What are the Types of Test signals?

For many practical control processes, the input drives are unknown in advance, unlike electrical circuits and communication systems.

In many cases, the actual inputs to a control system generally can vary randomly with respect to time. A designer faces a challenge since it is difficult to design a control process that works satisfactorily with any type of input signal. 

Purpose of Test Signals

Test signals are for analysis and design purposes. To evaluate the system’s performance against these test signals, it is necessary to assume several basic types of input functions.  

The correct selection of these signals allows not only the mathematical treatment of the problem to be systematized but also the prediction of the system performance with other more complicated inputs.

In the design problem, performance criteria can be specified with respect to these test signals, so that a system can be designed according to such criteria.

Following are the typical test signals, that are used to facilitate time-domain analysis –

Impulse function

Step function

Ramp function

Parabolic function

The form of input to which the system will be most frequently subjected, under normal operating conditions, determines which of the typical input signals should be used to analyze the characteristics of the system.

The common feature of all these test signals is that they can be mathematically described. Right from the impulse function to the parabolic, all these test signals become progressively faster with respect to the system.

Ramp function

If the inputs to a control system are gradually changing functions over time, that signal would be a good test signal. The ramp function has the characteristic of testing the system with respect to a linear variation in the system.

Step function

If a system is subject to sudden disturbances, a step function would be a good test signal. The unit step function is very useful as a test signal since its initial instantaneous rise in amplitude discloses a lot of information about the response speed of the system.

Also, since this function has, in principle, a very broad spectrum of frequencies as a result of the jump or discontinuity, this test signal is equivalent to the application of many sinusoidal signals with a very wide range of frequencies.

Impulse function

For a system subject to shock inputs, impulse function would be the best. When a control system is designed based on test signals, its performance in response to actual inputs is generally satisfactory. 

The control process to which an impulse function is applied provides at its output a signal whose Laplace transform is, directly, the transfer function of the system.

Parabolic input function                                                                                                       

Parabolic functions are one degree faster than ramp functions. It is hardly ever necessary to use a faster test signal than the parabolic function in practice. This is because, as will be seen later Further, for a system to follow or respond to higher-order input, it must also be higher-order.

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