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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.
The transfer function of a two-port electronic circuit, such as an amplifier, might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical actuator might be the mechanical displacement of the movable arm as a function of electric ...
, is process transfer function; the input into the block is flow rate and output is tank level. The output as a function of the setpoint, r , is known as the closed-loop transfer function . g c l = g p g c 1 + g p g c , {\displaystyle {\mathit {g_{cl}}}={\frac {\mathit {g_{p}g_{c}}}{1+g_{p}g_{c}}},} If the poles of g c l , {\displaystyle ...
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).
A simple first-order network such as a RC circuit will have a roll-off of 20 dB/decade. This is a little over 6 dB/octave and is the more usual description given for this roll-off. This can be shown to be so by considering the voltage transfer function, A, of the RC network: [1]
One way to determine the parameters for the first-order process is using the 63.2% method. In this method, the process gain ( k p ) is equal to the change in output divided by the change in input. The dead time θ is the amount of time between when the step change occurred and when the output first changed.
The closed-loop transfer function is measured at the output. The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be waveforms, images, or other types of data streams. An example of a closed-loop block diagram, from which a transfer function may be computed, is shown below:
The bilinear transform is a first-order Padé approximant of the natural logarithm function that is an exact mapping of the z-plane to the s-plane.When the Laplace transform is performed on a discrete-time signal (with each element of the discrete-time sequence attached to a correspondingly delayed unit impulse), the result is precisely the Z transform of the discrete-time sequence with the ...