Tuning Parameters and Noises in the Modelling of PID Controller via Simulation

Lim, Zhi Xuan (2021) Tuning Parameters and Noises in the Modelling of PID Controller via Simulation. Final Year Project (Bachelor), Tunku Abdul Rahman University College.

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Abstract

In this work, the tuning parameters and the effect of noises in the Proportional-Integral-Derivative (PID) closed loop are studied via process modelling and simulations. The inclusions of noises are limited to Gaussian white noise and 1/f noise. For each type of these noises, a simple process model and its variations are simulated with the noise added into the process variable in a negative feedback loop. In this way, subsequent process variables after each PID control action will be tainted with previous noise contributions. This leads to an accumulative effect of a series of noises that can propagate through each iteration of time. The time response of the process variables resulting from these additional Gaussian white noise and 1/f noise are then investigated in the PID simulations with a time-delayed non-linear model. The simulations are performed with many different PID tuning parameters via the LabVIEW programming platform. The time profiles for both the noise-free models and the models with noises are compared. The time-dependence of the temporal onset of the noise is also considered in the modelling with various delay times for the initial process variable at a suitable sampling rate. By adjusting the timing between the period originated from a disturbance frequency and either the sampling time or the delay time for the process variables, the time response profiles are found to exhibit a formation of wavelets with periodic characteristics. Using the settling time in the time profile as a key performance criterion, the results are compared and the effect of noises on the performance are discussed. The modelling approach in this study may be useful for studying a dynamical self-correcting PID controller in a feedback system with noises.