PID control implementation in multiple input and multiple output (MIMO) water mixing tank via Ziegler–Nichols and direct synthesis methods

Abstract

This study deals with the modeling of two PI controllers to control first-order systems [cold water (CW) to tank
level and hot water (HW) to temperature] using Ziegler–Nichols (ZN) and direct synthesis methods and to test both
controllers for set-point tracking and disturbance rejection modes for multiple input and multiple output (MIMO)
water mixing tank. The ZN method is a technique used for tuning controllers, and it used both proportional and
integral actions in the present investigation. This method was performed by setting the integral (I) and derivative
(D) gains to zero. It was applied to the open-loop reaction of the process to the change in the water level and the
temperature (the control variables) and the plotter on the computer recorded the response. The evaluated process
variables, such as K (for the proportional action) and ? (for the integral action), are plugged into the ZN equation
with the specific multiplier constants for the gains of a controller with PI actions. The ZN technique was utilized to
obtain a PI controller for both the CW to tank level system and the HW to temperature system. The direct synthesis
(DS) method was applied to a desired closed-loop transfer function. The design of the controller was based on a
process model. This method was applied to set-point changes in the control system and later fixed to responses
to disturbances. The DS technique was implemented on the two systems, the CW to tank level and the HW to
temperature. It was able to control the impact of the sensitive HW to temperature system. However, the controller
performance across the CW to tank level system was extremely inefficient as oscillations were observed