Simulink PID Controller Tuning
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I am a new user to Simulink. I created a model and added a PID controller. When I tune the controller it says the response should be about 1 second with a 20% overshoot. When I run the model the reality is 1000 seconds with 10,000% overshoot. What could cause this to happen?
I created my own PID controller and modified the coefficients and it seems to be working, but I would definitely like to get the built-in PID controller working since I am spending about 5 hours just to tune my homemade controller.
I have been debugging for about a week now, I am not sure what look for. Any assistance would be greatly appreciated.
Arkadiy Turevskiy 2011-4-22
Alan actually sent me his model. He is trying to control the quadrotor position and orientation by controlling 4 rotor speeds.
1) In the most general case this is a coupled MIMO system, and PID Tuner would not work - it only works for SISO systems or MIMO systems that can be designed as a set of SISO loops. For a MIMO system like the quadrotor, the right tools are Robust Control Toolbox and/or Simulink Design Optimization.
2) The specific case Alan was working with is to make the quadrotor go up from 0 to 1 m, without changing x and y positions, and while keeping all attitude angles at zero. In this specific case all 4 rotor speeds are the same. The system effectively becomes a SISO loop described by the equation
where z is altitude, lift is PID Controller output, m is mass, and g is gravity. Alan applied PID Tuner to this system. When he accepted the design and ran it in Simulink, he observed huge overshoots he wrote about in his question.
This happened because PID Tuner works by linearizing the Simulink model. When linearizing the model zdotdot=lift/m-g, the resulting linearized model is zdotdot=lift/m. In other words, the tuner cannot see g - gravity, which in this case can be thought of as a huge input disturbance (10 times larger than the reference signal). So there is no error in the tuner here - it just does not know about the huge input disturbance acting on the system.
There are 2 ways to deal with this:
A. The better way: compensate for gravity in the feedforward path. You know what the gravity is, so just cancel it. Effectively your PID will then be calculating the lift force required in addition to gravity, not the total lift force. To do this in Simulink, add a constant term, equal to g*m to PID output.
B. The other, not recommended option - crank the bandwidth of the PID all the way up to cancel input disturbance. Not recommended as option 1 makes more sense in this case.
We have also put together a comprehensive page with resources on designing and implementing PID controllers in MATLAB and Simulink. It might provide some help as well.