1. LECTURE#10 PID CONTROLLER
AUTOMATION & ROBOTICS
LECTURE#10 PID CONTROLLER
By: Engr. Irfan Ahmed Halepoto
Assistant Professor 1

2. PID Controller Theme---Background
80% of industrial control applications are installed by feedback control loop and devices.
The controller compares a measured value from a process with a reference setpoint value.
Error signal is then processed to calculate a new value for a manipulated process input, which is responsible to bring the process measured value to its desired setpoint.
Unlike simpler control algorithms, PID controller can adjust process inputs based on the history and rate of change of the error signal, which gives more accurate and stable control.
It can be shown mathematically that a PID loop will produce accurate stable control in cases where other control algorithms would either have a steady-state error or would cause the process to oscillate.

3. PID controller
A Proportional-Integral-Derivative controller (PID controller) is a generic controller widely used in industrial control systems.
PID controllers can be used to regulate flow, temperature, pressure, level, and many other industrial process variables.
PID controller describes the mathematic calculations that are applied to calculate the error between the current result and the desired set-point.
PID control equation involves three separate parameters; the Proportional, Integral and Derivative terms.
Proportional term responds instaneously to the current error (providing instaneous response).
Integral term (past errors) responds to the accumulation of errors in the form of average (providing a slow response that drives the steady-state error towards Zero).
Derivative term (future errors) responds to the rate at which the error is changing (providing some anticipatory response).

4. Life before PID controller –Manual Control
With manual, all regulation tasks will have to be done manually.
For example: To keep constant the temperature of water discharged from an industrial gas-fired heater, an operator will have to watch a temperature gauge and adjust a fuel gas valve accordingly
If the water temperature becomes too high for some reason, the operator has to close the gas valve a bit–just enough to bring the temperature back to the desired value.
If the water becomes too cold, he has to open the gas valve.

5. Life with PID Controller
Through PID controller Set Point feature, operator can set the desired temperature ranges.
The Controller’s Output (CO) sets the position of the control valve.
When everything is functional, PID controller compares the PV to its SP and calculates the difference b/w the two signals as an Error (E).
Based on the Error and PID controller’s tuning constants, controller takes an appropriate action that opens the control valve to the right position for keeping the temperature at the set point.
If the temperature rise above its set point, controller will reduce the valve position and vice versa.

6. PID CONTROLLER BASICS
Not “optimal”, based on good properties of Three modes.
In a PID loop, the correction that's added is calculated from the error in three ways
To cancel out the present error (proportional mode)
Average out past errors (Integral mode)
Anticipate the future a bit from the slope of the error(s) over time (Derivative mode).

7. PID Equation Ti and Td constants are referred to as the time value.
In PID control algorithm equation each of the three parts of the equation are given a K constant.
However, PID controllers having the Integral and Derivative constants are represented as
Ti and Td constants are referred to as the time value.
Ti is defined as the time required by the integral term to generate an output equivalent to the proportional term.
Td is defined as the time required by the proportional term to repeat the output provided by the derivative term.
With these substitutions, our equation now becomes:
In this equation, you can see that the proportional term (Kp), has an amplifying effect on the entire algorithm.

8. PID Control----Terms
Proportional: To handle the present, the error is multiplied by a negative constant P and added to the controlled quantity.
Note: When error is zero, proportional controller's output is zero.
Integral: To handle the past, error is integrated (added up) over a time period, multiplied by a negative constant I and added to the controlled quantity. I finds the process output's average error from the setpoint.
A simple proportional system oscillates around the setpoint, because there's nothing to remove the error.
By adding a negative proportion of the average error from the process input, average difference between the process output and the setpoint is reduced and the process output will settle at the setpoint.
Derivative: To handle the future, the first derivative (slope) of the error is calculated, multiplied by negative constant D, and added to the controlled quantity.
The larger this derivative term, more rapidly the controller responds to changes in the process output.
The D term dampens a controller's response to short term changes.

9. PID PROCESS CONTROLLER

10. PID CONTROLLER: CLOSED-LOOP MODEL

11. PID Control Algorithms
Controller manufacturers arrange the Proportional, Integral and Derivative modes into three different controller algorithms or controller structures. 
These are called Series, Ideal and Parallel algorithms.
Some controller manufacturers allow you to choose between different controller algorithms as a configuration option in the controller software.

12. Interactive Algorithm
This very popular controller algorithm is called as Series, Classical, Real or Interactive algorithm.
The pneumatic and electronic controllers had this algorithm and it is still found it in many controllers today.  
The Ziegler-Nichols tuning rules are based on this controller algorithm.

13. Noninteractive Algorithm
Noninteractive algorithm is also called the Ideal, Standard algorithm. 
In this standard form, inner summation produces a new single error value which is compensated for future and past errors.
Addition of proportional and derivative terms predicts the error value at Td seconds in future.
Integral component adjusts the error value to compensate for the sum of all past errors in Ti seconds .
The resulting compensated single error value is scaled by the single gain Kc.
The Cohen-Coon PID tuning rules were designed for this algorithm.

14. Parallel Algorithm
This parallel form, parameters are treated as simple gains,
This algorithm is simple to understand, but not perceptive to tune. 
Reason is that it has no controller gain (affecting all three control modes), it has a proportional gain instead (affecting only the proportional mode). 
Adjusting the proportional gain should be supplemented by adjusting the integral and derivative settings at the same time.

