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  2. Settling time - Wikipedia

    en.wikipedia.org/wiki/Settling_time

    The settling time for a second order, underdamped system responding to a step response can be approximated if the ... MATLAB function for computing settling ...

  3. Root locus analysis - Wikipedia

    en.wikipedia.org/wiki/Root_locus_analysis

    The following MATLAB code will plot the root locus of the closed-loop transfer function as varies using the described manual method as well as the rlocus built-in function: % Manual method K_array = ( 0 : 0.1 : 220 ). ' ; % .' is a transpose.

  4. Step response - Wikipedia

    en.wikipedia.org/wiki/Step_response

    A typical step response for a second order system, illustrating overshoot, followed by ringing, all subsiding within a settling time.. The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions.

  5. Second-order arithmetic - Wikipedia

    en.wikipedia.org/wiki/Second-order_arithmetic

    The first-order functions that are provably total in second-order arithmetic are precisely the same as those representable in system F. [4] Almost equivalently, system F is the theory of functionals corresponding to second-order arithmetic in a manner parallel to how Gödel's system T corresponds to first-order arithmetic in the Dialectica ...

  6. Double integrator - Wikipedia

    en.wikipedia.org/wiki/Double_integrator

    Feedback system with a PD controller and a double integrator plant In systems and control theory , the double integrator is a canonical example of a second-order control system. [ 1 ] It models the dynamics of a simple mass in one-dimensional space under the effect of a time-varying force input u {\displaystyle {\textbf {u}}} .

  7. Numerov's method - Wikipedia

    en.wikipedia.org/wiki/Numerov's_method

    Numerov's method (also called Cowell's method) is a numerical method to solve ordinary differential equations of second order in which the first-order term does not appear. It is a fourth-order linear multistep method. The method is implicit, but can be made explicit if the differential equation is linear.

  8. Transfer function - Wikipedia

    en.wikipedia.org/wiki/Transfer_function

    In engineering, a transfer function (also known as system function [1] or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input. [2] [3] [4] It is widely used in electronic engineering tools like circuit simulators and control systems.

  9. Van der Pol oscillator - Wikipedia

    en.wikipedia.org/wiki/Van_der_Pol_oscillator

    Near the origin = =, the system is unstable, and far from the origin, the system is damped. The Van der Pol oscillator does not have an exact, analytic solution. [13] However, such a solution does exist for the limit cycle if f(x) in the Lienard equation is a constant piece-wise function.