Modeling and position control of the inverted pendulum system

Abstract

It is difficult to find the unknown/unmeasurable parameters of in system and the control parameters of the system by experimenting on the real system. The aim of this study is to first find the unknown parameters of the system by creating a mathematical model of the system in a simulation environment, and then to obtain the PID control parameters in the simulation environment with the found parameters. Thus, to see the conformity of the control of the real system to the mathematical model and to show that the unknown parameters can be easily found through simulation. In this study, the position control of the inverted pendulum system, which is one of the control system examples, was carried out to maintain balance. For position control, a mathematical model of the system was first created, then a simulation model was created and experiments were conducted. Experiments were then conducted on a real system using the parameters obtained from the system simulation model. In this study, the car to which the pendulum was connected was controlled to maintain the inverted pendulum system in balance. In the system, a servo motor is used to move the car. The balance position is controlled by moving the car along the horizontal axis. An encoder with a full revolution of 4096 pulses was used to obtain the balance position information of the inverted pendulum. The sensitivity of the encoder used is approximately 11.37 pulses per degree. The experimental setup of the system was created by connecting the rod used as an inverted pendulum to the Encoder. The experimental setup was controlled with a program written in PLC (programmable logic controller). The servo motor that moves the car to ensure that the inverted pendulum remains in balance is controlled by the driver. The servo motor driver was driven by a control signal with ±10 volts sent from the PLC. The servo motor driver is programed to run at ±1000 rpm in response to this control signal. The unmeasurable parameters of the system were experimentally determined. For this purpose, the parameters in the mathematical model were obtained by swarm optimization (PSO) using the measurement values obtained by operating the experimental setup as a simple pendulum. A simulation model of the system was created using the parameters obtained with PSO and the mathematical model. PID (Proportional Integral Derivative) controller was used in the simulation model. The PID parameters required to control the system were obtained using particle swarm optimization in the simulation model. The PID parameters obtained using PSO were used as the parameters of the PID controller in the real experimental system.  It was observed that the results obtained in the simulation system and those obtained in the real system overlapped, and the design of the simulation model in this study was successful.