148

2.6 Control Systems Cascade Loops

F. G. SHINSKEY (1970, 1985) B. G. LIPTK (1995) R. BARS, J. HETTHSSY (2005)

INTRODUCTION

Cascade control has a multi-loop structure, where the outputof the controller in the outer loop (the primary or master)is the set point of a controller in the inner loop (the second-ary or slave).

The slave measurement is an intermediate process vari-able that can be used to achieve more effective control of theprimary process variable. In the cascade configuration theprocess is divided into two parts and therefore two controllersare used, but only one process variable (m) is manipulated.

In Figure 2.6a the primary controller maintains the pri-mary variable y1 at its set point by adjusting the set point r2of the secondary controller. The secondary controller, in turn,responds both to set point r2 and to the secondary controlledvariable y2. This secondary controlled variable also affectsthe primary process and therefore the primary controlledvariable (y1), hence the loop is closed.

This cascade loop can also be shown in a more detailedblock diagram form (Figure 2.6b). Here, the primary control-ler (C1) generates the set point for the secondary controller(C2), while the secondary controlled variable (y2) also affectsthe primary process (P1) and therefore it also affects theprimary controlled variable (y1).

Cascade control is advantageous on applications where theP1 process has a large dead time or time lag and the time delaysin the P2 part of the process are smaller. Cascade control isalso desirable when the main disturbance is in the secondaryloop. This is because with the cascade configuration, the cor-rection of the inner disturbance di occurs as soon as the sec-ondary sensor (y2) detects that upset.

Cascade System Advantages

There are two main advantages gained by the use of cascadecontrol:

1. Disturbances that are affecting the secondary variablecan be corrected by the secondary controller beforetheir influence is felt by the primary variable.

2. Closing the control loop around the secondary part ofthe process reduces the phase lag seen by the primarycontroller, resulting in increased speed of response.This can be seen in Figure 2.6c. Here, the response ofthe open loop curve shows the slow response of thesecondary controlled variable when there is no second-ary controller. The much faster closed loop curvedescribes the response of the secondary controlled vari-able when the cascade configuration adds a secondaryinner control loop.

Other advantages of using cascade control include theability to limit the set point of the secondary controller. Inaddition, by speeding up the loop response, the sensitivity ofthe primary process variable to process upsets is also reduced.Finally, the use of the secondary loop can reduce the effectof control valve sticking or actuator nonlinearity.

COMPONENTS OF THE CASCADE LOOP

The primary or outer control loop of a cascade system isusually provided with PI or PID control modes and isdesigned only after the secondary loop has already beendesigned. This is because the characteristics of the slave loophave an effect on the master loop.

For example, if the secondary measurement is nonlinear,such as the square root signal of an orifice-type flow sensor,it would produce a variable gain in the primary loop if thesquare root was not extracted.

For these reasons, the secondary loop requirements willbe discussed first.

The Secondary Loop

Ideally, the secondary variable should be so selected as tosplit the process time delays approximately in half. This

FIG. 2.6aThe cascade control system divides the process into two parts.

Secondaryprocess

Secondarycontroller

Primarycontroller

Primaryprocess

Disturbances

m r2

y2 y1

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2.6 Control Systems Cascade Loops 149

means that the secondary loop should be closed around halfof the total time lags in the process. To demonstrate this need,consider two extreme cases:

1. If the secondary variable responded instantly to themanipulated variable (no time delay in the secondaryloop), the secondary controller would accomplishnothing.

2. If the secondary loop was closed around the entire pro-cess, the primary controller would have no function.

Therefore, the dynamic elements of the process should bedistributed as equitably as possible between the two control-lers. When most of the process dynamics are enclosed in thesecondary loop, that can cause problems. Although theresponse of the secondary loop is faster than the open loopconfiguration, in which a secondary controller does not evenexist (Figure 2.6c), its dynamic gain is also higher, as indicatedby the damped oscillation. This means that if stability is to beretained in a cascade configuration, the proportional band ofthe primary controller must be wider than it would be withouta secondary loop; such de-tuning reduces responsiveness.

The right choice of the secondary variable will allow areduction in the proportional band of the primary controllerwhen the secondary loop is added because the high-gainregion of the secondary loop lies beyond the natural fre-quency of the primary loop. In essence, reducing the response

time of the secondary loop moves it out of resonance withthe primary loop.

Secondary Control Variables

The most common types of secondary control variables arediscussed next, discussed in the order of their frequency ofapplication.

