I need to make a PI feedback loop for a hydro power plant. The discharge through one gate is given by Q in equation 4.2. I need to keep (regulate) H = 116 m.a.s.l (meters above sea level) where H = Hg + D/2.
As I understand this, the variables Q, D, and Hg, in equation (4.1) are functions of time. I need to find the state variables and the control input variables. How should I go around this problem? Should I try to find Laplace equation for this and use the well known feedback equation, or should set it up in state space model?
What I have done so far is following:
So the state space form is:
I´m not sure if it's okay to choose x_1 = Q^2 / D^2?