Controller Modes

1. ON-OFF controller/two position controller2. Three-position controller3. Proportional Action Control4. Integral/Reset Action Control5. Derivative/Rate Action Control6. P+I Control7. P+D Control8. P+I+D Control

• Discontinuous control mode• Also called two-position control• The simplest form of control• It is very commonly used in industry• The manipulated variable is quickly changed to

either a maximum or a minimum value• The minimum value of the manipulated variable is

usually zero (off)• Transmit only two output signals: ON (100%), OFF

(0%)• Only responds when it’s above or below the setpoint

ON-OFF Control

ON-OFF Controller• Example : Process : Water tank of 10 litres Target: Reach + maintain a temperature of 90oC.

Water : 10 Litres

Heater

Sensor

Two-positions controller with hysteresis

ON-OFF Controller made from Op- amps

Vin reaches VH Comparator ON state(V0)Vin falls below a value VL Comparator OFF state (0)

Vsp = Setpoint voltage

The HIGH (ON) or V1=Vsp switch voltage isVH = Vsp

The LOW (OFF) switch voltage isVL = Vsp – R1/R2 V0

Vin0

V0

Vout

(ON)

(OFF)

VL VH

Example:Level measurement in a sump tank is provided by a transducer scaled as 0.2 V/m. A pump is to be turned on by application of +5V when the sump level exceeds 2.0m. The pump is to be turned back off when the sump level drops to 1.5m. Find R2 if R1 is given 5kΩ

Three-Position Controller made from Op- amps

• In this circuit assumed:The output of the comparators is 0V for the OFF stateVo volts for the ON state

• The summing amplifier includes a bias voltage input VB which allows the three-position mode response to be biased up or down in voltage to suit particular needs.

• The inverter is to convert the sign of the inverting action of the summing amplifier

• Equation presented the generic three-mode controller response:

Vin < Vsp1 Vout = VB

Vsp1 < Vin < Vsp2 Vout = VB + R3/R1 Vo

Vin > Vsp2Vout = VB + R3/R1 Vo + R3/R2 Vo

Response of the three-position controller with the bias equal to zero

Example:The level in a sump tank is to be controlled with a three-position controller. The following specifications are given:1. The level measurement sensor has a transfer function of 0.45 V/m2. The valve is linearly driven from fully open to fully closed by a voltage from 0 to 8V3. The following specifications are given:

level < 2m valve 20% openlevel > 2m < 3m valve 65% openlevel > 3m valve 100% open

Comparators are available that have outputs of 0 V for OFF and 5V for ON. Design a three position op amp controller. R3 is given by 10kΩ

Proportional Controller (P Mode)• Continuous control mode• Typical behavior/characteristics:

The signal output of a controller is proportional to the input or error

Stay at the same ratio

• Proportional control is a pure gain adjustment acting on the error signal to provide the driving

input to the process.

• Implementation of this mode requires a circuit which has a response given by

Where: U =controller output (0 100%) K = Proportional gain (controller transfer function) PB = proportional band in percentage Ep = error in percent of variable range Pp = controller output with no error (bias)

Example:A proportional controller has the scale 0-10 volts corresponds to a 0-100% output. If R2 = 10 KΩ, and full scale error is 10 volt, find the value of V0 and R1 to support a 20% proportional band about a 50% zero-error controller output.

Advantages: Simple Easiest of the continuous controllers tune Provides good stability, rapid response and

relatively stable.

Disadvantages: Only control results in offset – Never reaches SP Action is instantaneous – As soon as error is

produced, control action is taken.Used to stabilize unstable output

Integral Action Control• Also called Reset Action Control• Continuous control mode• Typical behavior/characteristic:

- The controller output is proportional to the integral of the error with respect to time

- The value of the controller output is changed at a rate proportional to the error “e”

• Used to removed offset• As long as error exist, integral action will work

to eliminate the error

Integral control is implemented through the introduction of an integrator. Implementation of this mode requires a circuit which has a response given by

Example:• Suppose that V(0)=0 for an integral controller. • It is required that the controller output should

saturate 15 seconds after a constant 5% error is applied.

• The input range is 0-5 volts and the output range is 0-10 volts. Calculate the integration gain and the suitable values of R and C. Assume C=50μF

Derivative Control• Also called Rate Control Action• Continuous control mode• Typical behavior/characteristic:

- The controller output is proportional to the rate of the error (time derivative)

• Faster/quick response compared to P• Can cause the damage to the FCE because of too

fast rate of change of the error• Can amplify the noise in the system• Cannot compensating the system error: e = w-x=0

• The derivative mode is never used alone because it cannot provide a controller output when the error is zero.

• Implementation of this mode requires a circuit which has a response given by

The value of R1 is selected so that the circuit will be stable for high frequencies by setting where f is the frequency in Hz.

SummaryRemark: Each mode has its advantages and drawbacks

individually• P mode Advantage: Fast response action • Drawback: Produces steady state error (offset) • I mode Advantage: Steady state error is null • Drawback: Increases the response time • D Mode Advantage: increases the damping of the system • Drawback: Amplifies the noise which can cause problems

including instability

• Therefore, the pure controller mode (P or I or D) is seldom used in process control because of the advantage of composite modes in providing good control.

Composite ControllerProportional- Integral Control (PI Mode)

This controller can: eliminate an offset due to integral action the system response is slow due to lag introduced = -90o

better dynamic response than integral alone I action repeats P action in Ti seconds the slope depends on Ti

Kp

Ki

Gp

Parallel controller - Mathematical

100/PB

1/Ti

Gp

Series controller - Practical

Ti – Time for integral action after the proportional action

I

t

I

t

I

t

P+I

Example: PI controller has a proportional band of 30% and an integration time =10 seconds. The 4-20mA input volts converts to a 0.4-2 volt error signal and the controller output range is 0-10 volts.Calculate values of Kp, KI, R1, and R2. C is given by 10μF

Proportional-Derivative Control (PD Mode)

This controller can: experience the offset but less than proportional only the system response is faster due to lead introduced = -90o

better dynamic response than integral alone I action repeats P action in Ti seconds the slope depends on Ti

Proportional-Derivative Control (PD Mode)

Three term Controller (PID Mode)