonlinear map cannot be derived in closed form due to the transcendental nature of the equation involved. In this project, the recently introduced Monodromy matrix approach is employed for the stability analysis of the periodic orbit in electrical drives. This method is based on Filippov’s method of differential inclusion and has been successfully applied in the stability analysis of periodic orbits in both low order and higher order DC-DC converters. This represents the first application of the technique in electrical drives. The Monodromy matrix approach involves computing the State Transition Matrix (STM) of the system around the nominal orbit including the STM at the switching manifold (sometimes referred to as the Saltation matrix). Also, by manipulating some of the parameters in the Saltation matrix, it is possible to control the instabilities and thus extend the system parameter range for nominal period-1 operation. The experimental validation of the nonlinear phenomena in a proportional integral (PI) controlled PMDC drive, which is absent in literature, is presented in this thesis. The system was implemented using dsPIC30F3010 which is a low cost and high performance digital signal controller.