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.