Feedback controller

For multiple-input-multiple-output (MIMO) control algorithms, these variables are written in bold type to denote that they are vectors of variables (e.g., u is a vector of manipulated variables). 

The material in this section is a brief overview of process control. The reader familiar with the contents of any recent undergraduate control textbook such as Seborg et al. (1988), Smith and Corripio (1985), or Stephanopoulos (1984) is encouraged to proceed directly to Section 9.3. 

The advantage of feedback control is that corrective action is taken regardless of the source of the disturbance. Its chief drawback is that no corrective action is taken until after the controlled variable deviates from the set point. Feedback control may also result in undesirable oscillations in the controlled variable if the controller is not tuned properly that is, if the adjustable controller parameters are not set at appropriate values. Although trial-and-error tuning can achieve satisfactory performance in some cases, the tuning of the controller can be aided by using a mathematical model of the dynamic process. 

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SHINSKEY Feedback Controllers for the Process Industries SHUGAR, DEAN The Chemist s Ready Reference Handbook SHUGAR, BALLINGER The Chemical Technicians Ready Reference Handbook... 

Figure Bl.27.8. Schematic view of Picker s flow microcalorimeter. A, reference liquid B, liquid under study P, constant flow circulating pump and 2, Zener diodes acting as heaters T and T2, thennistors acting as temperature sensing devices F, feedback control N, null detector R, recorder Q, themiostat. In the above A is the reference liquid and C2is the reference cell. When B circulates in cell C this cell is the working cell. (Reproduced by pemiission from Picker P, Leduc P-A, Philip P R and Desnoyers J E 1971 J. Chem. Thermo. B41.)...

Nearly four biUion L/yr of ethanol are added to gasoline and sold as gasohol (18). The starting or driveabiUty difficulties have been solved, in part, by the advances in vehicle technology employing fuel feedback controls. 

In 1966, the name was proposed (5) for receptors blocked by the at that time known antihistamines. It was also speculated that the other actions of histamine were likely to be mediated by other histamine receptors. The existence of the H2 receptor was accepted in 1972 (6) and the receptor was recognized in rat brain in 1983 (7). receptors in the brain appear to be involved in the feedback control of both histamine synthesis and release, whereas release of various other neurotransmitters, eg, serotinin (5-HT), dopamine, noradrenaline, and acetylcholine, is also modulated (8) (see Neuroregulators). 

Some of the inherent advantages of the feedback control strategy are as follows regardless of the source or nature of the disturbance, the manipulated variable(s) adjusts to correct for the deviation from the setpoint when the deviation is detected the proper values of the manipulated variables are continually sought to balance the system by a trial-and-error approach no mathematical model of the process is required and the most often used feedback control algorithm (some form of proportional—integral—derivative control) is both robust and versatile. 

The main disadvantage of the feedback control strategy is that no corrective action is taken until after a deviation between the measured controlled... 

The feedforward control strategy (Fig. lb) addresses the disadvantages of the feedback control strategy. The feedforward control strategy measures the disturbance before it affects the output of the process. A model of the process determines the adjustment ia the manipulated variables(s) to compensate for the disturbance. The information flow is therefore forward from the disturbances, before the process is affected, to the manipulated variable iaputs. 

The primary advantage of the feedforward over the feedback control strategy is that corrective action is initiated before the controlled variable is upset. Feedforward control, however, has its own drawbacks, ie, variables used to characterize the disturbances must be measurable a model of the response of the controlled variable to the disturbance must be available (when the feedforward strategy is used alone, the control performance depends on the accuracy of the model) and the feedforward control strategy does not compensate for any disturbance not measured or modeled. 

In most process plant situations where feedforward control is appropriate, a combination of the feedforward and feedback control is usually used. The feedforward portion reduces the impact of measured disturbances on the controlled variable while the feedback portion compensates for model inaccuracies and unmeasured disturbances. This control strategy is referred to as feedforward control with feedback trim. 

