If Kp is increased further it will only lead to increase in ripples or overshoot. Also observe that the ripples have started appearing in the output. Keeping Kp = 200, Ki = 0, Kd = 0 the step response of the system is So it’s clear now that increasing Kp will reduce the steady state error. Keeping Kp = 100, Ki = 0, Kd = 0 the step response of the system is Now let me increase the Kp further and observe the response. Much better than the open loop response! (The curve in red shows the open loop step response of the plant) Keeping Kp = 10, Ki = 0, Kd = 0 the step response of the system is Lets see the effect of proportional element on the system output.

Now lets see what is the effect of PID controller on the system response. That’s quite high! Also observe that the settling time is around 3 sec. It can be seen that the step response output is close to 0.035. (Click on the image to get an enlarged picture) The open loop step response of the above plant is – The step response of a system is the output of the system when the input to the system is a unit step. Let the transfer function of the plant be 1 / ( s^2 + 20s + 30 ). Let me assume a suitable mathematical model for the plant and then go ahead with designing the controller. The matlab code is provided at the end of this article. So I simulated a PID controller in matlab. The best way to understand something is by simulating it. Kp, Ki, Kd are the gains of P, I and D elements respectively. The block diagram of a PID controller is shown below –Ī PID controller consists of a Proportional element, an Integral element and a Derivative element, all three connected in parallel. Mathematically model the plant to be controlled. The two steps in the design of a control system are –ġ.

The input to the controller is the error. The input to the system is the ‘setpoint’, ie the desired output. This is an attempt to explain PID controller with minimum use of maths.Ī simple closed loop control system consisting of a controller and a process (or plant) is shown below.

Kd max response