6_P-I-D_Controller.pdf

UNIKL MALAYSIAN INSTITUTE OF INDUSTRIAL TECHNOLOGY
Autonomous System & Robotics Research Group
Recaps
I In the previous lesson, we learnt on process dynamic.
I In general, process can be categorised (1) non-integrating, (2) integrating.
I Common control strategy
I feedback control;
I feedforward control;
I cascade;
I ratio control;
I selector control;
I More advance control strategy
I Linear Quadratic Regulator;
I Fuzzy Logic Controller;
I Model Predictive Controller;
Dr. Mohd Ismail Yusof, PhD MIET (UK)
Instrumentation & Control Engineering 3 / 34

Control Block Scheme
Assume a heat-exchanger control loop example. It is non-integrating (self-regulate) process
with time-delay.

Control Block Scheme (cont)
1. Sense. Measure the current condition of the process using a sensor, which can be a
thermocouple or RTD transmitter.
2. Compare. Evaluate the measurement of the current condition against the set point
using an electronic PID controller.
3. Respond. Reacts to any error that may exist between the measured temperature
value and the temperature set point by generating a corrective pneumatic signal.
4. Affect. Actuate the control valve that will produce a change in the process variable.

The simplified P&ID for heat-exchanger.

Control system block diagram visualisation,

Proportional-Integral-Derivative Controller

PID Controller
I PID (Proportional-Integral-Derivative) is a type of
controller that is widely used in manufacturing
industry.
I Conventional PID controller is an electronic
devices. Usually it is installed at control panel
near field.
I PID control algorithm can also be programmed in
PLC and DCS software.
I PID controller (or algorithm) give some sort of
transient and dynamics that we wanted it to be
rather than transient response that it naturally
have.

PID Form
Three Common PID Forms
I Parallel Form.
I Standard, aka ISA Form.
I Series, aka Classical Form.
DeltaV has choice
I Standard (Default)
I Series

PID Controller Function-Effect on Proportional gain only
I The use of proportional control alone has a large drawback – offset
I As long as the liquid flow remains constant, the liquid temperature will
remain at its set point.
I But, if the operator should increase/decrease the liquid flow, the liquid
temperature will begin to change due to the changes of liquid flow.
I While the liquid temperature change, the error increases and our
proportional controller increases the controller output proportional to this
error.
I Consequently, the valve controlling the flow into the tank opens wider and
more steam flows into the shell.
I As the temperature continues to decrease, the valve continues to open
until it gets to a point where the measured temperature again matches
the setpoint.
I At this point the liquid temperature (and error) will remain constant.
Because the error remains constant our P-controller will keep its output
constant and the control valve will hold its position.
I The system now remains at balance, but the liquid temperature remains
below its set point. This residual sustained error is called Offset.

PID Controller Function-Proportional action summary
Features
I Proportional mode responds only to change in error.
I Proportional mode alone will not return the PV to SP.
Advantages
I Simple.
Disadvantages
I Offset.

PID Controller Function-P+I action summary
Features
I Output is repeat of the proportional action as long as error exists.
I The units are in terms of repeats per minute
Advantages
I Eliminates error.
Disadvantages
I Reset windup and possible overshoot.

PID Controller Function-P+D action summary
Features
I A function of the speed of change of the error.
I The units are minutes.
Advantages
I Rapid output reduces the time that is required to return PV to SP in slow process.
Disadvantages
I Dramatically amplify noisy signals, can cause cycling in fast process.

Selection of Control Mode
I Not every process requires a full PID control strategy.
I If a small offset has no impact on the process, then P control alone may be sufficient.
I PI control is used where no offset can be tolerated, where noise may be present, and
where excessive dead time is not a problem.
I In processes where no offset can be tolerated, no noise is present, and where dead
time is an issue, customers ca use full PID control.

Fundamental of PID Control Parameter
Tuning

Online Controller Tuning
I The control systems for modern industrial plants typically include thousands of
individual control loops.
I During control system design, preliminary controller settings are specified based on
process knowledge, control objectives, and prior experience.
I After a controller is installed, the preliminary settings often prove to be satisfactory.
I But for critical control loops, the preliminary settings may have to be adjusted in order
to achieve satisfactory control.

