Peter Nachtwey
Member
The is the first system that uses complex or imaginary poles. Complex poles oscillate. RLC circuits, masses on springs, pendulums, masses on shafts and hydraulic cylinders are examples of systems with complex poles. I designed this spread sheet to be more challenging yet, but I know there will be some that do quite well.
If you notice the damping factor is set to .1. This is very low and I would have strong words with a mechanical designer that designed a system like this. If you get stuck you may increase the damping factor to about .7 until you get the feel for tuning the system. Then gradually move the damping factor back down.
These systems that oscillate can be quite challenging when the desired actual profile is not allowed to overshoot the target profile.
After you get the system tuned you should try doubling the frequency and halving the amplitude. Notice that it is impossible to tune the system if the target frequency is higher than the natural frequency of the system. Too many times I see systems where the controller is to control an actuator above the natural frequency. This is impossible many times because the system gain drops and the controller can only output +/- 10 volts. Notice that the frequency of the target generator is double the natural frequency of the system. This system is on the edge, but that is why it will be a challenge.
There are three graphs on this sheet. One where the target velocity is doing a sine waving, one where it makes step jumps and the last is just to show you how much the system rings in open loop.
I can get the ISE to 153 for the sine wave and the ITAE to 44.69 for the ITAE with out cheating. Have fun.
Tuning a PID Controlling a Mass on a Spring
If you notice the damping factor is set to .1. This is very low and I would have strong words with a mechanical designer that designed a system like this. If you get stuck you may increase the damping factor to about .7 until you get the feel for tuning the system. Then gradually move the damping factor back down.
These systems that oscillate can be quite challenging when the desired actual profile is not allowed to overshoot the target profile.
After you get the system tuned you should try doubling the frequency and halving the amplitude. Notice that it is impossible to tune the system if the target frequency is higher than the natural frequency of the system. Too many times I see systems where the controller is to control an actuator above the natural frequency. This is impossible many times because the system gain drops and the controller can only output +/- 10 volts. Notice that the frequency of the target generator is double the natural frequency of the system. This system is on the edge, but that is why it will be a challenge.
There are three graphs on this sheet. One where the target velocity is doing a sine waving, one where it makes step jumps and the last is just to show you how much the system rings in open loop.
I can get the ISE to 153 for the sine wave and the ITAE to 44.69 for the ITAE with out cheating. Have fun.
Tuning a PID Controlling a Mass on a Spring