Valve Position Control (Positioner) The position assumed bythe plug of a control valve is affected by forces other than thecontrol signal, principally friction and line pressure. A changein line pressure can cause a change in the inner valve positionand thereby upset a primary variable, and stem friction has aneven more pronounced effect.

Friction produces hysteresis between the action of the con-trol signal and its effect on the valve position. Hysteresis is anonlinear dynamic element whose phase and gain vary withthe amplitude of the control signal. Hysteresis always degradesperformance, particularly where liquid level or gas pressure isbeing controlled with integral action in the controller.

The combination of the natural integration of the process,reset integration in the controller, and hysteresis can cause alimit cycle that is a constant-amplitude oscillation. Adjust-ing the controller settings will not dampen this limit cyclebut will just change its amplitude and period. The only wayof overcoming a limit cycle is to close the loop around thevalve motor. This is what a positioner (a valve position con-troller) does; and this action can be considered to be thesecondary loop in a cascade system.

Flow Control A cascade flow loop can overcome the effectsof valve hysteresis as well as a positioner can. It also ensuresthat line pressure variations or undesirable valve characteristicswill not affect the primary loop. For these reasons, in compo-sition control systems, flow is usually set in cascade.

Cascade flow loops are also used where accurate manip-ulation of flow is mandatory, as in the feedforward systemsshown in Section 2.8.

FIG. 2.6bBlock diagram of a cascade control system.

C1(s) C2(s) P2(s)

di do

P1(s)

Setpointr

Outercontroller Saturation

Innercontroller

Process

Inner (secondary) loop

Outer (primary) loop

y2 y1

sensor2

sensor1

u

FIG. 2.6cThe response of the secondary variable is much improved whencascade control is used.

Secondarycontrolled variable Closed loop

Open loopTime

r2

(y2)

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150 Control Theory

Temperature Control Chemical reactions are so sensitive totemperature that special consideration must be given to con-trolling the rate of heat transfer. The most commonlyaccepted configuration has the reactor temperature controlledby manipulating the coolant temperature in cascade. A typicalcascade system for a stirred tank reactor is shown inFigure 2.6d.

Cascade control of coolant temperature at the exit of thejacket is much more effective than at the inlet because thedynamics of the jacket are thereby transferred from the pri-mary to the secondary loop. Adding cascade control to thissystem can lower both the proportional band and reset timeof the primary controller by a factor of two or more.

Since exothermic reactors require heating for startup aswell as cooling during the reaction, heating and coolingvalves must be operated in split range. The sequencing of thevalves is ordinarily done with positioners, resulting in a secondlayer of inner control loops or cascade sub-loops in the system.

In Figure 2.6d, the secondary variable is the jacket tem-perature and the manipulated variables are the steam and coldwater flows. Under control, the secondary variable willalways come to rest sooner than the primary variable becauseinitially the controller will demand a greater quantity of themanipulated variable than what is represented by the equiv-alent step change in the manipulated variable.

This is particularly true when the secondary part of theprocess contains a dominant lag (as opposed to dead time).Because with a dominant lag the gain of the secondary con-troller can be high, closing the loop is particularly effective.The dominant lag in the secondary loop of Figure 2.6d is thetime lag associated with heat transfer across the jacket.

Secondary Control Modes Valve positioners are proportionalcontrollers and are usually provided with a fixed band of about5% (gain of 20). Flow controllers invariably have both propor-tional and integral modes. In temperature-on-temperature cas-cade systems, such as shown in Figure 2.6d, the secondarycontroller should have little or no integral. This is because resetis used to eliminate proportional offset, and in this situation asmall amount of offset between the coolant temperature and itsset point is inconsequential. Furthermore, integral adds the pen-alty of slowing the response of the secondary loop. The propor-tional band of the secondary temperature controller is usuallyas narrow as 10 to 15%. A secondary flow controller, however,with its proportional band exceeding 100%, does definitelyrequire an integral mode.

Derivative action cannot be used in the secondary control-ler if it acts on set-point changes. Derivative action is designedto overcome some of the lag inside the control loop and ifapplied to the set-point changes, it results in excessive valvemotion and overshoot. If the derivative mode acts only on themeasurement input, such controllers can be used effectively insecondary loops if the measurement is sufficiently free of noise.

Cascade Primary Loop

Adding cascade control to a system can destabilize the pri-mary loop if most of the process dynamics (time lags) arewithin the secondary loop. The most common example ofthis is using a valve positioner in a flow-control loop.

