I have nonlinear model, which I linearized around operating point. I've design PID loops to stabilize and control the system and it works fine for nonlinear model as well.
Then I decided to try LQR design. Again, I've used linearized plant to design LQR and then try it on non/linear model. For linear, it works beautifully. For nonlinear model, it doesnt work at all, even though I dont put any initial conditions nor disturbance, I just leave the system be as it is and run the simulation. This is my result: pitch is the yellow line, yaw is blue line.
As you can see, it stabilize itself in some sorts of different equilibrium and I have no idea how that happened and what can I do to fix it? Can it be also by just changing the coefficients in Q and R?
Thank you for any help, I'm getting desperate
LQR stands for linear quadratic regulator. Here regulator means that it wants to drive the state to zero. However, I assume that you are looking at a step response, so you are not trying to drive the entire state to zero. There are two common adaptations for LQR such that one can achieve reference tracking. Namely, by adding a feedforward term or by adding an integrator, which is also known as the linear quadratic integrator (LQI). It can be noted that a steady state feedforward can be added by just multiplying the reference with a gain matrix. However, this gain should only drive the tracking error to zero when you have a good model of your system. So, the linearized model might give some steady state in the tracking error, while LQI is probably more robust in driving the tracking error to zero.