Meeting w12 chapter 4 part 2

Chapter 4 Process Control

Time Response of a ControllerOther Process Control Loop

5. Time Response of a Controller

Every controlled system possess its own time response.

This time response depends on machine/ system design & is established through experiment or theoretical analysis.

The controller which is also a system, possess its own time response.

This time response cannot be influenced by control engineer but it is able to be specified in order to achieve good control performance.

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Cont.

3 components determine the time response of continuous-action controller are:

1. Proportional component (P component)

2. Integral component (I component)

3. Differential component (D component)

These components indicate how the manipulated variable is calculated from the system deviation.

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Basic P, I & D

Proportional Integral Differential

Manipulated variable output is proportional to the system deviation

The rate of change of manipulated variable is proportional to the system deviation

The value of manipulated variable is proportional to the speed of change of system deviation 4

Proportional Controller

In proportional controller, manipulated variable output is proportional to the system deviation.

Since manipulated variable only present when there is a system deviation, proportional controller cannot be achieved if system deviation is zero (no control).

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Cont.

For an ideal proportional controller, the time response is exactly the same as the input variable as the following figure.

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Cont.

Kp/xp (or similar) is proportional coefficient or proportional gain which is a relation between manipulated variable and system deviation given by,

This value can be set and determine how manipulated variable is calculated from system deviation.

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op x

yK

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Question 1

What is happening if the proportional value, Kp is set too high and too low?

Answer:

Too high: manipulated element will make great change for small deviation (difficult to control).

Too low: controller response become too weak and result unsatisfactory control.

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Cont.

Practically, controller always have delay time – manipulated variable will not response until pass certain time after change in system deviation.

However in electrical controller, this delay time can be set.

The most important property of P controller is as a result of dependency of manipulated variable to the system deviation, some system deviation always remain.

This become the disadvantage of P controller due to the inability to compensate the remaining system deviation.

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Integral controller

Integral controller adds the system deviation over time (integrated) as figure below.

A constant present of system deviation will continuously increase the manipulated variable since it is dependent on summation over time.

The manipulated variable increment will result the system deviation to reduce until it become zero.

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Cont.

Thus, permanent system deviation is avoided and this become the purpose of integral controller.

The rate of change (not the value) of the manipulated variable is proportional to the system deviation as the following figure.

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Question 2

Explain how integral controller acts when it detects large system deviation.

Answer:When it detects large deviation, manipulated variable change quickly. System deviation will reduce and manipulated variable will change more slowly until equilibrium is reached.

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Question 3

Give disadvantage of integral controller.

Answer:

It causes oscillation of the closed loop/ respond too slow to system deviation in a long time response system.

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PI Controller Pure I controller –output respond slowly to rapid change

of error signal. Pure P controller – react quickly but cannot reduce error

to zero. Since this controller is a combination on Proportional

and Integral controller, the advantage of both controller are combined as well.

The fast reaction and compensation of remaining system deviation are able to achieve by this type of controller.

The reset time (integral-action time) is introduced in this system as a result of I component.

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Cont.

The reset time is a measure of how fast the controller resets the manipulated variable (in addition to manipulated variable generated by the P component) to compensate the remaining system deviation.

The reset time is simply a time by which PI controller is faster than pure I controller.

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Cont.

The reset time is a function of proportional gain, Kp (for greater Kp, rate of change of manipulated variable is faster).

For long reset time, summation of system deviation is slow (small effect of the integral component) and vice versa.

The PI controller effects is increase with the increase of Kp and I component (decrease reset time).

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Question 4

Explain what will happen if both Kp and I component are increased to maximum value.

Answer:Too large value for both will results the entire control loop to oscillate and unstable response.

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PD Controller

Differential action describes the rate of change of the system deviation.

The greater the rate of change, the greater the differential component.

Derivative-action time, Td is introduced as a measure for how much faster PD controller compensates a change in the controlled variable compare to pure P controller as the following figure.

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Cont.

There are 2 disadvantages of PD controller:1. Unable to completely compensate remaining system deviation2. Slight increment of D component will result quick instability to the control loop and the controlled system begin to oscillate.

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PID Controller

It is an addition to PI controller where rate of change of the system deviation is taken into account.

D component ensures high change in manipulated variable if system deviation is high.

When the change in system deviation is slight, the behaviour of D component is negligible.

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Cont.

The advantage of PID controller is it gives faster response and quick compensation of system deviation.

The disadvantage is the control loop is prone to oscillate and difficult setting.

The time response of PID controller can be seen from the following figure.

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Cont.

The derivative-action time, Td of PID controller is faster than Td of PI controller.

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6. Other Process Control Loop

For automatic process control, closed-loop feedback control system is always the simplest strategy that compensates process upsets.

Due to merely react when there is an upset in the process, it becomes the disadvantage of the system.

Meaning, the system only active when there is a disturbance in the process that propagates through the process which result a deviation from the set value.

This deviation used by the feedback to take corrective action thus it depends on deviation in controlled variable to initiate corrective action.

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Cont.

This type of control strategy was used almost 80% in many industrial practices due to satisfaction in safety, product quality and production rate.

However feedback control is unacceptable for tighten process requirement, or in slow dynamics processes, or in processes with too many or frequently occurring upsets where other strategies is necessary to provide the performance required.

Among them are cascade, feedforward and ratio control which are complement of the feedback control and are not intend to replace the system.

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Cascade

Based on the above figure, the feedback controller strives to maintain the desired level in the tank, disregarded the outflow.

