**ME 406 Control Systems **

In ME 406, we emphasize *model based
*design. In particular, we find parametric models of the rectilinear plant in
1 DOF and 2 DOF modes. The quality of control delevered from the ensuing model
is directly limited by the quality of the model. 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 compare the response of several 1 DOF systems.
They first investigate the effects of varying system mass, stiffness, and
damping. By using the known differences between effective system inertia, they
are then able to solve an overdetermined system of equations to get a good
estimate of system effective mass and stiffness. System damping then follows
from a lumped parameter model of the system. Although the linear models match
the experimental model well, there are some differences due to unmodeled
non-linearities in the real system. This lab emphasizes second order response
characteristics, and basic mechanical system modeling.*

**
Lab 2: ***In
this laboratory, the students use the system experimental frequency response to
determine a transfer function model of the system in 2 DOF mode with rigid body
dynamics included. Building on the paramters determined in Lab 1, and using
linear modeling theory, they are able to construct a parametric state-space
model. This lab emphasizes the meaning of Bode plots, rigid body dynamics,
transmission zeros, and advanced mechanical system modeling.*

**
Lab 3:*** In
this laboratory, the students investigate the properties of basic control
actions. Using the system mass determined in Lab 1, and system gain from the
user's manual, they form a double-integrator plant model. The student's are then
able to directly select the P I and D gains to match closed-loop requirements.
Students are encouraged to physically feel the control forces due to P, D, and I
control. They should then be able to better quantify the effects of each type of
feedback. Interested students are encouraged to try Ziegler-Nichols tuning of P
and PID gains for extra credit.*

**
Lab 5:*** This
is a software lab, used to review some of the features of the Matlab Control
Toolbox. The CAD package SISOTOOL is introduced. The students will perform
computer aided design of P, PI, PD, and PID controllers. This exercise helps to
reinforce the relationship between the Root Locus plot and the Bode
plot.*

**
Lab 6: ***In
this lab the students design a lead-lag cascade controller for the 1 DOF system.
They then implement the controller on the hardware plant, and iterate their
design to meet a steady-state error requirement.*

**
Lab 7:
***In
this lab the students design a lead-notch controller for the 2 DOF system
identified in Lab 2. They use SISOTOOL extensively for this design. After
implementing their design in the lab, they are encouraged to investigate ways to
increase closed-loop gain and hence decrease steady state error.*

**
Lab 9: ***In this lab the students use Ackermann's formula to directly place the
closed-loop poles at desired location using state feedback. The 2 DOF plant
identified in Lab 2 is used. The professor provides sets of good closed-loop
poles based on the LQR root locus. Performance is shown to improve drastically
by using state feedback.*

**
Lab 10: ***In this lab the students attempt to match the performance of the state
feedback controller by choosing the desired closed loop poles and designing a
dynamic prefilter and return path compensation by solving the Diophantine
equations. *