I am designing a PI controller for a heating coil. Air flowing around the heating coil is heated before being supplied to a heated space. Hot water flows through the heating coil. In the suggested control system, the controlled variable is the temperature of air and the manipulated variable is water flow rate through the coil. The equation describing the dynamics of the system is shown below:

Cah*DTair/dt=Mw(Twi-Two)+ Ma(Ta-Tair)

Cah= heating capacity ,which is contant

Tair= Temperature of air supplied to heating space, varies of time

Mw= Mass of water flowing through the coil, varies with time since its the manipulated variable

Twi= Temperature of water supplied to the coil, varies with time since it is part of another process

Two=Temperature of water exiting the coil, constant

Tao=Temperatue of air before approaching the coil, constant

In the above equation, Mw and Twi are both variables (function of time), and therefore the equation is nonlinear due to Mw*Twi; To design a controller, I should linearize around an operating point, which will restric the validity of the controller to this specific point (or around that point). Can anyone guide me regarding a better control design approach? should I check nonlinear control theory? multivariable control? etc..

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