Nonlinear Feedforward Control

There are no inherent linear limitations in feedforward control. Nonlinear feedforward controllers can be designed for nonlinear systems. The concepts are illustrated in Example 11.3. 

In a nonlinear system the addition of a feedforward controller often permits tighter tuning of the feedback controller because the magnitude of the dis turbances that the feedback controller must cope with is reduced. 

Rearranging Eq. (11.36) to find F(,j, the manipulated variable, in terms of the disturbance Caoh))) gives the nonlinear feedforward controller relating the load variable Cao to the manipulated variable F. 

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

Feedforward control provides a linear correction and therefore can provide only partial compensation to a nonlinear process. Nevertheless, feedforward control can be effective when properly implemented, since it can reduce the amount of feedback correction required. When tuning a feedforward controller for a nonlinear process, care should be taken to ensure that the feedforward controller is tuned with consideration to both increases and decreases in the disturbance level. 

Chapter 21. Chapter 7 in Shinskey [Ref. 3] is again an excellent reference for the practical considerations guiding the design of feedforward and ratio control systems. It also discusses the use of feedforward schemes for optimizing control of processing systems. Good tutorial references are the books by Smith [Ref. 2], Murrill [Ref. 8], and Luyben [Ref. 9]. The last one has a simple but instructive example on the nonlinear feedforward control of a CSTR. 

V.20 In Example 6.4 we developed the linearized model of a nonisothermal CSTR. Develop a nonlinear steady-state feedforward controller which maintains the value of c A at the desired set point in the presence of changes in cAp Tt. The coolant temperature Tc is the manipulated variable. 

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. 

Feedforward control is probably used more in chemical engineering systems than in any other field of engineering. Our systems are often slow-moving, nonlinear, and multivariable, and contain appreciable deadtime. All these characteristics make life miserable for feedback controllers. Feedforward controllers can handle all these with relative ease as long as the disturbances can be measured and the dynamics of the process are known. 

Linear Feedforward Control / 9.2.2 Nonlinear Feedforward Control Openloop-Unstable Processes... 

Kuhnen, K. Janocha, H. Inverse feedforward controller for complex hysteretic nonlinearities in smart material systems. Control and Intel . Sys. 29, 3 (2001), pp. 74-83... 

Recall the observer-based dynamical inverse (or feedforward controller) (Eq. 16), drop its dynamic component (Eq. 16a), replace the state Xj by the setpoint x, and obtain the nonlinear SF controller (Eq. 16c)... 

To account for nonlinearity, disturbances, and oflier undesirable effects not captured in fire model, a feedback controller (Co( )) can be integrated with fire feedforward controller. As shown in Fig. 16, the feedback loop is arranged such that the feedforward and feedback inputs (Uj s) and Ujb(s), respectively) are added to produce 17i(5). 

The nonlinear simulation was used to illustrate the closed-loop response of the controlled variable X2 following a 30 percent increase in feed composition. The results are shown in Figure 21.4b with the feedback-only dual and PID algorithms. Control is immensely improved with the feedforward action. The slight deviation in X2 with feedforward control is due to inaccuracies in the linear model and the long sampling time relative to the process dead time. The... 

Thus, the feedforward controller calculates the required value of the manipulated variable D from measurements of the disturbance variables, F and z, and knowledge of the composition set points Xgp and ygp-Note that the control law is nonlinear owing to the product of F and z. 

In this section, we consider the design of feedforward control systems based on dynamic, rather than steady-state, process models. We will restrict our attention to design techniques based on linear dynamic models. But nonlinear process models can also be used (Smith and Corripio, 2006). 

In the previous two sections, we considered two design methods for feedforward control. The design method of Section 15.3 was based on a nonlinear steady-state process model, while the design method of Section 15.4 was based on a transfer function model and block diagram analysis. Next, we show how the two design methods are related. 

The steady-state design method of Section 15.3 produces a feedforward control law that has the general nonlinear form ... 

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. 

Feedforward control is less effective for nonlinear processes, where nonlinearities exist between the disturbance measurement and controlled variable. 

AQ represents the changes in heater duty required to produce a 1°C change in the product temperature. Equation W6.1 is not necessarily exact at all values of the feed tenperature because of the process nonlinearity. An exact expression is not necessary for successful feedforward control even if the calculated duty is incorrect by 50 per cent, the controller will still perform better than with no feedforward action. 

E. Rush, T. O. Drews, D. L. Ma, R. C. Alkire, and R. D. Braatz, J. Process Contr., 16, 409 (2006). Robust Nonlinear Feedback-Feedforward Control of a Coupled Kinetic Monte Carlo-Finite Difference Simulation. 

R.D. Bartusiak, C. Georgakis, and M.J. Reilly. Nonlinear feedforward/feedback control structures designed by reference synthesis. Chemical Engineering Science, 44 1837-1851, 1989. 

We showed through nonlinear dynamic simulations how the process reacts to various disturbances and changes in operating conditions. We have not shown any attempts to optimize process performance, to improve the process design, or to apply any advanced control techniques (model-based, nonlinear, feedforward, valve-position, etc.). These would be the natural next steps after the base-level regulatory control system had been developed to keep the process at a stable desired operating point. 

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