Demand from the downstream process is a major disturbance to the level control.

FEEDBACK CONTROLLER

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Cont.

If the tank outflow is strong, feedback controller should be able to maintain the level very closely to the desired value.

However, due to the large time constant in level control system, it may take a while before the level can be stabilized.

Furthermore, a few disturbances at the inlet flow influenced the stabilization process such as pressure differential across the valve FCV-1 and upstream line pressure from other processes connected to the main supply.

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Cont.

Even feedback controller may maintain the tank level to the desired value; change in upstream line pressure will change the control valve flow rate and upset the level.

Therefore, some consideration is needed for changes in line pressure if the system required tight level control & such approach is known as cascade control.

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Cont.

Figure above shows the cascade control where 2 feedback controllers are incorporated in the system.

It is arranged in such a way where the output of one feedback controller becomes an input to the second controller.

CASCADE CONTROLLER

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Cont.

From the figure, the outflow from flow control valve FCV-1 (inflow to tank) is monitored and the valve is manipulated in order to maintain a consistent flow rate.

Meanwhile, a secondary controller is set up to control the valve flow rate and takes set point input from primary controller which is working on feedback from the tank level and a primarily responsible for maintaining the level.

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Cascade block diagram

The cascade block diagram is given by the above figure.

Compared to outer primary loop, secondary loop is set up to have faster response.

FCV

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Feedforward

Conventional negative-feedback controller works only when an error exists in the system.

However, an ideal control system should operate with zero (minimal amount) error and make corrective action prior to the error build up in the system.

Let’s see 2 cases to differentiate between a feedforward and feedback system in driving a car at a constant speed.

An assumption that the road is straight without any curves and its free from traffic but entail small hills and valleys.

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Case I: Feedforward (Driver control) An experienced driver will able to maintain the car

speed at the desired value (70 km/h) regardless of the conditions mention above.

During level course, the driver will give constant pressure on the accelerator and the car rolling at constant speed.

When the driver encounter upward slope (hill), extra pressure will be applied to the pedal so that the car keep at constant speed even it travel uphill.

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Cont.

When the driver encounter downward slope, a small pressure on the accelerator will be applied hence constant speed is achieved from all 3 different road condition.

Precisely, from driver’s visual cue a deduction (deduce) is made followed by action in advance to keep the speed constant.

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Case II: Feedback (Cruise control) A car with cruise control is able to perform the same

task without to acknowledge driver expertise. Once cruise control is set at certain speed in its

memory, the car will travel at constant speed by constantly comparing the car actual speed with the speed in memory.

During level stretch, cruise control can easily maintain the constant speed.

When the car travel uphill, the speed will reduce since the car was inject with same amount of fuel.

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Cont.

Cruise control will senses the speed drop (error) and increases the fuel intake to restore the constant speed.

With no visual indication, cruise control relies on feedback information in order to take action when the error has set.

http://auto.howstuffworks.com/cruise-control.htm

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Feedforward – Disturbance signal

What is disturbance signal? In example of home heating system, name

disturbances that upset the steady-state plant operation.

How these disturbance can be avoided in the system?

What does feedforward control system role in the system?

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Problem example

The level in the tank is maintained by upstream flow control valve, FCV-1.

To maintain the level, the inflow through FCV-1 should match outflow of the tank.

However, the tank outflow depends on the demand from the downstream.

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Cont.

If downstream required large flow rate, FCV-2 need to be opened.

Because inlet flow rate through FCV-1 has not yet changed, tank level starts to drop.

This drop is detected by level transmitter (LT) and send the signal as a feedback to the level controller.

Level controller will open FCV-1 to compensate the drop of the tank level.

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Cont.

Since it is very difficult to predict the demand of the downstream system, feedback level controller can only take action if an error has developed in the system.

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System improvement (feedforward)

The problematic system can be improved by incorporating flow transducer in outflow line.

The flow transducer will generate signal to feedforward controller to control FCV-1 in conjunction with level transmitter signal.

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System operation

Flow transducer measures the disturbance in outflow rate & feeds to a controller called feedforward controller.

This controller generates correction signal which added to feedback controller output and adjust the valve FCV-1 accordingly.

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Cont.

Feedback controller still responsible for error correction while feedforward controller used to modify manipulated output signal based on disturbance signal.

For a system where external disturbance is a main source of error, feedforward controller plays bigger role while feedback controller simply acts to remove the remaining error.

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System block diagram

If the mathematical model of the process is known, then it is possible to make correction through the feedforward mechanism.

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Cont.

But in any case, the feedforward controller has not provided a precise compensation for a disturbance signal.

In practical systems, an approximate correction is acceptable, because the feedback controller takes care of the remaining error in the system.

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Ratio

Processes in industry include blending and mixing where 2 material/ substance/ compound are required to be blended or mixed in predefined ratio with respect to each other.

For instance, hot and cold water mixing in a shower where 2 water-flow rates are required to maintain the ratio so a set of water temperature is obtained.

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Cont.

For ratio control system, 2 independent controllers are required for each flow stream plus third controller as ratio controller.

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Cont.

The ratio control process: One of 2 flow streams is considered primary flow stream & the

flow rate is controlled by the process requirement. Ratio controller gets feedback from flow transducer at primary

flow stream and generates output (desired flow rate) for secondary flow controller.

Secondary controller ensures flow rate at second stream remains at desired value.

If there is changes in primary stream, the ratio controller will pass the required change to the secondary flow stream hence consistence final flow (product) is achieved.

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