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This state-space realization is called controllable canonical form because the resulting model is guaranteed to be controllable (i.e., because the control enters a chain of integrators, it has the ability to move every state). The transfer function coefficients can also be used to construct another type of canonical form ˙ = [] + [] () = [] ().
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 ...
This state-space realization is called controllable canonical form (also known as phase variable canonical form) because the resulting model is guaranteed to be controllable (i.e., because the control enters a chain of integrators, it has the ability to move every state). The transfer function coefficients can also be used to construct another ...
In control theory, given any transfer function, any state-space model that is both controllable and observable and has the same input-output behaviour as the transfer function is said to be a minimal realization of the transfer function. [1] [2] The realization is called "minimal" because it describes the system with the minimum number of ...
System in open-loop. If the closed-loop dynamics can be represented by the state space equation (see State space (controls)) _ ˙ = _ + _, with output equation _ = _ + _, then the poles of the system transfer function are the roots of the characteristic equation given by
In control theory there are two main methods of analyzing feedback systems: the transfer function (or frequency domain) method and the state space method. When the transfer function method is used, attention is focused on the locations in the s-plane where the transfer function is undefined (the poles) or zero (the zeroes; see Zeroes and poles ...
Transfer function representation [ edit ] Taking the Laplace transform of the state space input-output equation, we see that the transfer function of the double integrator is given by
As in the finite-dimensional case the transfer function is defined through the Laplace transform (continuous-time) or Z-transform (discrete-time). Whereas in the finite-dimensional case the transfer function is a proper rational function, the infinite-dimensionality of the state space leads to irrational functions (which are however still ...