# Do FIR filter have any application in control theory?

I know about IIR filter as discrete pendent to transfer functions in the Laplace domain. So it is actually quite simple to convert the function of the control system and finally receive the discrete output vector. (Bilinear Transform...)

But, how about FIR filter? Can we use them to approximate functions of control systems.

FIR filters are fairly common in some areas of control theory. As they usually incur a lot of added phase/time-delay, they are not really usable in the feedback path of regular control systems, but they are useful when the added phase/time-delay is not affecting the system in an adverse way, or when the particular phase response and time-delay is desired.

Examples:

1. Feed-forward control. FIR filters are useful for producing filters that approximate arbitrary frequency responses, hence they can be used to shape a reference signal. A typical example is to use an FIR filter with the inverse frequency response of the plant -- trying to counteract the dynamics of the plant in order to get a desired output. Phase/time-delay is not interfering with the stability or performance since the computation can be done offline. FIR filters can often produce higher performance than IIR filters, especially where there are non-minimum phase zeros.
2. Learning systems (iterative learning control [ILC] and repetitive control [RC]). In these systems, again, FIR filters are often used to generate an inverse response filter of the plant. This is done to improve the performance of the learning, as this enables a higher gain to be used for a larger bandwidth. The time-delay is here desired (RC), or it does not matter, as the computations are done offline (ILC). Low-pass FIR filters are also used here for their linear-phase properties, as the linear-phase property makes the filter not interfere with the phase of other filters, and this improves performance.

Here are examples of use of FIR filters in a control context:

Two identification algorithms, a least squares and a correlation analysis based, are developed for dual-rate stochastic systems in which the output sampling period is an integer multiple of the input updating period. The basic idea is to use auxiliary FIR models to predict unmeasurable noise-free (true) outputs, and then use these and system inputs to identify parameters of underlying fast single-rate models. The simulation results indicate that the proposed algorithms are effective.

The inherent stability of FIR filters could be a practical interest.

FIR filters may be used to "clean" signals before they are processed by IIR. You would try to avoid noise from input the IIR, since it could lead to unstable states.

• so you mean like a low pass (moving average)? – Randy Welt Apr 25 '15 at 17:03
• This could be one interpretation. It depends on the nature of your signal and noise. – Moti Apr 26 '15 at 3:54