Classical Feedback Control. The majority of controllers ia a continuous process plant is of the linear feedback controller type. These controllers utilize one or more of three basic modes of control proportional (P), iategral (I), and derivative (D) action (1,2,6,7). In the days of pneumatic or electrical analogue controllers, these modes were implemented ia the controller by hardware devices. These controllers implemented all or parts of the foUowiag control algorithm ... 

Dead-Time Compensation. Dead time within a control loop can greatiy iacrease the difficulty of close control usiag a PID controller. Consider a classical feedback control loop (Fig. 18a) where the process has a dead time of If the setpoiat is suddenly iacreased at time t, the controller immediately senses the deviation and adjusts its output. However, because of the dead time ia the loop, the coatroUer does aot begia to see the impact of that change ia its feedback sigaal, that is, a reductioa ia the deviatioa from setpoiat, uatil the time t +. Because the deviatioa does aot change uatil... 

Technology has been introduced for on-line estimation of the kappa number based on absorption of ultraviolet light (35). This breakthrough ia optical sensor technology permits closed-loop feedback control of digesters from on-line measurement of the kappa number. 

Electrochemical Microsensors. The most successful chemical microsensor in use as of the mid-1990s is the oxygen sensor found in the exhaust system of almost all modem automobiles (see Exhaust control, automotive). It is an electrochemical sensor that uses a soHd electrolyte, often doped Zr02, as an oxygen ion conductor. The sensor exemplifies many of the properties considered desirable for all chemical microsensors. It works in a process-control situation and has very fast (- 100 ms) response time for feedback control. It is relatively inexpensive because it is designed specifically for one task and is mass-produced. It is relatively immune to other chemical species found in exhaust that could act as interferants. It performs in a very hostile environment and is reHable over a long period of time (36). 

Spreadsheet Applications. The types of appHcations handled with spreadsheets are a microcosm of the types of problems and situations handled with fuU-blown appHcation programs that are mn on microcomputers, minis, and mainframes and include engineering computations, process simulation, equipment design and rating, process optimization, reactor kinetics—design, cost estimation, feedback control, data analysis, and unsteady-state simulation (eg, batch distillation optimization). 

Electrotransport technology offers a number of benefits for therapeutic appHcations, including systemic or local adininistration of a wide variety of therapeutic agents with the potential adininistration of peptides and proteins long-term noninvasive administration, improving convenience and compliance controlled release, providing a desired deflvery profile over an extended period with rapid onset of efficacious plasma dmg levels and in some cases reduced side effects and a transport rate relatively independent of skin type or site. Additional benefits include easy inception and discontinuation of treatment, patterned and feedback-controlled deflvery, and avoidance of first-pass hepatic metaboHsm. 

C. D. Ealk andj. J. Mooney, Three-Way Conversion Catalysts—Effect of Closed Eoop Feedback Control and Other Parameters on Catalyst Efficieny, SAE 800462, Society of Automotive Engineers, Warrendale, PA., 1980. 

Feedback Control In a feedback control loop, the controlled variable is compared to the set point R, with the difference, deviation, or error e acted upon by the controller to move m in such a way as to minimize the error. This ac tion is specifically negative feedback, in that an increase in deviation moves m so as to decrease the deviation. (Positive feedback would cause the deviation to expand rather than diminish and therefore does not regulate.) The action of the controller is selectable to allow use on process gains of both signs. 

Feedfoi ward control is usually combined with feedback control to eliminate any offset resulting from inaccurate measurements and calculations and unmeasured load components. The feedback controller can either bias or multiply the feedfoi ward calculation. 

General References SPinskey, Feedback Controllers foi- the Fiocess... 

FIG. 8-23 Both load regulation and setpoint response require high gains for 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) ... 

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. 

FIG. 8-31 (a) Feedback control of a heat exchanger, (h) Feedforward control... 

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. 

One such approach is called cascade control, which is routinely used in most modern computer control systems. Consider a chemical reactor, where reac tor temperature is to be controlled by coolant flow to the jacket of the reac tor (Fig. 8-34). The reac tor temperature can be influenced by changes in disturbance variables such as feed rate or feed temperature a feedback controller could be employed to compensate for such disturbances by adjusting a valve on me coolant flow to the reac tor jacket. However, suppose an increase occurs in the... 

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