New Orleans, Louisiana
June 26, 2016
June 26, 2016
August 28, 2016
This paper will present a classroom-proven control system experiment that conveys the fundamental concepts of designing a closed-loop system, including the PID controller tuning. The proposed experiment provides an opportunity for students to model, design, simulate, and implement a complete feedback control system in a very inexpensive way by using only a couple of quad op-amp ICs and a few discrete resistors and capacitors.
A mass-spring-damper mechanical system can be mathematically modeled as a position control system with object mass, viscous friction coefficient, and spring constant as parameters. A transfer function of this second-order system can be developed with force as input and position as output to study open-loop response of the system. Then a closed-loop position control system using a PID controller can be designed with reference position as input and actual position as output. Students can simulate the complete system using Matlab/SIMULINK and develop a set of proportional (KP), integral (KI), and derivative (KD) coefficient values to meet the system’s step response specifications in terms of overshoot/undershoot, settling time, rise/fall time, system stability, and steady-state error. Once the design is verified via simulation, the laboratory implementation of the system can start. As shown in Figure 1, the second-order mechanical system can be modeled with three op-amps, and the error generation circuit and PID controller can be implemented with one and four op-amps, respectively. This implementation approach lets students clearly see and manipulate each block of a typical feedback control system while still realizing a complete system with only two inexpensive quad op-amp ICs such as LM324A. From a pedagogical standpoint, students are able to study the effects of KP, KI, and KD on system dynamics just by varying the three 100 k potentiometers, independently or any combination thereof. This provides a simple and direct way to study the following commonly used PID controller configurations: P, I, PI, PD, and PID. Figure 2 shows the system response for PI and PID controller configurations, illustrating the benefit of adding a derivative component to the controller in reducing overshoot and improving transient response and system stability.
The full paper will present details of modeling, Matlab/SIMULINK simulation, and laboratory implementation of the proposed control system with a focus on studying the effects of KP, KI, and KD on the system’s dynamic performance and stability as well as steady-state error. A key goal of this paper is to present an inexpensive and easily implementable control system experiment via which students can investigate fundamental concepts relating system dynamics to controller configurations in a clear and concise manner. A strong feature of the proposed experiment is that students have full access to the system, allowing them to investigate controller-plant interaction at a fundamental level.
Figure 1: Implementation of a closed-loop feedback control system with PID tuning capability.
Figure 2: System response with PI Controller (KP = 66, KI = 13) [left] and PID Controller (KP =60, KI = 17, KD = 1.2) [right].
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