This page takes you to a simulator for a first order system being controlled by a proportional controller implemented digitally.  By clicking here, you can get the simulator.  It will allow you to simulate the system below.

• In the simulator, we assume that the plant is a first order system.
• The plant is assumed to have a time constant,t.  You can set the time constant in the simulator.  That means that the system is dynamic, and that the system dynamics will affect the performance of the entire closed loop system.
• For steady state operation, the output is proportional to the control effort (control signal) entering the actuator.  That constant is called K in the introductory note on proportional control.
• In the simulator, the A/D and D/A operate every two seconds.
• In the simulator, the following items can be set.
• K - The DC gain for G(s)
• In other words, it is the ratio of the steady state output to the steady state input to the plant, assuming a constant input, or an input that becomes constant after some time.
• t - The time constant for G(s)
• K_p - The proportional gain in the controller.
• The Input.
• The input is a constant, but you can set the value.
• To operate the simulator,
• Enter the parameters as listed above.
• Click the Start button.  A plot will be generated.
• Use Alt+PrintScreen to put a copy of the plot picture on the clipboard after highlighting the plot window.

        Here are some problems to help you understand the operation of proportional control to control first order systems.

P1

• First, predict the steady state for these conditions.
• K = 2
• K_p = 5
• t = 50 seconds
• Desired Output = 2.0
• Run the simulator and determine the steady state for those conditions.
• Compare the theoretical and simulated steady state value.
• Note the form of the response.  Does it look like the system has time constant behavior?  Can you compute a time constant for this system?

• Now, re-do Problem P1 but change the value of the proportional gain to the value below.
• K_p = 10
• Run the simulator and determine the steady state for those conditions.
• Compare the theoretical and simulated steady state value.
• Determine the time constant of the complete system when it is being controlled and compare your experimental time constant value with the valiue of the time constant set (as above).  In addition, compare the time constant in this problem with the time constant for Problem P1 if that is possible.