Apply the predictive control law of Example 20.2 to a fifth-order process:

$\frac{Y(s)}{U(s)} =\frac{1}{(5s+1)^{5} }$ (20-23)

Evaluate the effect of tuning parameter J on the set-point responses for values of $J = 3, 4, 6, and 8$ and $Δt = 5 min$ .

Question

Apply the predictive control law of Example 20.2 to a fifth-order process:

[latex]\frac{Y(s)}{U(s)} =\frac{1}{(5s+1)^{5} }[/latex] (20-23)

Evaluate the effect of tuning parameter J on the set-point responses for values of [latex]J = 3, 4, 6, and 8[/latex] and [latex]Δt = 5 min[/latex].

Accepted Answer

The [latex]y[/latex] and [latex]u[/latex] responses for a unit set-point change at [latex]t = 0[/latex] are shown in Figs. 20.5 and 20.6, respectively.As [latex]J[/latex] increases, the [latex]y[/latex] responses become more sluggish while the [latex]u[/latex] responses become smoother. These trends occur because larger values of [latex]J[/latex] allow the predictive controller more time before the [latex]J[/latex]-step ahead prediction [latex]\hat{y}(k + J)[/latex] must equal the set point. Consequently, less strenuous control action is required. The [latex]J[/latex]th step-response coefficient [latex]S_{J} [/latex] increases monotonically as [latex]J[/latex] increases. Consequently, the input moves calculated from Eq. 20-22 tend to become smaller as [latex]S_{J} [/latex] increases. (The u responses for [latex]J = 4[/latex] and [latex]8[/latex] are omitted from Fig. 20.6.)

[latex] \Delta u(k)=\frac{y_{sp} -\hat{y} ^{\circ } (k+J)}{S_{J} }[/latex] (20-22)

Question 20.3: Apply the predictive control law of Example 20.2 to a fifth-...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions