Feedback with feedforward systems

Feedforward control systems have gained wide acceptance in chemical engineering in the past two decades. They have demonstrated their ability to improve control, sometimes quite spectacularly. We will illustrate this improvement in this section by comparing the responses of systems with feedforward control and with conventional feedback control when load disturbances occur. 

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. 

Thus we have described a system and process having a multiplicity of iterative feedbacks and feedforwards from each component and subprocess, to every other component and subprocess, all increasing the energy collected in the system and furnished to the load. In open-loop operation, this results in COP >1.0 permissibly, since the excess energy is freely received from an external source. In closed-loop operation, the COP concept does not apply except with respect to operational efficiency. In that case, the operational... 

Using Eq. (52) and an effective delay of about 41 seconds (as in Section V.D) to estimate the likely PI performance, indicates a total residence time of about 25 minutes for a two-CSTR system with combined feedforward and feedback and a total residence time of 75 minutes without feedforward. As the cost of the feedforward controller is small compared to the cost of an extra tank or the extra civil work to accommodate a residence time above 30 minutes, the scheme with feedforward control and two CSTRs seems likely to be the preferred option to achieve good control. 

Figure 15.54b is a schematic of a feedforward controller applied for steam drum level control. If the flow rate of the makeup feedwater is equal to the steam usage, the drum level remains constant. One is tempted to conclude that the feedforward controller is aU that is needed for this application. Unfortunately, the measurements of the steam usage and the feedwater flow rate are not perfectly accurate. Even small errors in measured flow rates add up over time, leading to one of two undesirable extremes. The drum can till with water and put water into the steam system, or the liquid level can drop, exposing the boiler tubes, which can damage them. As a result, neither feedback nor feedforward are effective by themselves for this case. In general, feedforward-only controllers are susceptible to measurement errors and umneasured disturbances, and, as a result, some type of feedback correction is typically required. 

On-line adaptation is not limited to feedback systems. On-line process identification can be coupled easily with feedforward, inferential, and other control systems, thus expanding the range of their applicability. Adaptation is particularly valuable for feedforward and inferential systems because they rely heavily on good process models for their successful implementation. 

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. 

Flow controllers set the rates of both streams, one being under flow-ratio control. In principle, either caustic soda or dilution water can be the master stream, with the other following it to maintain the ratio. Blending is controlled by a feedforward system, ultimately reset by the product concentration or density. Feedback from caustic concentration measurement (usually by density) could be used for final adjustment, but the concentration of the hypochlorite solution is the more important variable. The simple flow-ratio controller mentioned here can be replaced by a multi-stream version that allows use of other streams in addition to the principal 50% NaOH and dilution water. A cooler downstream of the mixing point removes the heat of dilution. The standard design is a titanium plate exchanger, which can also provide turbulence to complete the mixing process. Chlorine joins the diluted caustic in the reactor. Its rate of addition is controlled by an oxidation-reduction potential (ORP) instrument. The reaction mass recirculates from a collection tank around the system to reduce the increase of temperature across the reactor and to promote turbulence. The net production is removed from the tank, normally under level control. 

There are two key mechanisms in control theory to keep variations between limits feedback and feedforward control (Goodwin et al, 2001). With feedback control, a system maintains its homeostatic action through adjusting the system according to monitored output properties. 

Where sudden load changes are encountered and close control is necessary, feedforward systems have proven effective. The heat-balance equation is similar to that solved for the heat exchanger in Fig. 8.4. The only difference is that fuel flow is manipulated instead of steam and heat of combustion takes the place of latent heat of vaporization. Although the loss of heat out the stack may be significant, it yaries directly with load and can be readily accommodated by the action of the feedback temperature controller, as is done in Fig. 8.17. 

Attempt a numerical simulation of a feedforward-feedback system in Fig R10.4. Consider the simplified block diagram with... 

Incidentally, don t blindly add a bypass capacitor in parallel with the (upper) feedback resistor, as suggested. That feedforward capacitor introduces another zero in the loop and can cause the system to go unstable. You should realize that this family of devices has a full-blown internal Type 3 compensation, so it even has an internal zero to emulate an external ESR zero. That is why this family is supposed to be able to handle ceramic capacitors at the output. If you introduce yet another zero (via the feedforward capacitor as suggested), you could have one too many zeros. And ultimately, your design could be one, too (a zero). 

Feedforward control. The basic idea is shown in Fig. 1.8. The disturbance is detected as it enters the process and an appropriate change is made in the manipulated variable such that the controlled variable is held constant. Thus we begin to take corrective action as soon as a disturbance entering the system is detected instead of waiting (as we do with feedback control) for the disturbance to propagate all the way through the process before a correction is made. 

However, we can describe the basic structure of several feedforward control systems. Figure 8.7 shows a blending system with one stream which acts as a disturbance both its flow rate and its composition can change. In Fig. 8.7a the conventional feedback controller senses the controlled composition of the total blended stream and changes the flow rate of a manipulated flow. In Fig. %.lb the manipulated flow is simply ratjoed to the wild flow. This provides feedforward control for flow rate changes. Note that the disturbance must be measured to implement feedforward control. 

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. 

Now, from its essential notion, we have the feedback interconnection implies that a portion of the information from a given system returns back into the system. In this chapter, two processes are discussed in context of the feedback interconnection. The former is a typical feedback control systems, and consists in a bioreactor for waste water treatment. The bioreactor is controlled by robust asymptotic approach [33], [34]. The first study case in this chapter is focused in the bioreactor temperature. A heat exchanger is interconnected with the bioreactor in order to lead temperature into the digester around a constant value for avoiding stress in bacteria. The latter process is a fluid mechanics one, and has feedforward control structure. The process was constructed to study kinetics and dynamics of the gas-liquid flow in vertical column. In this second system, the interconnection is related to recycling liquid flow. The experiment comprises several superficial gas velocity. Thus, the control acting on the gas-liquid column can be seen as an open-loop system where the control variable is the velocity of the gas entering into the column. There is no measurements of the gas velocity to compute a fluid dynamics... 

For control purposes, somewhat simplified mathematical models usually are adequate. In distillation, for instance, the Underwood-Fenske-Gilliland model with constant relative volatilities and a simplified enthalpy balance may be preferred to a full-fledged tray-by-tray calculation every time there is a perturbation. In control situations, the demand for speed of response may not be realizable with an overly elaborate mathematical system. Moreover, in practice not all disturbances are measurable, and the process characteristics are not known exactly. Accordingly feedforward control is supplemented in most instances with feedback. In a well-designed system (Shinskey, 1984, p. 186) typically 90%... 

The feedback control in loops 1 and 2 is combined with a feed-forward controller in loop 3 which measures the inlet, temperature T calculates the change in cooling water flow rate Few which is required to bring the reactor temperature Fback to its set point Ts and sends this signal to the feedback controller (the feed-forward controller consists of a model of the process and is therefore not of P-, PI- or PID-type). The feedforward control loop will therefore theoretically eliminate any disturbances in inlet temperature Tv The feedback part of the control system, loop 1, will compensate for any inaccuracies in the feed-forward control model as well as eliminate the effect of other, unmeasured disturbances, e.g. in inlet flow rate Fr... 

Although the MPC paradigm encompasses several different variants, each one with its own special features, all MPC systems rely on the idea of generating values for process inputs as solutions of an on-line (real-time) optimization problem. That problem is constructed on the basis of a process model and process measurements. Process measurements provide the feedback (and, optionally, feedforward) element in the MPC structure. Figure 1 shows the structure of a typical MPC system. It makes it clear that a number of possibilities exist for the following ... 

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