The Web Based Controller

The Web Based Controller (WBC) is a simulation of a Plant (mass-spring-damper) with its position controlled by a PID regulator with independent gains. The plant is oscillatory with a lot of damping. It has a Mass in kg, a Damping Constant in N.s/m and a Spring Constant in N/m. PID gains for proportional (Kp), integral (Ki) and derivative (Kd) may be set and the resulting step response is displayed, along with the %Overshoot, the time constant Tc to reach 63% and the Bandwidth (1/Tc) in rad/sec. These may be used for studying the effects of PID gain settings and to practise tuning a PID controller.

Leave the parameters for the Plant at the default values. Below are several exercises. It will not be possible to obtain an exponential step response with the given Plant parameters.

1. Find Kp and Ki to give the highest Bandwidth with no overshoot.
2. Find Kp and Ki to give a Bandwidth = 1.0 r/s with no overshoot. Repeat for 0.5 r/s. Think about the ratio of Ki and Kp.
3. Find Kp and Ki to find the greatest Bandwidth and less than 7% overshoot.
4. Add Kd=50 and readjust Kp and Ki for the fastest response with no overshoot. Think about the powerful effect of derivative gain.
5. Adjust Kp, Ki and Kd to make the system unstable. Numerical errors in the simulation may result in invalid results after 3 or more cycles.

Set the Plant parameters to mass=0, b=10, k=2. This tuning simulates a variable speed drive speed loop.
Set Kd=0 to make a PI regulator.

1. Adjust Kp and Ki to give a Bandwidth = 5.0 r/s with no overshoot. Repeat for 2.5 r/s. This response should be exponential. Think about the ratio of Ki and Kp for this example.

Because it is easy to get lost in simulation space, the Stable button returns you to some reasonable conditions if you want to start afresh with any of these exercises.