05_PID_RoT1_SimulinkS10

05_PID_RoT1_SimulinkS10 - PID_RoT_1/2 CHE 461 -...

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Unformatted text preview: PID_RoT_1/2 CHE 461 - "Rules of Thumb" - Effects of PID Parameters PID = proportional (P), integral (I) and derivative (D) actions in one "3-mode" controller. The IDEAL PID control algorithm consists of the following equation for p '(t ) : p(t ) = the output signal from the controller p = the nominal steady-state value of p = the "bias" e(t ) = ysp (t ) − ym (t ) = the error in the control loop See Eq (8-1) pg 188 and Fig 11.8 pg 264 in SEM2 t ⎡ 1 de ⎤ Then p '(t ) = p(t ) − p = K c ⎢ e(t ) + ∫ e(t*)dt * + τ D ⎥ dt ⎦ τI 0 ⎣ ⎛ ⎞ 1 Then the ideal PID controller transfer function is Gc ( s ) = K c ⎜ 1 + +τ Ds ⎟ ⎝ τIs ⎠ ⎛ τ s + 1⎞ ⎛ τ Ds + 1 ⎞ and the commercial "real" PID controller has Gc , real ( s ) = K c ⎜ I ⎟⎜ ⎟ ⎝ τ I s ⎠ ⎝ ατ D s + 1 ⎠ "Rules of Thumb" =A general characteristic often observed, but not a law or "guaranteed" behavior. Exceptions may be COMMON, not just RARE !! Use with caution - it's better to understand something than to just "remember advice". Controller Gain = Proportional Action : "Increasing the gain increases the speed of response." Integral Action : "Increasing integral action leads to more oscillatory behavior." Derivative Action : "Increasing the derivative action stabilizes the loop." On the back of this page are 3 plots demonstrating the above three "Rules of Thumb". A fourth plot shows if the derivative time constant is made "too big", instead of "stabilizing" the loop, the derivative action causes the loop to become unstable! In other words the Rule of Thumb for "derivative action" is shown to be completely WRONG when derivative action is already "high". The base case "real" controller has K c = 1 , τ I = 0.5 , τ D = 0.2 and α = 0.05 for the loop below. Time delay = 0.05 Sum PIDalpha Y_setpoint PID_real 4 0.5s2 +1.5s+1 Gp1 Time Delay Y_graph PID RoT 2/2 I-action : Solid = Base(TauI=0.5), Dash = more (TauI=0.25), Dots = less (TauI=1) 1.6 P-action:Solid = Base(Kc=1), Dash = more (Kc=2), Dots = less (Kc=0.5) 1.6 1.4 y ' , Process Output Variable y ' , Process Output Variable 1.4 1.2 1 0.8 0.6 0.4 1 0.8 0.6 0.4 0.2 0.2 0 0 1.2 1 2 3 Time 4 5 0 0 6 D-action : Solid = Base(TauD=0.2), Dash = more (TauD=0.4), Dots = less (TauD=0.1) 1.6 2 3 Time 4 5 6 D-action : Solid = Base(TauD=0.2), Dash = lots (TauD=1.6), Dots = too much (Tau =3) D 3 2.5 1.2 2 y ' , Process Output Variable 1.4 y ' , Process Output Variable 1 1 0.8 0.6 0.4 0.2 0 0 1.5 1 0.5 0 -0.5 1 2 3 Time 4 5 6 -1 0 1 2 3 Time 4 5 6 Page 1 of 5 Appendix C in SEM2 = pages 689‐692 = COMPUTER SIMULATION WITH SIMULINK Start MATLAB and enter “simulink” at the Command prompt. This opens the Simulink Library Browser and you can use the drop down menu under File to make a “new”, “model” window appear. Page 2 of 5 Sources Sinks Continuous (dynamics) Commonly Used Blocks Page 3 of 5 In the Simulink model shown here, the results of the simulation are written to variables in the Workspace and then manual commands are entered in the Command Window to create a plot of those variables. Page 4 of 5 Page 5 of 5 Note: To match the plot shown in Figure C.5 on page 692, the time delays were set to 1.0, not 5.0 which was the value of time delay in transfer functions on page 690 and shown in Figure C.2 page 690. Here both the Print Screen and Copy Figure results are shown in the WORD document. PC graph Plot: CHE at OSU 1.5 Blocks461.mdl = Commonly used Blocks for CHE 461. yout, output variable 1 0.5 0 0 10 20 30 Time 40 50 ...
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This note was uploaded on 04/17/2010 for the course CHE 461 taught by Professor Staff during the Winter '08 term at Oregon State.

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