Laplace transform[1]. Starting with a signal in the time domain, you can take the Fourier transform to map it into the frequency domain and then the Laplace tra

Laplace transform[1]. Starting with a signal in the time domain, you can take the Fourier transform to map it into the frequency domain and then the Laplace transform (Z-transform[2]) to map it into discrete time domain. Discrete time is what digital computers do. At this point implementing the control loop on a digital computer is remarkably straight forward. Taking your system's closed loop transfer function[3], you can use the above Laplace and Z-transforms to produce the desired closed loop control algorithm to "optimally" control your system. (I put "optimally" in quotes because it is optimum for the system as defined; if your understanding / definition of your system is wrong, it will be optimally controlling for a different system and be suboptiomal for your actual system.) [1] https://en.wikipedia.org/wiki/Laplace_transform https://en.wikipedia.org/wiki/Laplace_transform [2] https://en.wikipedia.org/wiki/Z-transform https://en.wikipedia.org/wiki/Z-transform [3] https://en.wikipedia.org/wiki/Control_theory#Closed-loop_transfer_function https://en.wikipedia.org/wiki/Control_theory#Closed-loop_tra...