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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?

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What I have done so far is following:

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So the state space form is:

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I´m not sure if it's okay to choose x_1 = Q^2 / D^2?

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  • $\begingroup$ Looks like homework - we are not a free completion service. Show what you have done so far. $\endgroup$
    – Solar Mike
    Dec 25, 2022 at 19:00
  • $\begingroup$ It's not a homework, it's a problem I am dealing with at my job. $\endgroup$
    – Grétar Már
    Dec 25, 2022 at 19:53

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