Nonlinear Dynamic Surface Control of Chaos in Permanent Magnet Synchronous Motor Based on the Minimum Weights of RBF Neural Network

This paper is concerned with the problem of the nonlinear dynamic surface control (DSC) of chaos based on the minimum weights of RBF neural network for the permanent magnet synchronous motor system (PMSM) wherein the unknown parameters, disturbances, and chaos are presented. RBF neural network is used to approximate the nonlinearities and an adaptive law is employed to estimate unknown parameters. Then, a simple and effective controller is designed by introducing dynamic surface control technique on the basis of first-order filters. Asymptotically tracking stability in the sense of uniformly ultimate boundedness is achieved in a short time. Finally, the performance of the proposed controller is testified through simulation results

Optimization of the Parameters of RISE Feedback Controller Using Genetic Algorithm

A control methodology based on a nonlinear control algorithm and optimization technique is presented in this paper. A controller called “the robust integral of the sign of the error” (in short, RISE) is applied to control chaotic systems. The optimum RISE controller parameters are obtained via genetic algorithm optimization techniques. RISE control methodology is implemented on two chaotic systems, namely, the Duffing-Holms and Van der Pol systems. Numerical simulations showed the good performance of the optimized RISE controller in tracking task and its ability to ensure robustness with respect to bounded external disturbances

Limit Cycle Analysis for Spacecraft with Pulsed Thrusters

Throughout the last decades, attitude control systems with switching actuators and discrete sensors have been used in satellites subjected to slowly varying disturbances. Sun sensors are usually employed. Such sensors are discrete and, typically, slower than actuators. Several types of on-off thrusters are employed as actuators, such as hydrazine, cold-gas and pulse plasma thrusters. These thrusters are typically affected by switching constraints. Due to these constraints and the disturbances, the system shall operate in limit cycle conditions. Two types of limit cycles can occur: • Saturation limit cycles. • Disturbance limit cycles. Our purpose is the development of a controller design method which avoids saturation limit cycles - that are very expensive in terms of fuel consumption - and produces a disturbance limit cycle which meets amplitude and bandwidth requirements. A reference scenario will be presented and simulations will be performed to test potential outcomes. The first part of the thesis will study the methods used to predict limit cycles. Particular emphasis will be given to the classical describing function theory. After that, we will develop the new dual-input describing function theory which can deal with slowly varying disturbances. In order to address strange behaviors the classical Tsypkin method will be presented and the hybrid Tsypkin-dual-input describing function method, which takes into account disturbances, will be applied to our case. In the second part, we will focus on the design methods of the controller. The Kharitonov approach, which is robust and uses the classical describing function theory, will be studied in detail. In the end we will introduce the new dual-input Kharitonov approach, developed by using the dual-input describing function theory and capable of dealing with slowly varying disturbances

Nonlinear Aeroelasticity and Active Control of Airfoils Subjected to Gusts

In this thesis, the coupling effects of structural nonlinearities and a gust input on the aeroelastic behaviour of an airfoil are studied, and an adaptive controller which is effective for suppressing limit-cycle oscillations (LCOs) is designed. The dynamics of the airfoil are approximated via two- (pitch and plunge) and three-degree-of-freedom (pitch, plunge and flap) models. Different types of structural nonlinearities, such as free-play and hysteresis are considered in the modelling. The nonlinear dynamics is analyzed based on time history, power spectral density (PSD), phase-plane, and Poincar\'{e} section plots, along with the estimation of the dominant Lyapunov exponent for the chaotic-like motion. It is found that free-play and hysteresis nonlinearities may considerably reduce the critical flow velocity compared to the linear system. The dynamic responses of the nonlinear system to sharp-edged and 1-cosine gust profiles are obtained at different flow velocities and compared to those of the system with no gust input. In addition, basin of attraction is plotted to show the stability boundary of the system subjected to a sharp-edged gust with various amplitudes. It is discussed that as the gust becomes stronger, the likelihood of the occurrence of LCO increases. Based on the nonlinear model with a control surface, the suppression of LCO is studied. Without uncertainties, a PD controller together with a partial feedback linearized controller can effectively alleviate oscillations due to gusts and structural nonlinearities. Considering some uncertain structural parameters, an adaptive controller with estimation parameter update law is further designed to stabilize the system. A Lyapunov function is constructed and utilized to prove the stability of the system

Time-Delay Systems

Time delay is very often encountered in various technical systems, such as electric, pneumatic and hydraulic networks, chemical processes, long transmission lines, robotics, etc. The existence of pure time lag, regardless if it is present in the control or/and the state, may cause undesirable system transient response, or even instability. Consequently, the problem of controllability, observability, robustness, optimization, adaptive control, pole placement and particularly stability and robustness stabilization for this class of systems, has been one of the main interests for many scientists and researchers during the last five decades