Step responses of Technical Systems

When planning the experiments, two aspects are of particular importance:

>> the selection of suitable test signals (system input signals);
>> the selection of the observation time, during which the signals are acquired.

The test signal must activate the system to be analysed sufficiently so that it is possible to detect the system characteristics with as large a signal-to-disturbance ratio as possible. It should also be as easy as possible to realise and detect. This is where test signals are particularly suitable which, at the start of the experiment, perform so-called stepchanges, i.e. by a specific amount (zero-point stage). Examples of this are electro-mechanical or electro-thermal devices, which change their operating status during the switching on or connection of electrical voltages or outputs, or the control of material or energy flow in process technology systems via (solenoid) valves or pumps. Step-type test signals of this type are often used in practice and with success. They should therefore also be used here for the experimental process analysis.

The reaction of a system to a step-change signal is known as step-response. If this step response is related to the step-change height of the input signal (standardised representation), then this is known as the transient function of a system. This is always on the assumption that the linearity range around the operating point is not exceeded during the transition process and that the system was in the stationary state at the operating point to starting the experiment. Picture 1 illustrates this process, where:

>> X0, Y0 – working point values;
>> y – step-change height of input signal y(t);
>> h(t) = x(t)/∆y – transient function;

Picture 1: Experimental determining of step response x(t)


At least with regard to practical matters, the step response, i.e. the transient function represents the most important form of a linear dynamic system model.

Depiction of response characteristic

The signal response characteristic of technical systems can be depicted qualitatively with the help of the transient function. Depending on the pattern of the transient function for long time periods (t → ...), we differentiate between systems with P-action (P elements), I-action (I-elements) and D-action (D-elements). Following step activation, proportional elements acquire a new stationary status, differing from the operating point value; integral elements assume a constant rate of change of the system output variable for long time periods (warning: observe linearity range), and in the case of differential elements, the output variable reverts to the stationary state of the operating point value. These basic characteristics of technical systems are illustrated in Picture 2.

Picture 2: Qualitative depiction of transient behaviour with the help of transient function