Stirred tank heater transfer functions

Temperature control in a stirred-tank heater is a common example (Fig. 2.9). We will come across it many times in later chapters. For now, we present the basic model equation, and use it as a review of transfer functions. 

Consider the stirred-tank heater again, this time in a closed-loop (Fig. 5.4). The tank temperature can be affected by variables such as the inlet and jacket temperatures and inlet flow rate. Back in Chapter 2, we derived the transfer functions for the inlet and jacket temperatures. In Laplace transform, the change in temperature is given in Eq. (2-49b) on page 2-25 as... 

We now walk through the stirred-tank heater system once again. This time, we ll take a closer look at the transfer functions and the units (Fig. 5.5). 

Example 9.1 Transfer Functions of a Stirred Tank Heater... 

For instance, in Example 21.2, for the stirred tank heater we can easily identify the static and dynamic parts of the process transfer functions [see eq. (21.4)] ... 

Find the transfer function between the effluent temperature T3 and the inlet temperature T, for the system of two stirred tank heaters described in Problem II.3 (Figure PII.3). Draw the corresponding block diagram. Sketch the response of T to a unit impulse change in T,. Is the process stable ... 

V.21 Derive the nonlinear, steady-state feedforward control system that will keep the exit temperature of a stirred tank heater at the desired set point despite any changes in the inlet temperature or flow rate, T, and F,. The feedforward control system should be capable of (1) rejecting the effect of disturbance changes, and (2) tracking any set point changes. Identify all relevant transfer functions. 

For a stirred-tank heater, assume the transfer function between the heater input change u t) (cal/sec) and the tank temperature change y t) (°C) can be modeled as... 

The two capacities in series may be two stirred tanks, two heaters, and so on, and have a transfer function... 

Having considered PID controllers in Chapter 8, we now consider the other components of the feedback control loop. As an illustrative example, consider the stirred-tank heating system in Fig. 9.1. A thermocouple measures the liquid temperature and converts it to a millivolt-level electrical signal. This signal is then amplified to a voltage level and transmitted to the electronic controller. The feedback controller performs the control calculations and sends the calculated value as an output signal to the final control element, an electrical heater that adjusts the rate of heat transfer to the liquid. This example illustrates the three important functions of a feedback control loop (1) measurement of the controlled variable (CV), (2) adjustment of the manipulated variable (MV), and (3) signal transmission between components. 

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