Tuning feedback controllers

There are a variety of feedback controller tuning methods. Probably 80 percent of all loops are tuned experimentally by an instrument mechanic, and 75 percent of the time the mechanic can guess approximately what the settings will be by drawing on experience with similar loops. We will discuss a few of the time-domain methods below. In subsequent chapters we will present other techniques for tinding controller constants in the Laplace and frequency domains. 

Feedfoward control is normally implemented in conjunction with feedback control. Tuning procedures for combined feedforward-feedback control schemes have been described in Section 15.7. For these control configurations, the feedforward controller is usually tuned before the feedback controller. 

The performance of a controller (and its tuning) must be based on what is achievable for a given process. The concept of best practical IE (lEb) for a step change in load Aq can be estimated (Shinskey, Feedback Controllers foi the Process Industries, McGraw-Hill, New York, 1994) ... 

Other Considerations in Feedforward Control The tuning of feedforward and feedback control systems can be performed independently. In analyzing the block diagram in Fig. 8-32, note that Gy is chosen to cancel out the effects of the disturbance Us) as long as there are no model errors. For the feedback loop, therefore, the effects of L. s) can also be ignored, which for the sei vo case is ... 

The tuning of the controller in the feedback loop can be theoretically performed independent of the feedforward loop (i.e., the feedforward loop does not introduce instability in the closed-loop response). For more information on feedforward/feedback control appications and design of such controllers, refer to the general references. 

Pet foods Ruminant feeds Feedback control, purpose of, 20 666 Feedback controllers, 20 666-667 tuning and stability of, 20 694 Feedback control systems, 20 691-695 Feedback loops, between science and technology, 21 615 Feed-back system, closed loop fuel metering system, 10 56 Feed characterization, in reverse osmosis, 21 666... 

This step response is sketched in Fig. 6.7 for several values of the damping coefTi-cient. Note that the amount of overshoot of the final sleadystate value increases as the damping coeflicient decreases. The system also becomes more oscillatory. In Chap. 7 we will tune feedback controllers so that we get a reasonable amount of overshoot by selecting a damping coefficient in the 0.3 to 0.S range. 

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. 

In this approach, the desired closedloop response for a given input is specified. Then, knowing the model of the process, the required form and tuning of the feedback controller is back-calculated. These steps can be clarified by a simple example. 

Note the very unique shape of the log modulus curves in Fig. 12.19. The lower the damping coefficient, the higher the peak in the L curve. A damping coefficient of about 0.4 gives a peak of about +2 dB, We will use this property extensively in our tuning of feedback controllers. We will adjust the controller gain to give a maximum peak of +2 dB in the log modulus curve for the closedloop servo transfer function X/X. ... 

The design of feedback controllers in the frequency domain is the subject of this chapter. The Chinese language that we learned in Chap. 12 is now put to use to tune controllers. Frequency-domain methods are widely used because they have the significant advantage of being easier to use for high-order systems than the time- and Laplace-domain methods. 

Notice that the closedloop characteristic equation depends on the tuning of both feedback controllers. 

The process is openloop stable with no poles in the right half of the s plane. The authors used a diagonal controller structure with PI controllers and found, by empirical tuning, the following settings X, =0.20, K 2 = —0.04, t, = 4.44, and t,2 = 2.67. The feedback controller matrix was... 

The tuning and/or structure of the feedback controller matrix is changed until the minimum dip in the curve is something reasonable. Doyle and Stein gave no definite recommendations, but a value of about — 12 dB seems to give good results. 

When processes are subject only to slow and small perturbations, conventional feedback PID controllers usually are adequate with set points and instrument characteristics fine-tuned in the field. As an example, two modes of control of a heat exchange process are shown in Figure 3.8 where the objective is to maintain constant outlet temperature by exchanging process heat with a heat transfer medium. Part (a) has a feedback controller which goes into action when a deviation from the preset temperature occurs and attempts to restore the set point. Inevitably some oscillation of the outlet temperature will be generated that will persist for some time and may never die down if perturbations of the inlet condition occur often enough. In the operation of the feedforward control of part (b), the flow rate and temperature of the process input are continually signalled to a computer which then finds the flow rate of heat transfer medium required to maintain constant process outlet temperature and adjusts the flow control valve appropriately. Temperature oscillation amplitude and duration will be much less in this mode. 

