**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.

This year we utilized ECP's Simulink drivers as our plants, and all of the labs were done in Simulink. The Simulink drivers were configured so that the ECP 210 systems used units of cm for both input and output, and the ECP 205 systems used units of radians for both input and output.

**Lab 1: ***In this laboratory, the students reviewed
using Simulink and using a Matlab script to drive a Simulink model. They
modified open loop systems to make closed loop systems and utilized a simple
model matching controller. They also went through a guide to be sure their
system was properly set up.*

*
Lab 1,
openloop_driver.m,
openloop.mdl,
state_model_1dof.mat,
guide.pdf*

**Lab 2: ***In this laboratory, the students estimate the
damping ratio and natural frequency of four systems we model as a second order
systems. There are models for both the rectilinear system and torsional systems. 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. *

*
Lab 2,
Log_Dec.m,
Log_Dec.fig,
compare1.m*

**Lab 3: ***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.*

*
Lab 3***,
***
process_data_1dof.m,
model_1dof.m,
get_A.m*

**Lab 4: ***In this lab the
students obtain two models of a two degree of freedom system. They then convert
this transfer function model to a state variable model.*

*
Lab 4 (rectilinear),
Lab 4 (torsional)
process_data_2dof.m,
model_2dof.m*

**Lab 5:*** In this laboratory, the students utilize
model matching approaches to control the behavior of the system. ITAE, Deadbeat, 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 6: ***This is a software lab, where the students
are introduced to Matlab's ***sisotool ***for designing controllers for
single input single output systems. *

**Lab 7: ***In this lab, the students control three one
degree of freedom systems using PID controllers with real and complex zeros.
They also explore the use of dynamic prefilters to cancel the zeros in the
closed loop transfer function.*

**Lab 8: ***In this lab the students 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 9: ***In this lab the students use state variable
feedback to control 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.*

*
Lab 9,
Basic_1dof_State_Variable_Model.mdl,
Basic_1dof_State_Variable_Model_Driver.m*

**Lab 10: ***In this lab the students first model a
regular pendulum on a single cart (a 2 dof system). They then control the
regular pendulum. After this is working correctly, the students get a model for
the inverted pendulum and try and control it. The students really like this lab!*

Lab 10, process_data_pendulum.m, model_pendulum_full.m, Basic_2dof_State_Variable_Model.mdl, Basic_2dof_State_Variable_Model_Driver.m, model_inverted_pendulum_full.m