Controlled System and Control Algorithm

Control Algorithm

A control algorithm is a mathematical expression of a control function. Using the temperature control loop example, V in the equation below is the fuel valve position, and e is the error. The relationship in a control algorithm can be expressed as:

V = f(±e)

The fuel valve position (V) is a function (f) of the sign (positive or negative) of the error (Picture 1).

Picture 1: Control Algorithm Example


Control algorithms can be used to calculate the requirements of much more complex control loops than the one described here. In more complex control loops, questions such as “How far should the valve be opened or closed in response to a given change in setpoint?” and “How long should the valve be held in the new position after the process variable moves back toward setpoint?” need to be answered.

Manual and Automatic Control

Before process automation, people, rather than machines, performed many of the process control tasks. For example, a human operator might have watched a level gauge and closed a valve when the level reached the setpoint. Control operations that involve human action to make an adjustment are called manual control systems. Conversely, control operations in which no human intervention is required, such as an automatic valve actuator that responds to a level controller, are called automatic control systems.

Controlled System

The controlled system has an input variable and an output variable. Its response is described in terms of dependence of the output variable on the input variable. These responses between one or several variables can normally be described using mathematical equations based on physical laws. Such physical relationships can be determined by experimentation. Controlled systems are shown as a block with the appropriate input and output variables (see Picture 2).

Picture 2: Block diagram of a Controlled System

Example

A water bath is to be maintained at a constant temperature. The water bath is heated by a helical pipe through which steam flows. The flow rate of steam can be set by means of a control valve. Here the control system consists of positioning of the control valve and the temperature of the water bath. This result in a controlled system with the input variable "temperature of water bath" and the output variable "position of control valve" (see Picture 3).

Picture 3: Water bath Controlled System


The following sequences take place within the controlled system:

>> The position of the control valve affects the flow rate of steam through the helical pipe.
>> The steam flow-rate determines the amount of heat passed to the water bath.
>> The temperature of the bath increases if the heat input is greater than the heat loss and drops if the heat input is less than the heat loss.
>> These sequences give the relationship between the input and output variables.


The advantage of creating a system with input and output variables and representing the system as a block is that this representation separates the problem from the specific equipment used and allows a generic view. All sorts of controlled systems demonstrate the same response and can therefore be treated in the same way.