Closing the loop around the valve increases its dynamicgain so much that the proportional band of the flow controllermay have to be increased by a factor of four to maintain

FIG. 2.6dWhen cascade control is provided for a stirred reactor, it is recommended to provide the cascade master with a PID algorithm and withexternal reset from the measurement of the secondary controller. In this case, there are two inner loops; both can be plain proportional.The gain of the temperature controller is usually 5 to 10, while that of the valve positioner is about 20.

Masterset-point

TT

TRC TY

HIC

TRC

PIDR/A

Manual loadingstation to settemperature

limitsSP

Slave #1

R/APB = 1020%I = some

ER

P

P

FC (= %)

FO (= %)

SP = Set pointER = External reset

Steam

Opens50100%

Opens500%

Slave #2

Coldwater

Slave #2

TRC OutputSteam valve

openingWater valve

opening0% 0% 100%

rottling

rottling

25 05075

100

0

100

000

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2.6 Control Systems Cascade Loops 151

stability. The resulting wide proportional band means slowerset-point response and deficient recovery from upsets. There-fore, in flow control loops, the existence of a large valvemotor or long pneumatic transmission lines causes problems,and a volume booster rather than a positioner should be usedto load the valve motor.

Instability Instability can also appear in a composition- ortemperature-control system where flow is set in cascade. Thesevariables ordinarily respond linearly to flow, but the nonlinearcharacteristic of a head flow meter can produce a variable gainin the primary loop.

Figure 2.6e compares the manipulated flow record fol-lowing a load change that has occurred at 40% flow with asimilar upset that took place at 80% flow. Differential pres-sure h is proportional to flow squared:

h = kF2 2.6(1)

If the process is linear with flow, the loop gain will varywith flow, but when h is the manipulated variable, becauseflow is not linear with h:

2.6(2)

Thus, if the primary controller is adjusted for 1/4-amplitudedamping at 80% flow, the primary loop will be undamped at40% flow and entirely unstable at lower rates.

Whenever a head-type flow meter provides the second-ary measurement in a cascade system, a square-root extrac-tor should be used to linearize the flow signal. The only

exception to that rule is if flow will always be above 50%of full scale.

Saturation When both the primary and secondary control-lers have automatic reset, a saturation problem can develop.Should the primary controller saturate, limits can be placedon its integral mode, or logic can be provided to inhibitautomatic reset as is done for controllers on batch processes.

Saturation of the secondary controller poses another prob-lem, however, because once the secondary loop is opened dueto saturation, the primary controller will also saturate. Amethod for inhibiting reset action in the primary controllerwhen the secondary loop is open (switched to manual) for anyreason is shown in Figure 2.6f.

If the secondary controller has integral, its set point andmeasurement will be equal in the steady state, so the pri-mary controller can be effectively reset by feeding back itsown output or the secondary measurement signal. But if thesecondary loop is open (in manual), so that its measurementno longer responds to its set point, the positive feedbackloop to the primary controller will also open, inhibiting resetaction.

Placing the dynamics of the secondary loop in the pri-mary reset circuit is no detriment to control. In fact it tendsto stabilize the primary loop by retarding the integral action.Figure 2.6f shows an application of this technique where theprimary measurement is at the outlet of a secondary steamsuperheater, whereas the secondary measurement is at itsinlet, downstream of the valve delivering water.

At low loads, no water is necessary to keep the secondarytemperature at its set point, but the controllers must be pre-pared to act should the load suddenly increase. In this examplethe proportional band of the secondary controller is generallywide enough to require integral action.

When putting a cascade system into automatic operation,the secondary controller must first be transferred to auto-matic. The same is true in adjusting the control modes, insofaras the secondary should always be adjusted first, with theprimary in manual.

FIG. 2.6eIf cascade ow with a nonlinear orice sensor is tuned at 80% ofrange, it will become unstable when the ow drops below 40%.

0 2 3 4 5 6 7 98 10 Flow

Time

dFdh kF

=

12

FIG. 2.6f External reset is provided for the primary controller to preventintegral windup when the secondary controller is in manual.

TTTT

TIC

TIC

Secondary

Secondarysuperheater

Primarysuperheater

Primary

Externalreset

Primarym

Secondary

Setpoint

Water

Steam

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152 Control Theory

Cascade Application Examples

Speed Control of a DC Motor When controlling the speedof a DC motor, the current can reach high peaks during thestart-up and shut-down phases or when loading or breakingthe motors. Therefore it is usual to apply cascade controlwith the armature current as the secondary variable. Satura-tion applied at the current set point (reference value) limitsthe maximum value of the current. The control system isshown in Figure 2.6g.

