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  2. State-space representation - Wikipedia

    en.wikipedia.org/wiki/State-space_representation

    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 ˙ = [] + [] () = [] ().

  3. Transfer function - Wikipedia

    en.wikipedia.org/wiki/Transfer_function

    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 ...

  4. Realization (systems) - Wikipedia

    en.wikipedia.org/wiki/Realization_(systems)

    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 ...

  5. Closed-loop pole - Wikipedia

    en.wikipedia.org/wiki/Closed-loop_pole

    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 ...

  6. State-transition matrix - Wikipedia

    en.wikipedia.org/wiki/State-transition_matrix

    The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form ˙ = () + (), =, where () are the states of the system, () is the input signal, () and () are matrix functions, and is the initial condition at .

  7. Full state feedback - Wikipedia

    en.wikipedia.org/wiki/Full_state_feedback

    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

  8. Ackermann's formula - Wikipedia

    en.wikipedia.org/wiki/Ackermann's_Formula

    In control theory, Ackermann's formula is a control system design method for solving the pole allocation problem for invariant-time systems by Jürgen Ackermann. [1] One of the primary problems in control system design is the creation of controllers that will change the dynamics of a system by changing the eigenvalues of the matrix representing the dynamics of the closed-loop system. [2]

  9. Transfer function matrix - Wikipedia

    en.wikipedia.org/wiki/Transfer_function_matrix

    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.