Tuning pid controller design and analysis of an inverted pendulum system

Inverted Pendulum systems are one of the most important engineering systems used in the solution of many engineering problems and control analysis with the application of control techniques. Before real-time control, balancing obtained by running computer mathematical models of these systems has been very challenging and important for modern control theory. Studies on these systems shed light on the design and control algorithms of many systems ranging from automotive, aircraft, spatial vehicles, defense vehicles, missile launchers to human marches, load bearing robots and earthquake resistant building designs. Inverted-Pendulum is one of the most important basic systems used in control engineering. In this study, firstly, a mathematical model for the system was created. A mathematical model is a mathematical equation representing a process or the behavior of a system. The dynamic equations expressing these equations were obtained by using Newton's Second Law of Motion. Inverted-Pendulum is a nonlinear system. The dynamics equations of system have been obtained by linearization of the obtained equations. After all these studies, the control analysis of the system was made. In order to make the control analysis has been found transfer function, characteristic equation, state-space model, poles, zeros and singular points of Inverted-Pendulum system. In control analysis of system, Root-Locus, Nyquist and Bode diagrams of system were obtained and discussed and were also investigated the controllability and observability of the system depending on the state variables. In addition to the PID (Proportional-Derivative-Derivative) and LQR (Linear Quadratic Regulator) controls made in the literature, the control of the system was also carried out successfully by designing the Tuning-PID control algorithm. Here, PID control coefficients (k_p,k_i,k_d) were determined by using the Ziegler-Nichols method. Finally, the performance of these control methods designed and the necessary control analyzes were performed and the results were obtained. Keyword: Inverted pendulum, PID controller, LQR control, MATLAB Program, Root-Locus.