ZIEGLER-NICHOLS TUNING USING A FUNDAMENTAL PROCESS MODEL. Design P, PI, and PID controllers for the three-tank system of Example 15.1 using Ziegler-Nichols tuning rules.

Question

ZIEGLER-NICHOLS TUNING USING A FUNDAMENTAL PROCESS MODEL.

Design P, PI, and PID controllers for the three-tank system of Example 15.1 using Ziegler-Nichols tuning rules.

Accepted Answer

From Example 14.9 we see from direct substitution that the proportional controller gain which brings the closed-loop response of the system to the verge of instability is:

[latex]K_{cu} = 5/3 = 1.667[/latex]

and the frequency of sustained oscillation at that point is:

[latex]\omega_{c} = 0.5 rad/min[/latex]

From this the ultimate period is obtained as:

[latex]P_{u} = \frac{2 \pi}{\omega_{c}} = 4 \pi = 12.56[/latex]

Thus the Ziegler-Nichols settings for the various controllers are then:

[latex]P: K_{c} = 0.8333[/latex]

[latex]PI: K_{c} = 0.75, 1/ au_{I} = 0.0955[/latex]

[latex] PID: K_{c} = 1.0, 1/ au_{I} = 0.159, au_{D} = 1.57[/latex]

The response to a set-point change for each type of controller is seen in Figure 15.6. Note that the P controller has some offset while the PI controller has large overshoot and slowly damped oscillations. By contrast, the PID controller provides a rather good response except that there is about 40 percent overshoot. Clearly, for the PI controller, the earlier, more rigorous controller designs are much better than the Ziegler-Nichols designs based on rules of thumb.

Question 15.4: ZIEGLER-NICHOLS TUNING USING A FUNDAMENTAL PROCESS MODEL. De...

Related Answered Questions

Verified Answer:

ZIEGLER-NICHOLS STABILITY MARGIN TUNING FROM A BODE PLOT. Consider the three-tank system with P control having the Bode plot of Figure 15.18. Determine the Ziegler-Nichols settings for P, PI, PID control. ...

Verified Answer:

BODE STABILITY TEST OF THREE-TANK PROCESS UNDER PID CONTROL. For the PID controller applied to the three-tank process discussed in Example 15.7, determine the range of stable controller gains using the Bode stability criterion. ...

Verified Answer:

Verified Answer:

DIRECT SYNTHESIS CONTROLLER TUNING FOR THE MULTIPLE-TANK PROCESS. Use the direct synthesis tuning procedure to obtain PID controller parameters for the three-tank system of Example 15.1. Recall that for this system: g(s) = 6/(2s + 1)(4s + 1)(6s + 1) (14.73) Assume that a reasonable closed-loop ...

Verified Answer:

CONTROLLER DESIGN BASED ON TIME-INTEGRAL OBJECTIVES. For the three-tank system of Example 15.1, determine the optimal PI controller settings and the optimal closed-loop responses for each of the integral-time criteria in Eq. (15.11). ...

Verified Answer:

Verified Answer: