System Identification of System with a PWM duty cycle input

Hi there

I am trying to perform system identification of a system that has a PWM input signal, so I want to identify the transfer function from PWM duty cycle to output (in this case speed). I have found a number of sources (including Frequency Response Estimation for Power Electronics Model Using Pseudorandom Binary Signal) that point to using a pseudo-random binary signal as the input signal for excitation purposes. However, I don't particularly understand how the PRBS corresponds to the duty cycle of the PWM or how one should set the amplitude of the PRBS.

Would greatly appreciate any help.

Answer 1

[Kartik]

Hi,

The basic idea behind using a pseudo-random binary sequence (PRBS) as an input signal for system identification is to inject a signal with a wide frequency content into the system. This allows you to excite and measure the system's response for a range of frequencies. By analyzing the input-output data, you can then estimate the system's transfer function.

In the context of a PWM system, you can think of the duty cycle as a continuous-time signal that switches between two levels (on and off). A PRBS is a discrete-time signal that also switches between two levels (1 and -1). To apply the PRBS signal to the PWM system, you can map the PRBS levels to the duty cycle levels. For example, you can map 1 in the PRBS to a high duty cycle (i.e., fully on) and -1 in the PRBS to a low duty cycle (i.e., fully off). The exact mapping depends on the nature of your PWM system and the PRBS sequence.

Regarding the amplitude of the PRBS signal, you can adjust it so that it corresponds to the range of duty cycles that you want to excite in your system. For example, if your system's duty cycle range is between 10% and 90%, you can scale the PRBS signal accordingly so that it also has a range between 10% and 90%. The exact scaling factor depends on the minimum and maximum values of the PRBS and the duty cycle range of your system.