Steady feedforward control equation

Ca may be substituted from the steady state mass balance to give the steadystate feedforward control equation for jacket temperature Tj... 

The preceding nonlinear feedforward controller equations were found analytically. In more complex systems, analytical methods become too complex, and numerical techniques must be used to fiud the required uouliuear changes in manipulated variables. The nonlinear steady-state changes can be found by using the nonlinear algebraic equations describing the process. The dynamic portion can often be approximated by linearizing around various steady states. 

In contrast, we could have done the derivation using steady state models. In such a case, we would arrive at the design equation for a steady state feedforward controller. We ll skip this analysis. As will be shown later, we can identify this steady state part from the dynamic approach. 

From this equation the steady state, feedforward control value of F can be calculated to compensate for variations in Cao with respect to time and based on the set point values for k and Ca-... 

The simplest feedforward controller and the easiest to implement is the steady-state one. As demonstrated in Example 21.2, we use simple steady-state balances for design. How does this modify the design equations (21.9) and (21.10) ... 

Equation (21.2) is the design equation for the steady-state feedforward controller. It shows how Q should change in the presence of disturbance or set point changes. Figure 21.3a depicts the resulting control system. 

Dynamic feedforward controller To improve the quality of control during the transient response we will design a feedforward controller using the dynamic heat balance and not its equivalent steady state, as above. Equation (4.5b) can be written as follows ... 

Equation (21.5) is the design equation for the dynamic feedforward controller and Figure 21.3b shows the resulting control mechanism. As can be seen from Figure 21.3a and b, the only difference between the steady-state and dynamic feedforward controllers for the tank heater is the transfer function (ts + 1) multiplying the set point. 

To design a feedforward controller, that is, to find Gf(s) we must know both G j) and Gm s). The objective of most feedforward controllers is to hold the controlled variable constant at its steady-state value. Therefore, the change or perturbation in T(j) should be zero. The output F(j) is given by the equation... 

In its simplest form, a feedforward controller merely proportions the corrective action to the size of the disturbance. In other words, the control equation is merely a gain based on steady state, i.e. mass or energy balance at steady state. This does not take into account any of the process dynamics of the system. If there is a difference, or lag, in the speed of the process response to the control action when compared with that of the disturbance, then it may be necessary to introduce some dynamic compensation into the control equation. The dynamic compensation correctly times the control action and response, thus giving increased accuracy in the feedforward control. 

When feedforward control is used, equations are needed to calculate the amount of the manipulated variable needed in order to compensate for the disturbance. This sounds simple enough however, the equations must incorporate an understanding of the exact effect of the disturbances on the process variable. Therefore, one disadvantage of feedforward control is that the controllers often require sophisticated calculations, as even steady models can be nonlinear and thus need more technical and engineering expertise in their implementation. 

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See also in sourсe #XX -- [ ]

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