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For instance, a gear train is often characterised simply by its gear ratio, a SISO transfer function. However, the gearbox output shaft can be driven round to turn the input shaft requiring a MIMO analysis. In this example the effort and flow variables are torque T and angular velocity ω respectively. The transfer matrix in terms of z ...
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 ...
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).
Mathematical analysis of the transfer function can describe how it will respond to any input. As such, designing a filter consists of developing specifications appropriate to the problem (for example, a second-order low-pass filter with a specific cut-off frequency), and then producing a transfer function that meets the specifications.
A simple example of a Butterworth filter is the third-order low-pass design shown in the figure on the right, with = 4/3 F, = 1 Ω, = 3/2 H, and = 1/2 H. [3] Taking the impedance of the capacitors to be / and the impedance of the inductors to be , where = + is the complex frequency, the circuit equations yield the transfer function for this device:
For example, elements can use real or integer values to simulate DSP functions or sampled data filters. Because the event-driven algorithm is faster than the standard SPICE matrix solution, simulation time is greatly reduced for circuits that use event-driven models in place of analog models.
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: