1 / 16

State Feedback

State Feedback. State Feedback. State Feedback. Closed loop matrices. R=0 the system is called regulator. State Feedback. The CL state matrix is a function of K. => Faster/stable system. By appropriate changing K we can change eig( A CL ). This method is called pole placement.

rahim-koch
Download Presentation

State Feedback

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. State Feedback

  2. State Feedback

  3. State Feedback Closed loop matrices R=0 the system is called regulator.

  4. State Feedback The CL state matrix is a function of K => Faster/stable system By appropriate changing K we can change eig(ACL) This method is called pole placement. WE MUST CHECK IF THE SYSTEM IS CONTROLLABLE

  5. State Feedback Eigenvalues of CL system: 3-k CL eigenvalues at -10 k=13

  6. State Feedback If the system is unstable create a controller that will stabilise the system. >> eig(A) >> rank(ctrb(A,B)) ans = -0.3723 5.3723 ans = 2

  7. State Feedback -10 and -11 Matlab If the system is n x n then you need to solve an n x n system of equations! K=place(A,B, [-10 -11]) P=[-10 -20 -30]; C=[0 0 1], D=0. Matlab

  8. State Feedback - LQR Matlab: State feedback Response of the system Reference signal Study the signal u=-Kx Place the poles at [-100 -110] Response of the system Study the signal u=-Kx K =[26 72]T P=[-10 -11]

  9. State Feedback - LQR Compromise between speed and energy that we use. Similar problem/dilemma if we had an input. Solution: Linear Quadratic Regulator (optimum controller) Q and R are positive definite matrices for all nonzero X Square symmetric matrices, positive eigenvalues Q: Importance of the error, R: Importance of the energy that we use (assume that is stable)

  10. State Feedback - LQR (assume that is stable) P is positive definite X=1 Reduced Riccati Equation

  11. State Feedback - LQR Steps to design an LQR controller: • To find the optimum P solve: 2.Find the optimum gain [K, P, E]=lqr(sys, Q, R) E are the eigenvalues of A-BK Find K, The eigenvalues of A-BK The response of the system For R=1 and Q=eye(2) and Q=2*eye(2) (X(0)=[1 1]). Matlab CAD Exercise

  12. Estimating techniques Magic trick

  13. Estimating techniques Example: A=[1 2;3 4]; B=[1 0]'; C=[1 0]; D=0;

  14. Estimating techniques The error between the estimated and real state is A is unstable Homogeneous ODE A is slow A=[1 2;3 4]; B=[1 0]'; C=[1 0]; D=0; U=1,

  15. Estimating techniques

  16. Estimating techniques G=place(A’, C’, P) But the system must be observable Where to place these eigenvalues??? A=[1 2;3 4]; B=[1 0]'; C=[1 0]; D=0; U=1,

More Related