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Lab 4: Steady-State Performance of Control Systems - EC2300, Slides of Control Systems

The procedure for lab 4 of the ec2300 control systems course, focusing on steady-state performance. Students will investigate the steady-state error of a control plant using step, ramp, and parabolic inputs. They will use the ecp software to execute the lab and analyze the results in matlab. The report should include the theory behind steady-state error, observations, and comparisons of error plots, identification of system type, and conclusions.

What you will learn

  • What causes steady-state error in a control system?
  • How is the steady-state error of a control plant determined using the ECP software?
  • Compare the steady-state error plots for step, ramp, and parabolic inputs.

Typology: Slides

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EC2300 Control Systems Lab 4 Steady-State Performance
1
Lab 4r4.doc, 5 April 2006
Lab 4: STEADY-STATE PERFORMANCE
Section 1 -- Background Information
The steady-state error is the difference between the output (actual state) and the input (commanded state)
after the transient response has passed. The primary source of steady-state error is due simply to the type
of input (step, ramp, or parabola) that stimulates the control plant. Another cause is attributed to the system
type as defined by the form of the transfer function G(s). The effects of these error sources will be
observed during this lab procedure.
Section 2 Procedure
2.1 Steady-State Error of the Control Plant with Step Input
For the first part of this lab, the control plant will be excited with a step input, and the steady-state error
determined.
2.1.1 Setup the Control Plant. The torsion system will be set up with two (2 each) weights loaded on the
bottom disk only. The weights are secured 180 degrees apart from each other such that the outside edge of
each weight is tangent to the 9-cm radius line (last line on the disk).
2.1.2 Start the ECP software program.
2.1.3 Record the ECP Station Number, as each ECP station will have slightly different system
characteristics.
2.1.4 Energize the control system by pushing the “ON” button on the ECP controller.
WARNING
The system is now energized and will rotate at potentially high speeds when a
control voltage is applied to the motor of the torsional system. At any point the
motion of the system can be stopped by pressing the OFF (red) button on the ECP
controller box.
2.1.5 Setup the ECP Program
a. Set the system units to degrees: SetupàUser Units, select degrees
b. Select SetupàControl Algorithm.
Select Continuous, then PI with Velocity Feedback
Click on Setup Algorithm. In the new window, enter the following:
o Kp = 0.2
o Kd = 0.02
o Ki = 0
o Feedback Encoder 1
Implement Algorithm, then click OK
c. Select Dataà Setup Data Acquisition
Sample Period (servo cycles) = 2
Selected Items should be Commanded Position and Encoder 1 Position
d. Select CommandàTrajectory
Select Impulse and Unidirectional moves. Click Setup.
Select Closed Loop Impulse and set
o Amplitude (degrees)=180
o Pulse width (msec) = 3000
o Reps = 1
o Dwell Time (msec)= 0;
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Lab 4: STEADY-STATE PERFORMANCE

Section 1 -- Background Information

The steady-state error is the difference between the output (actual state) and the input (commanded state) after the transient response has passed. The primary source of steady-state error is due simply to the type of input (step, ramp, or parabola) that stimulates the control plant. Another cause is attributed to the system type as defined by the form of the transfer function G(s). The effects of these error sources will be observed during this lab procedure.

Section 2 – Procedure

2.1 Steady-State Error of the Control Plant with Step Input For the first part of this lab, the control plant will be excited with a step input, and the steady-state error determined.

2.1.1 Setup the Control Plant. The torsion system will be set up with two (2 each) weights loaded on the bottom disk only. The weights are secured 180 degrees apart from each other such that the outside edge of each weight is tangent to the 9-cm radius line (last line on the disk).

2.1.2 Start the ECP software program.

2.1.3 Record the ECP Station Number, as each ECP station will have slightly different system characteristics.

2.1.4 Energize the control system by pushing the “ON” button on the ECP controller.

WARNING The system is now energized and will rotate at potentially high speeds when a control voltage is applied to the motor of the torsional system. At any point the motion of the system can be stopped by pressing the OFF (red) button on the ECP controller box.

2.1.5 Setup the ECP Program a. Set the system units to degrees: Setup‡User Units, select degrees b. Select Setup‡Control Algorithm.

  • Select Continuous, then PI with Velocity Feedback
  • Click on Setup Algorithm. In the new window, enter the following: o Kp = 0. o Kd = 0. o Ki = 0 o Feedback – Encoder 1
  • Implement Algorithm, then click OK c. Select Data‡ Setup Data Acquisition
  • Sample Period (servo cycles) = 2
  • Selected Items should be Commanded Position and Encoder 1 Position d. Select Command‡Trajectory
  • Select Impulse and Unidirectional moves. Click Setup.
  • Select Closed Loop Impulse and set o Amplitude (degrees)= o Pulse width (msec) = 3000 o Reps = 1 o Dwell Time (msec)= 0;

e. Utility ‡ Zero Position (to reset encoders to zero)

2.1.6 Select Command ‡Execute, Normal Data Sampling. Click Run to load and execute the program. With the trajectory set up as described above, the disk should rotate 180 degrees very rapidly and hold this position for 3 seconds before relaxing to its rest position.

2.1.7 Plot Data: Select Plotting ‡ Setup Plot. For the left axis choose Commanded Position and Encoder 1 Position. Select Plot Data.

2.1.8 Export the raw data and plot the data in Matlab. Using the Matlab subplot command, make two plots: 1) In the first subplot window, show the commanded position and the actual position of the disk with time on the horizontal axis. 2) In the second subplot window, show the error. This is just the difference between the commanded and the actual position, also with time on the horizontal axis.

2.2 Steady-State Error for a Ramp Input For this part of the lab procedure, you will utilize the ramp input of the ECP program to explore the steady- state error.

2.2.1. Select the following in the ECP program window: Select Command‡Trajectory a. Select Ramp and Unidirectional moves. Click Setup. o Distance (degrees)= o Velocity (degrees/sec) = 720 o Dwell Time (msec) = 0 o Number of reps = 1 b. Utility ‡ Zero Position (to reset encoders to zero) c. Command ‡ Execute. Click Run.

2.2.3 Plot the Data: Select Plotting ‡ Plot Data.

2.2.4 Save and Plot the Data in Matlab.

2.3 Steady-State Error for a Parabolic Input For this part of the lab procedure, you will utilize the parabolic input of the ECP program to explore the steady-state error.

2.3.2. Select the following in the ECP program window: a. Command‡Trajectory. Select Parabolic and Unidirectional moves. Click Setup. o Distance (degrees)= o Velocity (degrees/sec) = 900 o Accel Time (msec) = 2500 o Dwell Time (msec) = 0 o Number of reps = 1 b. Utility ‡ Zero Position (to reset encoders to zero) c. Command ‡ Execute. Click Run.

2.3.3 Plot the Data: Select Plotting ‡ Plot Data.

2.3.4 Save and Plot the Data in Matlab.

Section 3 -- Report

Submit a report in the standard format for this class. In the Introduction discuss the relevant theory that was presented and explored during the lab. In the Results and Analysis discuss your observations of the