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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 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]
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).
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 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 ...
In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to multiple-input and multiple-output (MIMO) systems. [1] The matrix relates the outputs of the system to its inputs.
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.
This relationship is used in the Laplace transfer function of any analog filter or the digital infinite impulse response (IIR) filter T(z) of the analog filter. The bilinear transform essentially uses this first order approximation and substitutes into the continuous-time transfer function, ()