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)