Control Systems/List of Equations

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The following is a list of the important equations from the text, arranged by subject. For more information about these equations, including the meaning of each variable and symbol, the uses of these functions, or the derivations of these equations, see the relevant pages in the main text.

Fundamental Equations[edit | edit source]


[Euler's Formula]


[Convolution]


[Convolution Theorem]


[Characteristic Equation]


[Decibels]

Basic Inputs[edit | edit source]


[Unit Step Function]


[Unit Ramp Function]


[Unit Parabolic Function]

Error Constants[edit | edit source]


[Position Error Constant]


[Velocity Error Constant]


[Acceleration Error Constant]

System Descriptions[edit | edit source]


[General System Description]


[Convolution Description]


[Transfer Function Description]


[State-Space Equations]


[Transfer Matrix]


[Transfer Matrix Description]


[Mason's Rule]

Feedback Loops[edit | edit source]


[Closed-Loop Transfer Function]


[Open-Loop Transfer Function]


[Characteristic Equation]


Transforms[edit | edit source]


[Laplace Transform]


[Inverse Laplace Transform]


[Fourier Transform]


[Inverse Fourier Transform]


[Star Transform]


[Z Transform]


[Inverse Z Transform]


[Modified Z Transform]

Transform Theorems[edit | edit source]


[Final Value Theorem]


[Initial Value Theorem]

State-Space Methods[edit | edit source]


[General State Equation Solution]


[General Output Equation Solution]


[Time-Variant General Solution]


[Impulse Response Matrix]

Root Locus[edit | edit source]


[The Magnitude Equation]


[The Angle Equation]


[Number of Asymptotes]


[Angle of Asymptotes]


[Origin of Asymptotes]


[Breakaway Point Locations]

or

Lyapunov Stability[edit | edit source]


[Lyapunov Equation]

Controllers and Compensators[edit | edit source]


[PID]

Control Systems