Elec 341 - PID Control
1
Proportional Control
1
(s+2)(s+3)
Motor
20
KDesired Pos(voltage)
s+1
1
Current Driver Actual Pos
Root-Locus / Response
K = 40
K = 20
K = 10
K = 5
K = 2
Ku = 60
Elec 341 - PID Control
2
PD Control
Order(Denom) > Order(Num)Avoids approximate derivative
Elec 341 - PID Control
3
I Control
Elec 341 - PID Control
4
PI Control
Elec 341 - PID Control
5
KI = 0 → 5
KP = 5
KI = 5 → 20
KP = 5
Elec 341 - PID Control
6
Kp = Kd = 25 Kp = Ki = 3
Ki = 1.5
PID Control
Elec 341 - PID Control
7
PID (KP = 9, KI = 6, KD = 3)
KP = 3KD KI = 2KD
PID Control Gain EffectsNormally – but not always
GainRise Time
Over-shoot
Settle Time
SS Error
Kp ↓ ↑ ↑ ↓
Ki ↓ ↑ ↑ 0
Kd ↑ ↓ ↓ n/a
Elec 341 - PID Control
8
Tuned: (KP = 18, KI = 12, KD = 8)
Start: (KP = 6.75, KI = 4.5, KD = 2.25)– Critically damped
PID (KP = 18, KI = 12, KD = 8)
PD (KP = 50, KD = 35)
PI (KP = 5.5, KI = 4.1)
Elec 341 - PID Control
9
PID Control
Simulink Differentiator Block
Inaccurate due to differentiator
PID BlockMatches output of Xfer function computed using Matlab function
Elec 341 - PID Control
10
Practical PID Block1 1
P I Ds P I Dss N s
N
s
Unity GainPole Far Away
O(Num) = O(Den)