Online Controller Tuning
From previous knowledge, several observations made:
I Controller tuning inevitably involves a tradeoff between performance and robustness.
I Controller settings do not have to be precisely determined.
I For most plants, it is not feasible to manually tune each controller.
I Diagnostic techniques for monitoring control system performance are available.

Continuous Cycling Method
I Ziegler and Nichols (1942) published a classic paper that introduced the continuous
cycling method for controller tuning.
I Z-N tuning relation have enormous impact on both process control research and
practice.
I Despite serious shortcoming, the Z-N relations and (various modifications) have been
widely used as a benchmark in comparisons of tuning relations.

Step for Z-N tuning relation is given as:
I After process has reached steady-state, introduce proportional only control.
I First set ⌧I = 1 and ⌧D = 0. i.e, using proportional control action only.
I Introduce a small, momentary set-point change so that controlled variable moves away
from the set-point.
I Increase Kc from 0 to a critical value Kcu at which the output first exhibits
sustained oscillations.

I If the output does not exhibit sustained oscillations for whatever value Kp may take,
then this method does not apply.
I Ultimate gain Kcu and the corresponding ultimate period Pcu are experimentally
determined.

I Then use table below to calculate controller setting.
Type of
Controller
Kp Ti Td
P 0.5Kcr 1 0
PI 0.45Kcr
1
1.2
Pcr 0
PID 0.6Kcr 0.5Pcr 0.125Pcr
I Z-N tuning relation reported were determined empirically to provide closed-loop
responses that have a 1/4 decay ratio.

Example
Example 1
Find PID controller setting
using Z-N setting with
Kcu = 7.88 and
Pcu = 11.66

Major disadvantages of Z-N continuous cycling method:
1. The trial-and-error determination of Kcu and Pcu can be quite time consuming if the
process dynamics are slow.
2. For many applications, continuous cycling method is objectionable because the
process is pushed to stability limit. Consequently, if external disturbances or process
changes occur duirng the test, unstable operation or a hazardous situation could
result.
3. This tuning procedure is not applicable to integrating or open-loop unstable processes,
because their control loops typically are unstable at both high and low values of Kc,
while being stable for intermediate values.

Step Test Method
I Simple experimental procedure for online tuning method.
I Experiment is done in open loop mode.
I After process has reached steady-state, the controller is placed in the manual mode.
I Then introduced small step change in the controller output.

Step Test Method
I Obtained output response from unit step input response via experiment.
I Unit step input exhibits S-shaped curve output if the plant involves neither
integrator(s) nor dominant complex-conjugate poles.
I The S-shaped curve characterised by 2 constants, (i) time delay ✓ (or td, L ), and (ii)
time constant ⌧ (or T).
I These constants are determined by drawing a tangent line at the inflection point of
S-shaped curve.

Step Test Method
I Intersection of tangent line to time axis (i.e., y = 0) indicate t0.
I Intersection of tangent line to steady-state output line (c (t) = K) indicate t1.
I TF can be approximated by first-order system with transport lag,
C (s)
R (s)
=
Ke td s
⌧s + 1
.

Step Test Method

Step Test Method
Type of
Controller
Kp ⌧I Td
P
⌧
✓ 1 0
PI 0.9
⌧
✓
✓
0.3
0
PID 1.2
⌧
✓ 2✓ 0.5✓

Example
Example 2
Parameter for heat exchanger process denoted by,
I Tin is the inlet temperature,
I Tout is the exit temperature,
I Tout_mea is the temperature measurement in mA , and
I Ps is steam pressure.
During an open-loop experimental test, the steam pressure, Ps, was suddenly changed from
18 to 20 psig and the step response output, Tout_mea, shown in Figure 2. At the nominal
conditions, the control valve and current-to-pressure transducers have gains of
KV = 0.9 psi/psi and KIP = 0.75 psi/mA, respectively. Determine appropriate PID
controller settings using process reaction curve method.

Example
Example 2
Figure 1: Heat exchanger process.

Example
Example 2
Figure 2: Step response output.

6_P-I-D_Controller.pdf

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