Controller output modes, operating equations, cascade control--part 2

Cascade control

Using the example of our feedheater, if we add another control loop, which is just to control the fuel flow, we will keep the fuel flow constant despite fuel flow pressure changes. If the OP of the temperature controller TC drives the SP of this newly added fuel flow controller, FC, then we have the situation that the OP of the temperature controller TC then drives the true flow and not just a valve position. Fuel flow pressure would practically no longer have any effect on the outlet temperature. This concept is called cascade control. The principle is shown.

+=+=+=+ Single loop temperature control: Air Fuel PV OP TC SP T2 Inlet T1

Cascade control terms:

In order to help identify which controller is which within a cascaded system, the following terms apply:

• The controller, whose SP is driven by another controller's OP may be called a 'downstream controller' (slave), or perhaps more often it’s referred to as a 'Secondary controller'.

• The controller whose OP drives the SP of a secondary controller is called an 'upstream controller' or 'Primary controller' (master).

If we have more than two controllers in a cascade system,

• The highest upstream controller is called the ultimate primary.

• The lowest downstream controller is called the ultimate secondary controller.

If we examine the requirements needed to start-up such a feed heater cascade control system manually, it will give us insight into the principles of operation. This, in turn, will also give us the background required to understand PV-tracking, initialization and the different equation types used in the related control algorithms.

This shows the basic cascaded system, with the temperature controller (TC) being the primary control, and the fuel control (FC) the secondary controller.

+=+=+=+ Two-controller basic cascade control--Air Inlet Fuel

The concept of process variable or PV-tracking:

PV-tracking is active if the secondary (FC) controller is in manual mode. Controllers can be set up to make use of PV-tracking or not. It’s the choice of the system designer.

The concept is that an operator sets the OP value of the fuel controller manually until they find an appropriate value for the process. We assume that this output value is the optimum value for the process, that is we have set the fuel flow rate to a manual value that is correct to maintain the output temperature, T2, at the required value. This leads to the conclusion that no correction of the OP value is necessary at this time. As no change of OP is the ideal requirement, no error (ERR) is permitted. To achieve this we have to keep the SP equal to the PV by the operator manipulating the OP value manually.

Hence for PV-tracking in MANUAL mode only: SP = PV. This is called PV-tracking.

The moment we change the mode to AUTOMATIC, the SP stays at its last value and is the reference previously created by manual manipulation of OP (when the mode was set to MANUAL). The output of the flow controller (FC) has an ABSOLUTE value as determined by what was set by the operator at the time of the transition from manual to automatic sufficient to hold the fuel valve in its required position.

Cascade system--Initialization

Initialization is actually a kind of manual mode, in which the operator doesn't drive the OP value of the primary controller (our temperature controller, TC, in this case). Instead, our FC supplies its setpoint (SP) value, back up the cascade chain, to the OP of the controller that will be driving it (the FC's SP) when the system is in automatic mode. If selected, PV-tracking can take place in the primary controller as it would occur in normal manual mode.

Steps of initialization:

Let us analyze how initialization is useful by looking into our feed heater example again.

• If the fuel flow controller FC is in manual mode and its OP value is driven by an operator until the desired outlet temperature (T2) has been reached, the PV of the fuel flow controller (FC) has the correct value in order to obtain the desired value of T2. (Open loop conditions exist in this loop at this point.)

• Via PV-tracking of the flow controller, its setpoint value, as manipulated by the operator, is at the value required to give the FC output its correct value to maintain T2 by establishing the correct flow rate.

• The SP value of the fuel flow controller FC has the exact value that the output of the temperature controller TC will require from it.

• The fuel flow controller, while in manual mode, passes back its SP value to the OP block of the temperature controller TC. The temperature controller allows this value to be set into its output block by receiving a signal from the FC that it’s in both 'cascade and manual mode' (accepting this command in a similar manner as to itself being placed in manual mode).

• This is called Initialization. If the primary controller (TC) performs PV-tracking, then the temperature SP follows the true temperature value, the PV of the primary controller.

• When the operator has found the correct OP value of FC, we have, by default, obtained an SP value for the correct flow. SP = PV.

• If we matched this SP with the primary controller's OP value, then we have the correct SP for temperature as well.

