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The Smith predictor (invented by O. J. M. Smith in 1957) is a type of predictive controller designed to control systems with a significant feedback time delay. The idea can be illustrated as follows.
A forth order filter has a value for k of 1, which is odd, so the summation uses only odd values of i for and (), which includes only the i=1 term in the summation. The transfer function, T 4 ( j ω ) {\displaystyle T_{4}(j\omega )} , may be derived as follows:
N th-order CIC filters have N times as many poles and zeros in the same locations as the 1 st-order. Thus, the 1 st-order CIC's frequency response is a crude low-pass filter. Typically the gain is normalized by dividing by () so DC has the peak of unity gain. The main lobes drop off as it reaches the next zero, and is followed by a series of ...
The transfer function for a first-order process with dead time is = + (), where k p is the process gain, τ p is the time constant, θ is the dead time, and u(s) is a step change input. Converting this transfer function to the time domain results in
First-order hold (FOH) is a mathematical model of the practical reconstruction of sampled signals that could be done by a conventional digital-to-analog converter (DAC) and an analog circuit called an integrator. For FOH, the signal is reconstructed as a piecewise linear approximation to the original signal that was sampled.
The transfer function coefficients can also be used to construct another type of canonical form ˙ = [] + [] () = [] (). This state-space realization is called observable canonical form because the resulting model is guaranteed to be observable (i.e., because the output exits from a chain of integrators, every state has an effect on the output).
In this, is the transfer function of the block . It works on the entry state i n b {\displaystyle in_{b}} , yielding the exit state o u t b {\displaystyle out_{b}} . The join operation j o i n {\displaystyle join} combines the exit states of the predecessors p ∈ p r e d b {\displaystyle p\in pred_{b}} of b {\displaystyle b} , yielding the ...
For an integrating process, a general transfer function is = (+), which, when combined with the closed-loop transfer function, becomes = (+) +.. Introducing a step change to the system gives the output response of () =.