LQR problem with controllable system
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Leonardo Costa 2021년 1월 31일
Good morning to everybody;
I need to design an LQR based control system for a 4 indipendent WaterJet boat.
The state vector is the following
where u is the longitudinal velocity, v is the lateral velocity and omega is the yaw rate.
I linearized the system starting from this function, in which I rotated the velocities and the forces in the fixed reference frame
f1, f2, f3, f4 are the thrust from the WaterJet
And after this i used the Jacobian function in order to create the A and B matrices.
But when i run the LQR this error appear:
Cannot compute the stabilizing Riccati solution S for the LQR design. This could be because:
* R is singular,
* [Q N;N' R] needs to be positive definite,
* The E matrix in the state equation is singular.
So i checked the controllability of the model by imposing zero velocities and all the Thrust = 10.
The rank of the controllability matrix was equal to 6, so my system is controllable.
I cannot understand where is the problem.
Thank you in advance.
Dongming 2022년 11월 13일
For high dimensional problem, try to use icare to solve Riccati equation
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