Control Systems/List of Equations

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 Euler's Formula Convolution Convolution Theorem Characteristic Equation Decibels Basic Inputs Unit Step Function Unit Ramp Function Unit Parabolic Function Error Constants Position Error Constant Velocity Error Constant Acceleration Error Constant System Descriptions General System Description Convolution Description Transfer Function Description State-Space Equations Transfer Matrix Transfer Matrix Description Mason's Rule Feedback Loops Closed-Loop Transfer Function Open-Loop Transfer Function Characteristic Equation Transforms Laplace Transform Inverse Laplace Transform Fourier Transform Inverse Fourier Transform Star Transform Z Transform Inverse Z Transform Modified Z Transform Transform Theorems Final Value Theorem Initial Value Theorem State-Space Methods General State Equation Solution General Output Equation Solution Time-Variant General Solution Impulse Response Matrix Root Locus The Magnitude Equation The Angle Equation Number of Asymptotes Angle of Asymptotes Origin of Asymptotes Breakaway Point Locations or Lyapunov Stability Lyapunov Equation Controllers and Compensators PID