Digital Control

Control Law Processor - PID controller
(Proportional-Integral-Derivative)
►Continuous ( Analog) Expression
Command Xi(t)
Feedback Xf(t) Output M(t)
e(t) = Xi(t) – Xf(t)
M(t) = Kp*e(t) + Ki*∫e(t)dt + Kd * ---- d e(t)
dt
►Difference ( digital ) Expression
-
+
----- (1)
----- (2)
Where -- e(t): Error signal; Kp: Proportional Gain; Ki: Integral Gain; Derivative Gain
n
m(n) = Kp × e(n) + Ki × ∑ e(i) × ∆t + Kd × ---------------e(n)
– e(n-1)
i=0
∆t
- (3)
m(n)= m(n-1) + Kp × [e(n)-e(n-1)] + Ki × e(n) × ∆t + Kd × [---------------e(n)
– e(n-1)
-
∆t
e(n-1) – e(n-2)
------------------- ] - (4)
∆t
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