This page takes you to a simulator for a second order system being controlled by a proportional controller.  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 second order system.
• The plant is assumed to have a damping ratio, z and an undamped natural frequency, w_n. You can set those parameters 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 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, assuming a constant input, or an input that becomes constant after some time.
• w_n -  The undamped natural frequency for G(s)
• z - The damping ratio 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 second order systems.

P1

• First, predict the steady state for these conditions.
• K = 2
• K_p = 5
• z = 2.0
• w_n = 0.1
• Desired Output = 2.0
• Run the simulator and determine the steady state for those conditions.
• Compare the theoretical and simulated steady state value.
• Determine the amount of overshoot in the closed loop system response.

• 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 amount of overshoot in the closed loop system response.  In addition, compare the overshoot in this problem with the overshoot for Problem P1.