Another cascade control example is the control of elec-trical drives in controlling the position of servomechanismswith velocity feedback. Here the primary measured variableis the position, and the secondary measured variable is thevelocity. The manipulated variable is the voltage applied tothe servomotor.

Room Temperature Control A possible room temperaturecontrol configuration is shown in Figure 2.6h. The room is

heated by a steam-heated heat exchanger, which warms theair supply to the room. The manipulated variable is the open-ing of the steam valve, which determines the steam flowthrough the heat exchanger. The primary variable is the roomtemperature. The variation in steam pressure can be the mainsource of upsets. The secondary variable is the inlet air tem-perature measured immediately after the heat exchanger, asthe disturbances in the steam pressure affect it much soonerthan they affect the room temperature.

Adding Valve Positioner to Tank Level Control When theliquid level in a tank is controlled by an outlet valve, placinga positioner on that valve forms a secondary cascade loop. Thisis desirable because the position of the valves inner valve isaffected by other factors besides the control signal, such asfriction and inlet pressure. Variations in the line pressure cancause a change in position and thereby upset a primary vari-able. Stem friction can have an even more pronounced effect.

FIG. 2.6gCascade control of a DC motor.

rw Speed controller

Currentcontroller

yristorunit

uA

Saturation

Currentsensor

DCmotor

Speedsensor

FIG. 2.6hCascade control of room temperature.

air

Slave(secondary)

Master(primary)

Heatexchanger

Steam

air

TC TCJo

Ji

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2.6 Control Systems Cascade Loops 153

Inner valve sticking due to friction produces a square-loop hysteresis between the action of the control signal andits effect on the valve position. Hysteresis always degradesperformance, particularly where liquid level is being con-trolled with integral action in the controller. The combinationof the integrating nature of the process and the integral actionin the controller with hysteresis causes a limit cycle thatresults in a constant-amplitude oscillation.

Adjusting the controllers tuning settings will not dampenthis limit cycle but will only change its amplitude and periodof oscillation. The only way of overcoming this limit cycleis to add a positioner and close the position-controlling slaveloop around the valve motor.

Composition Control In composition control systems, flowis usually set in cascade. A cascade flow loop can overcomethe effects of valve hysteresis. It also ensures that line pres-sure variations or undesirable valve characteristics will notaffect the primary loop.

Cascade Controller Design and Simulation

The process controlled by a cascade system is shown inFigure 2.6i. The nominal values of the parameters and theuncertainties in their values are as follows:

The dual design objectives are:1. First design a single-series PID controller, with feed-

back taken from the output signal y1. Design objec-tives are stability and good reference signal (setpoint) tracking properties characterized by zerosteady-state error and about 60 of the phase marginto keep the overshoot below 10%, when a step changeis introduced in the set point.

2. Design a cascade control system with feedback takenfrom the primary and secondary (outer and inner) con-trolled variables (process outputs) y1 and y2, respec-tively. Both control loops have to be stable. The designobjectives for tracking the set point (reference signal)are the same as before. Fast response is also requiredto any upsets in the secondary loop or measurement.

The design should consider the theoretical processmodel, and the effects of the possible errors or uncertaintiesin the model should be checked.

Single-Series Primary Controller The block diagram of thesingle control loop is shown in Figure 2.6j. To ensure accuratetracking of the set point (step reference signal), the controllermust have an integral mode. The addition of rate action canaccelerate the system response. A PID controller combinesthese two effects. With pole-cancellation technique the sug-gested PID controller transfer function is

2.6(3)

The ratio of the time constants of the PD part was chosen tobe four.

The loop transfer function is

2.6(4)

Gain A of the controller has to be chosen to ensure therequired phase margin. In case of systems with dead time ,a phase margin of about 60 is obtained if the cut-off fre-quency c in the loops Bode amplitude-frequency diagramis at slope of 20 dB/decade and is located at about 1/2.

FIG. 2.6iThe process controlled by a cascade control system consists of twosegments (P1 and P2) and has a measurable inner variable (y2).

u

P2

d2

y2P1

d1

y1K2 K1 es1 + sT2 1 + sT1

K K K Kn n

n

1 1 2 21 0 8 1 2 1 0 8 1 220 18

= < < =