Steady-state model feedforward control

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. 

For noninteracting control loops with zero dead time, the integral setting (minutes per repeat) is about 50% and the derivative, about 18% of the period of oscillation (P). As dead time rises, these percentages drop. If the dead time reaches 50% of the time constant, I = 40%, D = 16%, and if dead time equals the time constant, I = 33% and D = 13%. When tuning the feedforward control loops, one has to separately consider the steady-state portion of the heat transfer process (flow times temperature difference) and its dynamic compensation. The dynamic compensation of the steady-state model by a lead/lag element is necessary, because the response is not instantaneous but affected by both the dead time and the time constant of the process. 

Feedforward (FF) gain is given as a multiple of the gain based on the nominal steady-state model. All times are in seconds. Feedback controller gains are given in m m N. ... 

Feedforward control was developed to counter some of these limitations. Its basic premise is to measure the important disturbance variables and then take corrective compensatory action based on a process model. The quality of control is directly related to the fidelity and accuracy of the process model. Two implementations of feedforward control which are widely used in polymer reactor control will be discussed, namely feedforward control design based on steady-state models, and... 

Feedforward Controller Design Based on Steady-State Models 15.3.1 Blending System... 

Step 1. Adjust Kf. The effort required to tune a controller is greatly reduced if good initial estimates of the controller parameters are available. An initial estimate of Kf can be obtained from a steady-state model of the process or from steady-state data. For example, suppose that the open-loop responses to step changes in d and u are available, as shown in Fig. 15.15. After Kp and K have been determined, the feedforward controller gain can be calculated from the steady-state version of Eq. 15-21 ... 

The effect of the disturbance on the controlled variable These models can be based on steady-state or dynamic analysis. The performance of the feedforward controller depends on the accuracy of both models. If the models are exac t, then feedforward control offers the potential of perfect control (i.e., holding the controlled variable precisely at the set point at all times because of the abihty to predict the appropriate control ac tion). However, since most mathematical models are only approximate and since not all disturbances are measurable, it is standara prac tice to utilize feedforward control in conjunction with feedback control. Table 8-5 lists the relative advantages and disadvantages of feedforward and feedback control. By combining the two control methods, the strengths of both schemes can be utilized. 

The above FF controller can be implemented using analog elements or more commonly by a digital computer. Figure 8-33 compares typical responses for PID FB control, steady-state FF control (.s = 0), dynamic FF control, and combined FF/FB control. In practice, the engineer can tune K, and Tl in the field to improve the performance oTthe FF controller. The feedforward controller can also be simplified to provide steady-state feedforward control. This is done by setting. s = 0 in Gj. s). This might be appropriate if there is uncertainty in the dynamic models for Gl and Gp. 

The example simulation THERMFF illustrates this method of using a dynamic process model to develop a feedforward control strategy. At the desired setpoint the process will be at steady-state. Therefore the steady-state form of the model is used to make the feedforward calculations. This example involves a continuous tank reactor with exothermic reaction and jacket cooling. It is assumed here that variations of inlet concentration and inlet temperature will disturb the reactor operation. As shown in the example description, the steady state material balance is used to calculate the required response of flowrate and the steady state energy balance is used to calculate the required variation in jacket temperature. This feedforward strategy results in perfect control of the simulated process, but limitations required on the jacket temperature lead to imperfections in the control. 

Based on the linearized models around the equilibrium point, different local controllers can be implemented. In the discussion above a simple proportional controller was assumed (unity feedback and variable gain). To deal with multivariable systems two basic control strategies are considered centralized and decentralized control. In the second case, each manipulated variable is computed based on one controlled variable or a subset of them. The rest of manipulated variables are considered as disturbances and can be used in a feedforward strategy to compensate, at least in steady-state, their effects. For that purpose, it is t3q)ical to use PID controllers. The multi-loop decoupling is not always the best strategy as an extra control effort is required to decouple the loops. 

The experimental curve in Figure 3 demonstrates overshoot in the tissue oxygen response. It was determined previously (22) that a term representing pure delay along with the steady-state blood flow vs. arterial oxygen tension data would cause overshoot. In this investigation it was found that a first-order time constant delay would also produce overshoot. Therefore, since exact controller mechanisms are not being postulated, the flow controlled dynamics used in this study include pure delay and time constant lag. To consider the problem of sensor location, feedback and feedforward control loops were superimposed on the capillary-tissue model. 

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. 

However, for feedforward controller design, model A should be used because having the correct steady-state gain is more important in feedforward control than the correct dynamics. 

Alternatively, we could attempt to obtain the feedforward gains (AO empirically by plant testing, providing that we can introduce a disturbance into feed enthalpy. We may be able to determine K from analysis of historical data but if these were collected while tray temperature (or some other composition) control was in service then it will only be possible to model steady state behaviour. Similarly we could identify K from steady state simulation. Dynamic compensation would then have to be tuned by trial and error. 

In this chapter, we consider the design and analysis of feedforward control systems. We begin with an overview of feedforward control. Then ratio control, a special type of feedforward control, is introduced. Next, design techniques for feedforward controllers are developed based on either steady-state or dynamic models. Then alternative configurations for combined feedforward-feedback control systems are considered. This chapter concludes with a section on tuning feedforward controllers. 

A useful interpretation of feedforward control is that it continually attempts to balance the material or energy that must be delivered to the process against the demands of the disturbance (Shinskey, 1996). For example, the level control system in Fig. 15.3 adjusts the feedwater flow so that it balances the steam demand. Thus, it is natural to base the feedforward control calculations on material and energy balances. For simplicity, we will first consider designs based on steady-state balances using physical variables rather than deviation variables. Design methods based on dynamic models are considered in Section 15.4. 

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). 

Next, we consider three examples in which we derive feedforward controllers for various types of process models. For simplicity, it is assumed that the disturbance transmitters and control valves have negligible dynamics, that is, Gt(s) = Kf and Gy(s) = Ky, where and Ky denote steady-state gains. 

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. 

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