A pole of this controller must be at zero and one of the zeros has to be very close To choose the proper gain that yields reasonable output from the beginning, we start with choosing a
Title( 'Response to a 0.1-m Step under PID Control')įrom the graph, the percent overshoot is 9mm, which is larger than the 5mm requirement, but the settling time is satisfied, You should see the response (X1-X2) to a step W like this: Keep in mind that we are going to use a 0.1-m step as our disturbance, to simulate this, all we need to do is to multiply
Let's see what the closed-loop step response for this system looks like before we begin the control process. Now we have created the closed-loop transfer function in MATLAB that will represent the plant, the disturbance, as well as We can find the transfer function from the road disturbance W to the output(X1-X2), and simulate: Now let's simulate the response of the system (the distance X1-X2) to a step disturbance on the road.
This can be implemented into MATLAB by adding the following code into your m-file: Let's assume that we will need all three of these gains in our controller. Where is the proportional gain, is the integral gain, and is the derivative gain. Recall that the transfer function for a PID controller is: The system model can be represented in MATLAB by creating a new m-file and entering the following commands (refer to the main problem for the details of getting those commands).ĭenp= ĭen1= Step, the bus body will oscillate within a range of +/- 5 mm and will stop oscillating within 5 seconds. For example, when the bus runs onto a 10-cm (X1-X2) has a settling time less than 5 seconds and an overshoot less than 5%. We want to design a feedback controller so that when the road disturbance (W) is simulated by a unit step input, the output Choosing the gains for the PID controllerįrom the main problem, the dynamic equations in transfer function form are the following:Īnd the system schematic is the following where F(s)G1(s) = G2(s).įor the original problem and the derivation of the above equations and schematic, please refer to the Suspension: System Modeling page.