4. [12 pts) The tank water level control system is shown in Figure 6 The measure

Question

4. [12 pts) The tank water level control system is shown in Figure 6 The measured water level response ht) is shown in Figure 7. The reference signal (dashed line) is a step function that increases from 14 to 16cm at 25 s. d, 1 Water Tank Pump Three data points of h() are listed in Table 2, where v point #2 is the peak point. Calculate the following specifications of the measured step response. 1) Percentage Overshoot; 2) Steady state error 3) Peak time. Water Basin Figure 6 Tank water level control system 6.5 16 3 15.5 15 14.5 -Measured response Reference signal 14 13.5 24 25 26 27 28 29 30 3 32 33 34 35 Time t (sec) Figure 7 Measured tank water level response of the closed-loop system Table 2 Data points in Figure 6 7 Point # 1 1 (sec) | h (cm) 25.0 14.00 26.8 16.19 3 34.7 15.94

Explanation / Answer

(1) overshoot occurs at t= 26.8seconds.

% overshoot is (16.19-16)/(16-14)*100=0.19/2 *100 = 9.5%

Percent overshoot = 9.5%

(2) steady state error can be determined from point 3.

Steady state error = (16-15.94)/(16-14) *100 = 3%.

Steady state error = 3%.

(3) overshoot occurs at peak time. From point 1, overshoot occurs at 26.8seconds. Therefore peak time is 26.8seconds.

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