Question: Answer these questions about the digital PID algorithm.
(a) Give the equations for the full-position and velocity PID controllers if a trapezoidal numerical integration were used for the integral mode.
(b) The digital controller can be simplified to the following form to reduce real-time computations. Determine the values for the constants (the A,s) in terms of the tuning constants and execution period for (i) PID, (ii) PI, and (iii) PD controllers.