• All there is to do is to put the secondary controller into CASCADE mode and the associated primary controllers output block should switch automatically to AUTO mode.

• We have thus achieved a smooth (bumpless) transfer from manual to automatic control.

Controller configurations--Equations

In cascade control, outputs from controllers drive the setpoints of secondary controllers, and, in essence all of these controllers consist of, or are capable of, independently calculating P, I and D algorithms, based on the error value derived from the two inputs, the setpoint value (SP) and the process variable PV. There are occasions where only certain functions within a cascade chain are required, and it becomes necessary to 're-arrange' the way the P, I and D functions are driven from the PV and SP variables.

There are three ways to do this, and they are known as controller equations type A, B or C. Equations A and C are the more commonly used of the three, and are interrelated, so these will be considered together.

+=+=+=+ the interconnections of a controller that determines the type of equation it represents.

+=Equations types A, B and C

Equation type A:

In Equation type A all control is based on the error term (ERR). A controller using equation type A makes no distinction between a disturbance in the PV input and an operator action on the SP. This is the standard way of calculating control actions of a PID-controller and this has been the way in which we have considered all controllers so far in this book. Where PV changes are fairly smooth with minimal or no step changes, they won’t cause dramatic or sudden changes to the controller's output. Additionally the SP of the controller is normally never or very seldom moved again not causing rapid changes of output, but in contrast, an operator may drive a valve through its complete range by a large step change of the SP. In such situations, we could consider the operator to be the most dangerous disturbance in the system.

Hence, when we require a smooth transition, even if the operator changes the SP dramatically, we need to 're-arrange' the construction of the controller to help us achieve this requirement. This leads to equation type C.

Equation type C:

As can be seen, Equation B works as PI controller on ERROR (ERR - PV - SP) and works as a D-controller on the PV only. Equation type C con figures the controller so that we can eliminate the problem of step changes to the output occurring by large and rapid changes being made to the setpoint value by the operator. We must remember that in most systems the SP of a primary controller is seldom changed much, either in magnitude or time. However when the SP is changed we need to ensure the resultant output change is as soft and gentle as possible, particularly when it’s driving SPs of secondary controllers. A nice way to do this is to integrate the step change, illustrated as: Resultant controller output step change by a SP change

Referring to 5 we see how equation C differs from the normal equation type A by:

• The proportional and derivative functions operating, via the gain block KC, directly from the PV and not from the ERR term.

• The ERR term is used exclusively by the integral function, again derived from either PV - SP or SP - PV. This means that a step change made to the SP becomes an integrated (ramped) output from the controller. This kind of control calculation calculates an identical PID-control action as with equation type A if the setpoint is a constant. This maintains the same control against real disturbances and the same loop behavior. The SP is the only variable treated differently. The details of equation type C are as follows: Equation C and the P-control When the SP = constant - What is the difference?

Answer: No difference, provided SP = constant.

Notes:

• Observe that the change of ERR, where ERR = (PV SP), ?- is identical to the term ? PV (the change of PV).

• There is identical P-control action based on PV, but the SP is ignored totally.

• The SP is not even part of the formula any more.

• The operator can do what he/she wants with the SP, but this will have no influence on P-control if equation type C is active.

Equation C and the I-control The availability of an integral control is the reason for the existence of these controller equations because:

• There are no differences in I-control with different equation types.

• I-control is available to the operator at all times for smooth bumpless changes of control from one SP to another.

• I-control will never cause any bump if a SP change takes place.

• Since the SP is an outside influence as far as the loop is concerned, the integral on SP has no effect on loop stability.

Equation C and the D-control

When the SP = constant - What is the difference ?

? OP = K × TDER × ((PV SP)) ?? - [Eq-type A]

? OP = K × TDER × ((PV) ?? [Eq-type C] Answer: No difference, provided SP = constant.

Notes:

• Observe ((SP PV) ?? - is identical to ((PV) ?? if there is no change of SP.

• There is identical D-control action based on PV, but the SP is ignored totally.

• The SP is not even part of the formula any more.

• The operator can do what he wants with the SP as he has no influence on D-control if equation type C is active.

This is one more example of the use and benefit of incremental algorithms.

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