The architecture of the self-tuning regulator is shown in Fig. 7.99. It is similar to that of the Model Reference Adaptive Controller in that it also consists basically of two loops. The inner loop contains the process and a normal linear feedback controller. The outer loop is used to adjust the parameters of the feedback controller and comprises a recursive parameter estimator and an adjustment mechanism. 

Figures 7. Simulated start-up of vinyl acetate polymerization at low emulsifier level (0.01 mol/L H20) under closed-loop control with arbitrarily selected controller tuning constants and manipulation of initiator flow rate at 50°C conversion in R1—STD feedback (--------------------------) vs. DTC (----)...

Most plant control systems are very simple and are normally standard feedback controllers, either P-, PI- or PID controllers. These will be described in more detail in this section, together with two techniques that can be used to tune these controllers. First, however, we need to define the control objective, i.e. what do we want the controller to do, and define what we mean by feedback control. 

A related approach which has been used successfully in industrial applications occurs in discrete-time control. Both Dahlin (43) and Higham (44) have developed a digital control algorithm which in essence specifies the closed loop response to be first order plus dead time. The effective time constant of the closed loop response is a tuning parameter. If z-transforms are used in place of s-transforms in equation (11), we arrive at a digital feedback controller which includes dead time compensation. This dead time predictor, however, is sensitive to errors in the assumed dead time. Note that in the digital approach the closed loop response is explicitly specified, which removes some of the uncertainties occurring in the traditional root locus technique. 

The equivalence of tuned PID controllers and optimal controllers can be demonstrated by augmentation of the state vector and judicious selection of the objective function (47), (48) ordinarily an optimal feedback controller contains higher order derivative terms, yielding significant phase advance (which can cause noise amplification and controller saturation). 

The next part involves controller tuning. We must determine the tuning constants for the controllers in the plant. While this task is often performed by using heuristics and experience, it can sometimes be a nontrivial exercise for certain loops. We recommend using a relay-feedback test that determines the ultimate gain and period for the control loop, from which controller settings can be calculated (Luyben and Luyben, 1997). 

A few comments about the method are warranted. The controlled (dominant) variables, Ycd, should be measured such that they belong to the set Yd for rapid control. Similarly, the manipulators in the feedback control loops should belong to the set, Ud. The feedback controllers should have integral action (PI controllers). These can be tuned with minimal information (e.g., ultimate gain and frequency from a relay test). The model Ms is usually quite simple and can be developed from operating data using statistical regressions. This works because the model includes all the dominant variables of the system, Y d, as independent variables by way of their setpoints, Y. The definition of domi-... 

On the surface it might appear that partial control does not require a first-principles model for its implementation. After all, M is a regression model and controller tuning is based on relay-feedback information. For simple systems this may be correct. However, for most industrially relevant systems it is not intuitively obvious what constitutes the dominant variables in the system and how to identify appropriate manipulators to control the dominant variables. This requires nonlinear, first-principles models. The models are run off-line and need only contain enough information to predict the correct trends and relations in the system. The purpose is not to predict outputs from inputs precisely and accurately, but to identify dominant variables and their relations to possible manipulators. 

We next try a more aggressive heat recovery alternative as shown in Fig. 5.24. The heat input to the furnace is quite small and most of the heat is provided by the large feed-effluent exchanger. With, our choice of measurement lags (two 1-minute lags in series) and the lag in the furnace., this system cannot be stabilized by feedback control around the furnace if the quench controller is in manual. However, it is possible to stabilize the system with just the quench controller in automatic and the furnace controller in manual. Subsequent tuning of the furnace controller is then easy since the new system is open-loop stable. 

---