Form regulator given state-feedback and estimator gains
rsys = reg(sys,K,L)
rsys = reg(sys,K,L,sensors,known,controls)
rsys = reg(sys,K,L) forms a dynamic regulator or compensator rsys given a state-space model sys of the plant, a state-feedback gain matrix K, and an estimator gain matrix L. The gains K and L are typically designed using pole placement or LQG techniques. The function reg handles both continuous- and discrete-time cases.
This syntax assumes that all inputs of sys are controls, and all outputs are measured. The regulator rsys is obtained by connecting the state-feedback law u = –Kx and the state estimator with gain matrix L (see estim). For a plant with equations
this yields the regulator
This regulator should be connected to the plant using positive feedback.
The plant inputs consist of controls u, known inputs ud, and stochastic inputs w.
Only a subset y of the plant outputs is measured.
The index vectors sensors, known, and controls specify y, ud, and u as subsets of the outputs and inputs of sys. The resulting regulator uses [ud ; y] as inputs to generate the commands u (see next figure).
Given a continuous-time state-space model
sys = ss(A,B,C,D)
with seven outputs and four inputs, suppose you have designed:
A state-feedback controller gain K using inputs 1, 2, and 4 of the plant as control inputs
A state estimator with gain L using outputs 4, 7, and 1 of the plant as sensors, and input 3 of the plant as an additional known input
You can then connect the controller and estimator and form the complete regulation system by
controls = [1,2,4]; sensors = [4,7,1]; known = ; regulator = reg(sys,K,L,sensors,known,controls)