Controlled System

The controlled system is the part of a machine or plant in which the controlled variable is to be maintained at the desired value and in which manipulated variables compensate for disturbance variables. Input variables to the controlled system include not only the manipulated variable, but also disturbance variables. Before a controller can be defined for a controlled system, the behaviour of the controlled system must be known. The control engineer is not interested in technical processes within the controlled system, but only in system behaviour.

Dynamic response of a system

The dynamic response of a system (also called time response) is an important aspect. It is the time characteristic of the output variable (controlled variable) for changes in the input variable. Particularly important is behaviour when the manipulated variable is changed. The control engineer must understand that nearly every system has a characteristic dynamic response.

Example 1

In the example of the water bath in Controlled System and Control Algorithm, a change in the steam valve setting will not immediately change the output variable temperature. Rather, the heat capacity of the entire water bath will cause the temperature to slowly "creep" to the new equilibrium (see Picture 1).

Picture 1: Time response of the controlled system "Water bath"

Example 2

In the example of a valve for volumetric flow control, the dynamic response is rapid. Here, a change in the valve setting has an immediate effect on flow rate so that the change in the volumetric flow rate output signal almost immediately follows the input signal for the change of the valve setting (see Picture 2).

Picture 2: Time response of the controlled system "Valve"

Description of the dynamic response of a controlled system

In the examples shown on Picture 1 and Picture 2, the time response was shown assuming a sudden change in input variable. This is a commonly used method of establishing the time response of system.

Step response

The response of a system to a sudden change of the input variable is called the step response. Every system can be characterized by its step response. The step response also allows a system to be described with mathematical formulas.

Dynamic response

This description of a system is also known as dynamic response. Picture 3 demonstrates this. Here the manipulated variable y is suddenly increased (see left diagram). The step response of the controlled variable x is a settling process with transient overshoot.

Picture 3: Step response

Equilibrium

Another characteristic of a system is its behaviour in equilibrium, the static behaviour.

Static behaviour

Static behaviour of a system is reached when none of the variables change with time. Equilibrium is reached when the system has settled. This state can be maintained for an unlimited time. The output variable is still dependent on the input variable – this dependence is shown by the characteristic of a system.

Example 3

The characteristic of the "Valve" system from our water bath example shows the relationship between volumetric flow and valve position (see Picture 4).

Picture 4: Characteristic curve of the "Valve" system


The characteristic shows whether the system is a linear or non-linear system. If the characteristic is a straight line, the system is linear. In our "Valve" system, the characteristic is non-linear. Many controlled systems that occur in practice are non-linear. However, they can often be approximated by a linear characteristic in the range in which they are operated.