Reference no: EM133141950
MECH365 Laboratory: Design and implementation of PID controllers Assignment -
Aim - The objectives of this lab is to develop skills in
i) evaluating whether a plant requires a controller by looking at the root locus and the desired dominate pole positions.
ii) Determine a PID controller
System design requirements -
Given the system of figure below, design a PID controller so that the system can operate with a peak time that is one-third that of the uncompensated system at PO overshoot and with zero steady-state error for a step input. The plant transfer function is given at the end and you will use the one allocated to you.
Designs and Experiments -
The following are designs and experiments to be conducted using MATLAB. The designs follow a design process typically used to design controllers and it is required that you go through each step evidencing your work. One word document containing scanned calculations, MATLAB figures, and explanations for each section should be submitted via turnitin.
Uncompensated system evaluation -
Evaluate the performance of the uncompensated system to determine how much improvements in transient response is required.
a) Plot the root locus of the uncompensated system using the rlocus command, and include it in your report.
b) Find on the rlocus, the gainK when the overshoot is as given in your specification. Do this by clicking on the graph which should show you the parameters. Copy the figure showing the system values and put it in your report.
c) Record the corresponding uncompensated dominant poles at the value of gain K.
d) Plot the step response of the uncompensated system. Note this is a unity feedback system so you need to work out the closed loop transfer function first. K*G(s)/(1+K*G(s)). Then use the step function to plot the response.
e) Find the steady state error of the uncompensated system by calculation using the new gain obtained in b. This has to be done by calculation and shown in your report. Scan calculation and add to word document as an image.
Design PD controller -
Design the PD controller to meet the transient response specifications. The design includes adding a zero location and changing the loop gain. To do this we add (s+z) where z is the new zero for the derivative term) which should be to the left of the dominant poles so as to push the root locus towards the left.
a) Plot the root locus of the (s+z)G(s). If this has not moved the RL to the left use a better value for the zero.
b) Find on the rlocus, the gain K when the overshoot is as given in your specification. Do this by clicking on the graph which should show you the parameters. Copy the figure showing the system values and put it in your report. What is the effect on damping?
c) Record the corresponding compensated dominant poles at the value of gain K.
d) Plot the step response of the compensated system and the uncompensated on the same graph and discuss the results.
PID controller -
Determine using either Method 1 or method 2, the PID parameters with chosen gain K of 1st part. For this we use the uncompensated system. Either solve analytically or plot the step response.
a) Determine the gain K1, K2, K3, the PID parameters.
b) Simulate the system to be sure all requirements have been met.
a) Plot the step response of the compensated and uncompensated systems on the same graphon MATLAB.
b) Compare between the two graphs. Did the designed PID controller achieve the requirements? Find the steady state error of the compensated system at the dominant poles.
c) Fine tune the design if the simulation shows that the requirements have not been met.
Attachment:- Design and implementation of PID Assignment File.rar