- 17 Pts 6 An Experimental Results Shows That The Actual Value Of Water Level Is 24 Cm If The Desired Value Of The Wat 1 (11.52 KiB) Viewed 32 times
- 17 Pts 6 An Experimental Results Shows That The Actual Value Of Water Level Is 24 Cm If The Desired Value Of The Wat 2 (46.88 KiB) Viewed 32 times
Proportional-Plus-Integral Control Action: The control action of a proportional-plus-integral controller is defined by u(t) = Kpe (0) + / [e e(t)dt (2.10.4) where T, is called the integral time. Proportional-Plus-Derivative Control Action: The control action of a proportional plus derivative controller is defined by de(t) u(t)= K₂e(t) + KpTa (2.10.5) dt where T is called the derivative time. Proportional-Plus-Integral-Plus-Derivative Control Action: The combination of proportional control action, integral control action, and derivative control action is termed proportional-plus- integral-plus-derivative control action. The combined action has the advantages of each of the three individual control actions. The equation of a controller with this combined action is given by u(t) = K₂e(t) + / [e(0)dt + K,Taª de(t) dt (2.10.6) 2.10.3.3 Time Domain Specifications Maximum Overshoot: Let y(t) be the unit-step response. Let ymax denote the maximum value of y(t): Yes is the steady-state value of y(t); and ymax 2 Yss. The maximum overshoot of y(t) is defined as Maximum Overshoot = ymax - Yss (2.10.7) The maximum overshoot is often represented as a percentage of the final value of the step response; that is, Percentage Maximum Overshoot = Maximum Overshoot Yss x 100% (2.10.8) The maximum overshoot is often used to measure the relative stability of a control system. The unit step response illustrated in Figure 2.10.2 shows that the maximum overshoot occurs at the first overshoot. Delay Time: The delay time ta is defined as the time required for the step response to reach 50% of its final value. 87