Closed-loop dynamic behavior

For an open-loop overdamped process, the closed-loop dynamic behavior will go through the same stages as the controller aggressiveness is increased overdamped, critically damped, underdamped, ringing, and unstable (see Fignre 15.12). For a PID controller, controller aggressiveness is increased as is increased or as X/ is decreased. 

The controllability analysis was conducted in two parts. The theoretical control properties of the three schemes were first predicted through the use of the singular value decomposition (SVD) technique, and then closed-loop dynamic simulations were conducted to analyze the control behavior of each system and to compare those results with the theoretical predictions provided by SVD. 

The steady-state and dynamic behavior in RD are addressed in this chapter. Fundamental understanding of multiplicity in a reactive flash is provided. Moreover, the domain knowledge is extended by dynamic analysis, whose tasks include model development, control structure selection, controller tuning and simulation of closed loop dynamics. The output of this section serves as reference case to be compared with that of the life-span inspired design methodology (c/. section 1.4). The material presented in this chapter answers partially Question 6. 

There is a dynamic advantage in having the extra degree of freedom of aqueous reflux. It can be used to improve the closed-loop dynamic response of the system. Since Figure 9.7 shows that aqueous reflux is only needed for water feed composition <70mol%, the use of a preconcentrator column before the azeotropic column may improve dynamic behavior. 

The simulations involve the solution of the rigorous tray-by-tray model of each sequence, given by equations 1 to 6, together with the standard equations for the PI controllers for each control loop (with the parameters obtained through the minimization of the lAE criterion). The objective of the simulations is to And out how the dynamic behavior of the systems compare under feedback control mode. To carry out the closed-loop analysis, two types of cases were considered i) servo control, in which a step change was induced in the set point for each product composition under SISO feedback control. 

In addition to the visual observations of the dynamic responses, a quantitative measure is needed to provide a better comparison. With such an objective, lAE values were evaluated for each closed-loop response. The PUL option shows the lowest lAE value of 5.607 x 10 , while the value for the Petlyuk column turns out to be 2.35 x 10. Therefore, the results of the test indicate that, for the SISO control of the heaviest component of the ternary mixture, the PUL option provides the best dynamic behavior and improves the performance of the Petlyuk column. Such result is consistent with the prediction provided by the SVD analysis. 

In regard dynamics and control scopes, the contributions address analysis of open and closed-loop systems, fault detection and the dynamical behavior of controlled processes. Concerning control design, the contributors have exploited fuzzy and neuro-fuzzy techniques for control design and fault detection. Moreover, robust approaches to dynamical output feedback from geometric control are also included. In addition, the contributors have also enclosed results concerning the dynamics of controlled processes, such as the study of homoclinic orbits in controlled CSTR and the experimental evidence of how feedback interconnection in a recycling bioreactor can induce unpredictable (possibly chaotic) oscillations. 

Since FCC units are usually operated at their middle unstable steady state, extensive efforts are needed to analyze the design and dynamic behavior of open loop and closed loop control systems to stabilize the desirable middle steady state. 

The dynamic behavior of industrial unit 1 is studied in this section. The steady-state behavior of unit 1 has been studied previously. Both open-loop and closed-loop feedback controlled configurations will be presented. 

The control loop affects both the static behavior and the dynamic behavior of the system. Our main objective is to stabilize the unstable saddle-type steady state of the system. In the SISO control law (7.72) we use the steady-state values Yfass = 0.872 and Yrdss = 1.5627 as was done in Figures 7.14(a) to (c). A new bifurcation diagram corresponding to this closed-loop case is constructed in Figure 7.20. 

The closed loop process control permits the process to be stabilized in the region of the unstable transition mode between B and C, allowing compensation for the dynamic behavior of the target oxidation by corresponding... 

Thus far we have considered only steady-state operation of fixed-bed reactors. The response to variations in feed composition, temperature, or flow rate is also of significance. The dynamic response of the reactor to these involuntary disturbances determines the control instrumentation to be used. Also, if the system is to be put on closed-loop computer control, a knowledge of the response characteristics is vital for developing a control policy. It is beyond the scope of this book to treat the dynamic behavior of reactors, but it is necessary to draw attention to the availability of information on the subject. 

Let us examine the dynamic behavior of the closed-loop system when the set point changes by a unit step. From eq. (14,25) we take... 

In Chapter 14 we examined the dynamic characteristics of the response of closed-loop systems, and developed the closed-loop transfer functions that determine the dynamics of such systems. It is important to emphasize again that the presence of measuring devices, controllers, and final control elements changes the dynamic characteristics of an uncontrolled process. Thus nonoscillatory first-order processes may acquire oscillatory behavior with PI control. Oscillatory second-order processes may become unstable with a PI controller and an unfortunate selection of Kc and t,. 

Quite often, though, we are not interested in the exact location of the root-locus branches and simple, but qualitatively correct graphs, will suffice to draw the general conclusions about the dynamic behavior of a closed-loop system. References 12, 13 and 14 give a set of general rules which can be used to draw the approximate root locus of any given system. 

Is it possible to analyze the closed-loop behavior of a DDC loop using continuous transfer functions in the Laplace domain for the various dynamic elements of the loop Explain why or why not. 

In many cases, the variation of the flow rate Q due to changes in 7 during the depletion of the upstream chamber ought to be minimized to homogenize incubation times. Looking at Eq. 9, the flow rate Q can be stabilized by an online adjustment of co. Such a dynamic adjustment of CO requires either a very well reproducible flow behavior or a closed loop control of r, e.g., via continuous tracking of the transient positions of the menisci and r>. 

As mentioned previously the studied fermentation process to produce ethanol presents challenges in its process dynamics that exhibit oscillatory behavior, which affect process productivity and sustainabhity. To address these challenges, this section introduces a new sustainable process control framework that combines the biomimetic control strategy detailed earlier and the GREENSCOPE sustainabihty assessment tool. In this case study, the controlled variable is the concentration of product, Cp (see objective function defined earlier), and the dilution rate, Djn, is chosen as the manipulated variable. GREENSCOPE is employed to evaluate the sustainability performance of the system in open-loop and closed-loop operations. The obtained GITEENSCOPE indicator scores provide information on whether the implementation of the biomimetic controller for the fermentation process enables a more efficient and sustainable process operation. 

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