**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. *

*
Lab3,
ITAE_0.m,
ITAE_1.m,
quadratic.m*

**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. *

**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.*

**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.*

**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.**