Consider the two stirred tank heaters system shown in Figure 1. We would like to control...

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Consider the two stirred tank heaters system shown in Figure 1. We would like to control temperature T₂(t) by manipulating the heating medium temperature in either the first or the second heater (i.e., Ts1 (t) or Ts2 (t)). It can be considered that temperatures of the heating media remain practically constant along the respective heating coils. The inlet flow rate F remains constant, while its inlet temperature Ti(t) changes, thus creating the need for control. The recycle stream flowrate F3 is equal to half of F₁. Assume that the changes in temperature in the tanks do not affect the density p and heat capacity of the fluid Cp. Tank 1 F, T/(t) T₁1(t) F3, T₂(t) F₁, T₁(t) Tank 2 F₂ T₂(t) Tsz(t) Figure 1. Two stirred tank heaters in series with recycle system Starting from the mathematical model in the time domain of the system shown in Figure 1, use Laplace transforms to determine all transfer functions that describe this process in deviation state in the open loop. Determine initially any first order dependencies between variables and calculate their respective gains and time constants. Furthermore, combine these first order transfer functions to obtain the transfer functions describing the effect of temperatures Ti(t) and T₂(t) to changes to the temperatures T₁ (t), T2 (t) and Ti(t). Clearly show all steps taken and clearly indicate the units of all involved variables. Consider the two stirred tank heaters system shown in Figure 1. We would like to control temperature T₂(t) by manipulating the heating medium temperature in either the first or the second heater (i.e., Ts1 (t) or Ts2 (t)). It can be considered that temperatures of the heating media remain practically constant along the respective heating coils. The inlet flow rate F remains constant, while its inlet temperature Ti(t) changes, thus creating the need for control. The recycle stream flowrate F3 is equal to half of F₁. Assume that the changes in temperature in the tanks do not affect the density p and heat capacity of the fluid Cp. Tank 1 F, T/(t) T₁1(t) F3, T₂(t) F₁, T₁(t) Tank 2 F₂ T₂(t) Tsz(t) Figure 1. Two stirred tank heaters in series with recycle system Starting from the mathematical model in the time domain of the system shown in Figure 1, use Laplace transforms to determine all transfer functions that describe this process in deviation state in the open loop. Determine initially any first order dependencies between variables and calculate their respective gains and time constants. Furthermore, combine these first order transfer functions to obtain the transfer functions describing the effect of temperatures Ti(t) and T₂(t) to changes to the temperatures T₁ (t), T2 (t) and Ti(t). Clearly show all steps taken and clearly indicate the units of all involved variables.

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System Description The system consists of two continuously stirred tank heaters connected in serie... View the full answer