Controller output modes, operating equations, cascade control--part 3

Using equation types and application

We have to make a careful assessment of the process and the process strategy before we decide on a particular equation type. As a general rule we can use the different types as follows:

Application of equation type A:

This is a general purpose calculation to be used if no special reason exists to use another type.

Important note: Eq-type A is a must for secondary controllers. If eq-type C were to be used in a secondary controller, I-control would be the only control between the OP of the primary controller and the OP of the secondary controller. This would add an unnecessary phase lag of 90 for the primary controller's loop. The result could be an unnecessary destabilization of the primary loop of a cascade control system.

Application of equation type B:

The principle considerations, how the control algorithms can work on PV only, are the same as explained for equation type C. Equation type B works as a PI-controller on error (ERR = PV- SP) and works as a D-controller on PV only.

Since eq-type B is in between eq-type A and eq-type C, it’s thus left to the discretion of the user to make decisions about the use of eq-type B. If, E.g., a secondary controller needs D-control for stability of the secondary loop and the OP of a primary controller contains all the control actions required for the primary loop (including D-control), then the secondary controller may be best used with eq-type B. In such a case, the full control action of the primary controller is passed on to the OP of the secondary controller via control of the secondary.

Application of equation type C:

Equation type C works as I-controller on error (ERR = PV - SP) and works as a PD-controller on PV only.

Mainly used as the ultimate primary controller. An operator cannot cause any sudden control actions that would result in sudden extreme positions of valves and other control equipment. This can only be fully appreciated if one has heard the noise created by the sudden hitting of an extreme valve position of a large valve. It can be felt in almost the whole plant as a big bang. This is most decidedly not good for maximizing the life of a valve.

Equation, Type; Comments on Use; Standard controller; Special uses; Primary controller

Table 1 Comparison of PID equation types and error calculations

Cascade control loop--Tuning

The approach for tuning is fairly straightforward. Firstly, tune the ultimate secondary controller (the most downstream controller) which in our example is the FC controller.

Then considering that controller as part of the process, tune the next upstream controller (the one whose output drives the setpoint of the last tuned controller). Continue in this manner, remembering to consider the last tuned controller as part of the process loop, finally tuning the most primary controller, again in our example the TC controller.

Secondary controller:

Secondary controllers are mostly used as flow controllers. Flow loops are in most cases intrinsically stable. Therefore, no D-control is required and most flow controllers are PI-controllers. Tuning is done with due consideration given to a sufficiently good control response and minimum wear and tear of the valve. The value of K should be smaller than 1 in order to pass on the full range of the primary controller's OP to the OP of the secondary controller.

Primary controller:

Primary controllers normally control a dynamically more complex loop and require careful stability considerations. Our example of a feed heater shows clearly that the temperature controller TC has to cope with most of the process lag. In most cases, primary controllers are therefore PID-controllers.

Exercise: Cascade control:

Will give practical experience on the topics of cascade control.

Cascade control with multiple secondaries

A control strategy can include controllers with multiple output calculations. In most cases, controllers with multiple outputs are primary controllers in a cascade control system with more than one secondary controller.

Multiple output calculations:

The result of the primary controller's PID calculation is the controller's dynamic output.

In digital controllers, this is the calculated value CV, which is calculated for each scan time interval and is used to increment each output independently. As every output of a controller may have a different absolute value at any given time, every output is incremented individually.

In actual fact, each output is calculated independently of each other with independent initialization, limit and alarm handling. As the amount of data for multiple outputs is too much for one display, industrial control equipment will display only the first output in the main detail display and has subsequent displays for additional data like multiple outputs.

One has to be aware of this from an engineering point of view in order to define the most significant output to be the first output of a controller. From an operator's point of view, it’s important to know that the most prominently displayed output value may not be the only output to be monitored, it may just be the most important one.

Exr 12: Cascade control with one primary and two secondaries Will give practical experience on the topics of controllers with multiple outputs.

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