Choosing a Stimulus Signal (Advanced Signal Processing Toolkit or Control Design and Simulation Module)

The choice of stimulus signals has an important role in the system behavior and the accuracy of the estimated model. These signals determine the operating points of the system. While the system under test often limits the choice of signals, you must choose stimulus signals to produce a response of the system under test. The response provides the information you need for developing an accurate model. The response is dependent on the physics of the system you want to study. Some systems tend to respond faster than others. Other systems have large time constants and delays. For these reasons, defining a stimulus signal that provides enough excitation to the system is important. You must choose the stimulus signal types according to the system under test to ensure the response contains the important features of the system dynamics. Use the following guidelines to choose input signal types.

• You want to test the system under conditions similar to the actual operating conditions. When you complete experiments in these conditions, you identify the system in the same conditions under which you will implement the resulting model. This criterion is extremely important for nonlinear systems.
• You want the inputs to the system under test to excite the system. Whether the system is excited is dependent on the spectrum of the input signal. Specifically, you must excite the system with an input frequency similar to the frequency at which such inputs change during normal operations.
• You want the amplitude of the step input to cover a wide range of variations. Therefore, in the data you use for model estimation, you must cover the normal operation range of system inputs, especially when you use the calculated model for model-based control. To cover the normal operation range, you can combine the positive and negative step changes of different magnitudes in the system inputs.
• You want the input signal to deliver as much input power to the system as possible. However, in the real-world, you must ensure that this input power stays within the limits of the physical system. The crest factor C_f, defined by the following equation, describes this property.

  

  The smaller the crest factor, the better the signal excitation. A better signal excitation results in larger total energy delivery and enhanced signal-to-noise ratio. The theoretical lower bound for the crest factor is 1.

You can use the following types of stimulus signals for exciting the system under test.

• Filtered Gaussian white noise
• Random binary signal
• Pseudo-random binary sequence
• Chirp waveform
• Step signals and step responses