ECE-320 Linear Control Systems

Since the predominant goal of this grant is to have students understand and appreciate the distinction between a model of a system and the real system, most of the Matlab routines used in the labs plot both the predicted response (based on the model) and the measured response (from the ECP system). A model of the system is necessary for the initial design of a controller, but the predicted response of the system may not match the true system response due to the simplified models being used.

Lab 1: In this laboratory, the students estimate the damping ratio and natural frequency of a system we model as a second order system. The system consists of a mass on a moving cart, springs, and damping. The parameters are estimated using both the log decrement method and by trying to match the measured step response with the predicted step response. Matlab GUI programs are used to make this more efficient.

Lab1, log_dec_step.m, log_dec_step.fig, fit.m, fit.fig

Lab 2: In this laboratory, the students estimate the damping ratio and natural frequency of a second order system using the log decrement method, then measure the frequency response of the same system. The frequency response of the transfer function estimated using the time domain method is compared with the measured frequency response. The measured frequency response is then used to estimate both the damping ratio and the natural frequency of the system. Matlab is used to compare the initial estimate of the frequency response with the measured frequency response, and then to determine the system parameters by optimizing the fit to the measured frequency response.

Lab2, log_dec.m, log_dec.fig, process_data.m, fit_bode.m, opt_fit_bode.m

Lab 3: In this laboratory, the students first estimate the natural frequency and damping ratio using both time domain and frequency domain methods. They then estimate the closed loop gain of the system (the motor is assumed to contribute only a gain). Finally, the students utilize model matching approaches to control the behavior of the system. Both ITAE and Quadratic Optimal closed loop transfer functions are utlized. Matlab is used to determine the controller when the plant and desired closed loop transfer functions are assumed to be known.

Lab 4: This is a software lab, where the students are introduced to Matlab's sisotool for designing controllers for single input single output systems.

Lab4, sisotool

Lab 5 and 6: In these labs, the students obtain a model of a single degree of freedom system, then attempt to meet design specifications utilizing integral (I), proportional plus integral (PI), proportional plus derivative (PD), and proportional plus integral plus derivative (PID) controllers. For each lab the students model and try to control different systems. The controllers are designed and simulated using Matlab's sisotool before they are implemented on the ECP equipment.

Lab5

Lab 7: In this lab the students obtain a model of a single degree of freedom system. the attempt to meet design specifications by choosing the desired closed loop poles and designing a controller by solving the Diophantine equations. Matlab is utilized to determine the controller when the plant and desired closed loop poles are known.

Lab7, diophantine.m

Lab 8: In this lab the students first obtain a model of a single degree of freedom system. They then convert this transfer function model to a state variable model. The closed loop poles are determined by either guessing state feedback gains or by utilizing Linear Quadratic Regulator control. Matlab is used to predict the response of the system (based on the model), determine the closed loop pole locations for the given feedback gains, and determine the appropriate prefilter gains.

Lab8, compare_tf_sv.m, state_variables_1cart.m

Lab 9:  In this lab the students first obtain a model of a two degree of freedom system. They then convert this transfer function model to a state variable model. The closed loop poles are determined by either guessing state feedback gains or by utilizing Linear Quadratic Regulator control. Matlab is used to predict the response of the system (based on the model), determine the closed loop pole locations for the given feedback gains, and determine the appropriate prefilter gains.

Lab9, process_data_2carts.m, model_2carts.m, state_variables_2carts.m

Lab 10:  In this lab the students first obtain a model of a three degree of freedom system. They then convert this transfer function model to a state variable model. The closed loop poles are determined by either guessing state feedback gains or by utilizing Linear Quadratic Regulator control. Matlab is used to predict the response of the system (based on the model), determine the closed loop pole locations for the given feedback gains, and determine the appropriate prefilter gains.

Lab10, process_data_3carts.m, model_3carts.m, state_variables_3carts.m

All of the laboratories listed above have either been utilized in ECE-320 or in ECE-521. In the fall of 2004 they will be utilized in ECE-320.