Nonlinear phenomena in piecewise-linear nonlinear mechatronic systems

Many unexpected irregular behaviours caused by nonlinearities arise in mechanical and mechatronics engineering systems. The most common nonlinearities in the engineering practice are the friction, saturation, hysteresis, dead band and the backlash. Another source of nonlinearities caused by the controlled switching actions in power electronics converter. They play important role in up-do-date high-performance digitally controlled engineering systems, from milling machines via robotics through to the utilization of renewable energies, as they enable the efficient conversion of electric power to mechanical power and vice versa, furthermore to convert the electric power from one form to another. In general, the power electronics converters are variable structure systems generated by a series of periodic switchings. Generally each structures can be modelled by linear time-invariant models therefore the systems are piecewise-linear. The overall systems are nonlinear as the switching times depend on one or more state variables or they are determined by nonlinear Pulse Width Modulation techniques. One of the main goals of the dissertation was the presentation, comprehension and explanation of some unexpected phenomena caused in piecewise-linear systems. The other goal of my work was to improve the reliability and extend the stability range of variable structure systems by novel auxiliary state vector technique. The dissertation is divided into three chapters based on the three main research topics. Chapter 1 presents the DC components and subharmonics generated by the carrier based PWM techniques for high speed or high-pole count motors, where the necessarily high fundamental frequency and the limited carrier frequency result in low frequency ratio. An expression providing the exact value of the DC component when the frequency ratio is integer is derived. By using the expression the effect of the frequency ratio, the amplitude ratio, the phase shifting between the carrier and the reference signal, the modulation technique and the sampling form is shown. Furthermore the significant effect of the subharmonic voltage, current and flux components developed by different carrier based PWM techniques for the operation of induction machine is presented, when the frequency ratio is not integer and small. The theoretical results are verified by simulations and experiments. Chapter 2 concerns with the stability analysis of two current controlled variable structure piecewise linear systems. One of them is the peak current mode controlled permanent magnet DC drive system and the other one is the digitally implemented average current mode controlled Power Factor Correction (PFC) converter. The stability analysis were carried for both cases by using an earlier published novel method implying the so-called auxiliary state vector. It is demonstrated that the method is capable to determine straightforward the Jacobian matrix without the derivation of the Poincar Map Function (PMF). Based on the eigenvalues of the Jacobian matrix the stability border could be calculated. Furthermore the chapter presents that the method inherently contains the feasibility to extend the stability range by adding a stabilizing signal into the control loop and the calculation of the parameters of the stabilizing signal. The theoretical results of the stability analysis and the effect of the stabilizing signal were verified for both systems by computer simulations and laboratory measurements Chapter 3 deals with a speed sensor-less Field Oriented Controlled induction machine drive, when shunt resistors, placed on the bottom of the three phase inverter legs, are applied to measure the stator currents which limits the sampling frequency of the current. It results that the ratio of the sampling to the actual fundamental frequency is low around the maximum speed of a high speed or high-pole count motor. The chapter demonstrates by computer simulation and experimental results that in this case the stability range of the drive can be extended by approximating the rotor flux angle change and applying Double Sampled Space Vector Modulation technique instead of Regular Sampled one.