PID Controller

Question 1

What is the problem statement for the proportional controller?

Answer 1

If we have a K block in a control system.
-increasing K lowers steady state error but increases damping of higher order systems

Question 1

How can steady state error be reduced in the proportional controller?

Answer 1

If there is a 1/s in the TF, the feedback loop is type 1
(zero steady state error)

Question 2

How can we achieve a type 1 with respect to disturbance?

Answer 2

Using integral control in the controller of the system

Question 3

Define integral control

Answer 3

When the output signal U(s) is the integral of the error signal times Ki.

u(t) = Ki ∫e(t)dt

Question 4

Parallel form for PI controller

Answer 4

Cpi(s) = Kp + Ki/s

=(Kps + Ki)/s

Question 5

Parallel form of PD controller

Answer 5

Cpd(s) = Kp + KdS

Question 6

Define the parameter Ti

Answer 6

Integral time - the time for the integral to intersect the proportional term for constant error input Ke(t)

Question 7

Define derivative control

Answer 7

a control method to increase damping without decreasing k
u(t) = Kd x de(t)/dt

Question 8

Define the parameter Td

Answer 8

Derivative time
the time required for the proportional term to biuld up to the derivative for a ramp error input

Question 9

How is a derivative term implemented in a control system?

Answer 9

We cannot know a pure derivative without knowing the future so it is approximated
C(s) = Kds/ (s/Pf +1 )

Question 10

Define a PID controller

Answer 10

creates a control signal that is the sum of the error signal, its integral and its derivative.
u(t) = k( e(t) + 1/Ti ∫e(t) + Td de(t)/dt )

Intgeral - feedback on past outputs
Proportional - present outputs
Derivative - future outputs

Question 11

Give 4 controller design methods

Answer 11

Tuning rules
Root locus
Analytical methods
Computer based Optimisation methods

Question 12

What are the 2 problems with PID controllers

Answer 12

Derivative
Integral windup

Question 13

What is a derivative kick and how is it fixed

Answer 13

When there is a large spike in the output signal
e(t) = r(t) - y(t)
It is fixed by differentiating y(t) rather than the error signal

Question 14

What is integral windup and how is it fixed?

Answer 14

When the integral term “winds up” due to the output of the PID being limited by saturation
-back calculation is used for antiwindup

Question 15

If steady state is an issue, what controller do we use?

Answer 15

PI

Question 16

If the system ocsillates too much or lacks stability, what controller do we use?

Answer 16

PD

Question 17

What are the pros/cons of PI controllers?

Answer 17

Pros:
-allows for steady state error to be reduced to 0
con:
-integral wind up may occur

Question 18

What are the pros/cons of PD controllers?

Answer 18

pros:
Increases damping and overshoot while allowing k to be a larger value
-faster response
cons:
-susceptible to noise and derivative kick which can cause instability