PID Loop Simulator: How it works
| Description How it works Derivative on PV Notes: Process Model Robustness Loop Tuning |
The calculations required for the simulation are done on Sheet2. Defined Formulae are used in the computation. The first order process is calculated using a difference equation, given by: Process Value = b x (Output at time offset by delay time) - a x Last PV; where a = - 1/exp ( -1 / Process Time Constant) and b = Process Gain x (1 + a) The error is calculated by taking the difference between the PV and SP values. The error values are accumulated in column F for the integral term calculation and the derivative term is calculated by taking the difference between the current error and the last error. The PID calculation determines the next output value. The PID calculation is: Next output = Controller Gain x error + Accumulated error / Integral time + Derivative x (Current error - Previous error) Note that this tool simulates an "academic" version of the PID controller. PID controllers used in industry are different from this version. Also, this tool uses scaled gains, unlike the typical implementation in industrial controllers. Finally, note that is not possible to use the ODE solver for this loop simulation because of the presence of time delay. The ODE solver can be used if the time delay is approximated with a Pade approximation. |