entc 395 lecture 7a. today 4 pid control –overview –definitions –open loop response 4 example...
TRANSCRIPT
ENTC 395
Lecture 7a
Today
PID control– Overview– Definitions– Open loop response
Example – SIMULINK implementation
Reading
Last time Laplace TransformsAppendix F.1-F.4
Today: Handout - Control Theory
Next time: Handout - Control Theory
Control Systems
Plant: A system to be controlled
Controller: Provides the excitation for the plant, controls the overall system behavior
Controller: Inputs and Outputs
R: Desired operating point
Y: Actual operating point
e: Error signal = R-Y
u: Correction signal
dt
tdeKdtteKteKtu DIp
)()()()(
PID Controllers
KP = Proportional gain
KI = Integral gain
KD = Derivative gain
Controller response may be a function of three components of the error signal
PID Controller Transfer Function
KP = Proportional gain
KI = Integral gain
KD = Derivative gain
In s space the transfer function looks like this:
DIP sKKs
Kse
su
1
)(
)(
Parameter Effects
The effect of the Ks on a system are summarized below. Actual relations are more complex. Ks are not independent.
CL RESPONSE RISE TIME OVERSHOOTSETTLING
TIME S-S ERROR
Kp Decrease Increase Small Change Decrease
Ki Decrease Increase Increase Eliminate
Kd Small Change Decrease Decrease Small Change
Example
Our old friend the spring mass damper system
kbsmssF
sX
sFsXkbsms
Fkxxbxm
xmFxbkx
xmF
2
2
1
)(
)(
)()(
Example
Our old friend the spring mass damper system
M = 1kg
b = 10 N.s/m
k = 20 N/m
F(t) = 1(Step input)
Example
The goal of this example is to demonstrate how KP, KI and KD modifies the system response.
Goals: Fast rise time
Minimum overshoot
No steady-state error
Example -- Open loop response
The open loop response is simply the response of the system with no controller in the loop.
Model of a spring, mass, damper systemOpen loop response
20
k
10
b
Sum
Scope
s
1
Integrator1s
1
IntegratorF(t)
1
1/m
Example -- Open loop response
For a step input of 20 N the mass moves 1.0 m
x=F/k
x=20N/20(N/m)
x=20m
Example -- Proportional Control
Change problem add an active proportional controller
Example -- Proportional Control
Change problem add an active proportional controller
Response now changes also
Example -- PD Control
Change active proportional controller
add KD
Response now changes also
Example -- PD Control- Response
Change active proportional controller
add KD
Response now changes also
Example -- PID Control
Change to active PID
controller
Example -- PID Control ResponseChange to active PID
controller