15. PID algorithm Pseudocode
A software loop that implements the PID algorithm in its 'ideal, parallel' form:
previous_error = setpoint - actual_position
integral = 0
start:
error = setpoint - actual_position
integral = integral + (error*dt)
derivative = (error - previous_error)/dt
output = (Kp*error) + (Ki*integral) + (Kd*derivative)
previous_error = error
wait(dt)
goto start

16. PID Control Modes Mode Combination Function Application
Proportional (P)
To provide GAIN
For small set points or small load changes
Proportional–plus-Integral (PI)
To eliminate OFFSETs
For large and slow set points or load changes
Proportional –plus-Derivative (PD)
To speed up the response and minimize the OVERSHOOT
For sudden set points or quick load changes in a slow response system
Proportional –Integral-Derivative (PID)
To speed up the response, minimize the OVERSHOOT and eliminate OFFSETs
For large and sudden set points or load changes in a slow response system

17. General rules of Design PID Controller
Use P, if system has small time constant, small disturbance and allow steady state error (off sets).
Use PI, if system has small time constant, small disturbance and requires no steady state error.
Use PD function, if system has large time constant and time delay (speed up process response).
Using PD if the system allows steady state error, then use PID
Use more advanced control scheme, if system has large time constant, large time delay and disturbance.

18. Proportional Control Mode
“correction proportional to error”

19. Proportional-only Controller
Proportional controllers are simple to understand and easy to tune.
The controller output is simply the output of the proportional control mode, plus a bias.
The bias is needed so that the controller can maintain an output (say at 50%) while there is no error (set point = process variable).
A proportional-only controller algorithm

20. Proportional Bias
The controller output u is proportional to error signal e:
is proportional band
P control has steady state error

21. Proportional Action
In Proportional mode, controller simply multiplies the Error by the Proportional Gain (Kp) to get the controller output.
Small proportional gain (Kp) is the safest way to get to setpoint, but your controller performance will be slow.
If the Kp is increased, Overshoot in the signal will be present.
Proportional action is useful for improving the response of a stable system but cannot control an unstable system by itself.
Additionally, the gain is the same for all frequencies leaving the system with a non-zero steady-state error.

22. Proportional Action Only
Proportional control mode is the main driving force of controller.
It changes the controller output in proportion to the error.
If the error gets bigger, the control action gets bigger, more control action is needed to correct large errors.
Adjustable setting for proportional control is called Controller Gain (Kc).
If the controller gain is set too high the control loop will begin oscillating and become unstable.
If the controller gain is set too low, it will not respond adequately to disturbances or set point changes.

23. Role of proportional Controller
The main purpose of the proportional control is minimize the fluctuations that occur within the system.
A proportional constant or value as entered into the controller will determine how large the "proportional band" is.
When process parameter is inside the proportional band, controller output will vary the amount of change required to reduce overshoot of the SP.
Proportional controller will also experience "droop".
when the process and set point values are equal, the process will generally stabilize somewhere below the set point.
The amount of droop increases with larger proportional bands.

24. Proportional Band and Gain
Proportional Band: the input change required to change the output 100%

25. Proportional Band
While most controllers use controller gain (Kc) as the proportional setting, some controllers use Proportional Band (PB), which is expressed in percent.
Table 1 shows the relationship between Kc and PB.
Controller Gain (Kc)
Proportional Band (PB) %
0.1
1000
0.2
500
0.5
200 1
100 2 50 5 20 10
Table 1.  Relationship between Kc and PB

26. Response Versus PB, Proportional Control Only

27. Proportional Gains
Consider an example of a Proportional controller with different Proportional Gains.
As the gain is increased the system time response is faster , but system starts to oscillates.
Comments: Clearly, it is not possible to achieve low steady state error and good transient response using only proportional control.
As the gain is increased, the response becomes faster, but it has a lower phase margin.
To remove the steady-state error and have better response, integral and/or derivative terms must be included in the controller.

28. Proportional Control- Limitations
The P-controller usually has steady-state errors unless the control gain is large.
As the control gain becomes larger, issues arise with the stability of the feedback loop.
For instance, reducing the rise time implies a high proportional gain, and reducing overshoot and oscillations implies a small proportional gain. This is not possible to achieve in all systems.
process output of proportional control

29. Proportional control------Solution
The way to eliminate these steady-state errors is by adding an integral action.
The integral term in the equation drives the error to zero.
Higher Integral constant (1 / Tt) drives the error to zero sooner but also invites oscillations and instability.
Watch out a sample process output diagram when integral control is added.
Response shows the reduction of overshoots and oscillations compared to the picture before adding the integral action.

30. Proportional-only Controller Dilemma
The use of proportional control alone has a large drawback of offset.
Offset is a sustained error that cannot be eliminated by proportional control alone.
For example: let’s consider controlling the water level in the tank with a proportional-only controller.
As long as the flow out of the tank remains constant, the level will remain at its set point.
But, if the operator should increase the flow out of the tank, the tank level will begin to decrease due to the imbalance between inflow and outflow.
While the tank level decreases, the error increases and our proportional controller increases the controller output proportional to this error.
Level control, with operator causing a disturbance

31. Proportional-only Controller Dilemma
Consequently, the valve controlling the flow into the tank opens wider and more water flows into the tank.
As the level continues to decrease, the valve continues to open until it gets to a point where the inflow again matches the outflow.
At this point the tank level (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.
The system now remains at balance, but the tank level remains below its set point. This residual sustained error is called Offset.