Interacting control loops

In general, we can write, from Fig. 7.74, for any pair of interacting control loops ... 

Shinskey, F. G., "The Stability of Interacting Control Loops with and without Decoupling," Proc. Fourth IFAC Multivariable Technological Systems Conference, 1977, 21. 

Effective decoupling of interacting control loops may be hampered by different response times for each of the interacting loops. Decouplers are intended to cancel out interactions by implementing certain adjustments in each control loop. Predictors are also used with decouplers to forecast the dynamic responses. These techniques require considerable periodic tuning due to changes in feed flow rates, feed compositions, and other external conditions, and their success is limited. 

A control system is composed of several interacting control loops. 

Two interacting control loops are perfectly decoupled only when the process is perfectly known, because only in this case are the transfer functions Hn, Hi2, H2n and H22 known exactly. Since this requirement is rarely satisfied in practice, the decouplers offer only partial decoupling, with some weak interaction still persisting between the two loops. 

Interacting capacities, 193, 197-200 Interacting control loops, 487-503 decoupling of, 504-8 references, 537-38 Interacting tanks, 199-200 Interaction factor, 198 Interaction index, 509 Interaction index array, 509 Interface, computer-process, 557-61 references, 670-71... 

Control Strategies for Multivariable Control Problems If a conventional multiloop control strategy performs poorly due to control loop interactions, a number of solutions are available ... 

Detuning a controller (e.g., using a smaller controller gain or a larger reset time) tends to reduce control loop interactions by sacrificing the performance for the detuned loops. This approach may be acceptable if some of the controlled variables are faster or less important than others. 

The selection of controlled and manipulated variables is of crucial importance in designing a control system. In particular, a judicious choice may significantly reduce control loop interactions. For the blending process in Fig. 8-40(d ), a straightforward control strategy would be to control x by adjusting w, and w by adjusting Wg. But... 

Decoupling Control Systems Decoupling control systems provide an alternative approach for reducing control loop interactions. The basic idea is to use additional controllers called decouplers to compensate for undesirable process interactions. 

In principle, ideal decouphng eliminates control loop interactions and allows the closed-loop system to behave as a set of independent control loops. But in practice, this ideal behavior is not attained for a variety of reasons, including imperfect process models and the presence of saturation constraints on controller outputs and manipulated variables. Furthermore, the ideal decoupler design equations in (8-52) and (8-53) may not be physically realizable andthus would have to be approximated. 

Distillation columns have four or more closed loops—increasing with the number of product streams and their specifications—all of which interact with each other to some extent. Because of this interaction, there are many possible ways to pair manipulated and controlled variables through controllers and other mathematical functions with widely differing degrees of effectiveness. Columns also differ from each other, so that no single rule of configuring control loops can be apphed successfully to all. The following rules apply to the most common separations. 

Chapter 5 comprises the computer simulation examples. The exercises are by no means mandatory or restrictive. Most instructive is to study the influence of important model parameters, using the interactive and graphical features of ISIM. Working through a particular example will often suggest an interesting variation, such as a control loop, which can then be inserted into the model. In... 

Those that have no interaction with other control loops. 

No interaction. Controller design is like single-loop systems. Strong interaction if 8 is close to 1 weak interaction if 8 1. One-way interaction... 

Several instrument vendors have developed commercial on-line adaptive controllers. Difficulties have been reported in two situations. First, when they are applied in a multivariable environment, the interaction among control loops can cause the adaptation to fail. Second, when few disturbances are occurring, the adaptive controller has little to work with and its performance may degrade drastically. 

Avoid control-loop interaction if possible, but if not, make sure the controllers are tuned to make the entire system stable. Up to this point we have discussed tuning only single-input-single-output (SISO) control loops. Many... 

Interaction among control loops in a multivariable system has been the subject of much research over the last 20 years. Various types of decouplers were explored to separate the loops. Rosenbrock presented the inverse Nyquist array (INA) to quantify the amount of interaction. Bristol, Shinskey, and McAvoy developed the relative gain array (RGA) as an index of loop interaction... 

It can be easily checked that the step response of the two controlled variables, Figure 10, is appropriated under single changes in the respective reference, but the interaction is rather strong and any change in one reference acts as a disturbance in the other control loop. 

For example, a typical billion Ib/yr ethylene plant may have 600 control loops with control valves and 400 interacting loops with a cost of about 6 million. (Skrokov. 1980. pp. 13, 49 see Sec. 3.1) the computer implementation of this control system will cost another 3 million. Figure 3.1 shows the control system of an ethylene fractionator which has 12 input signals to the computer and four outgoing reset signals to flow controllers. 

Interaction between control loops is discussed in Section 7.15. 

Substantial effort in modelling and/or experimental measurement is required in order to derive GFFA(s) and GFFB(s). Due to errors in determining the individual transfer functions (GM(s), G 2(s), etc.), to errors in measurement, and to load variables which have not been accounted for in the models, feed-forward compensation can never be perfect, and considerable drifting of the controlled variable(s) can occur. On the other hand, the two variable feed-forward control model expressed by equation 7.165 automatically takes into account any interaction between the reflux and steam flow control loops (see also Section 7.15). 

Interaction can be between two or more processes or between actions produced by different control loops applied to a single process. The former has already been discussed in Section 1.53. Some degree of interaction between control loops will nearly always occur in a multiple-input/multiple-output (MIMO) system. For example, consider the distillation process described in Section 7.3 (Fig. 7.9). Suppose it is desired to control simultaneously the compositions of both the overheads product stream (by manipulating the reflux flowrate) and the bottoms product stream (by regulating the steam flowrate to the reboiler). A typical arrangement is shown in Fig. 7.73. 

Fig. 7.74. Block diagram illustrating interaction between control loops on distillation column shown in Fig. 7.73...

Mn. This will not only act as a suitable control signal for C2 but will also produce an undesired disturbance in control loop 1 and cause C, to deviate from its desired value. However, A/Vl can be varied by a quantity M t which compensates for this interaction effect from A/v2. If the deviation in C, due to interaction is %, then My can be determined from equation 7.166a, i.e. ... 

Estimating tha Degree of Interaction Between Control Loops... 

The degrees of interaction between different sets of control loops controlling a MIMO plant can usually be determined by the use of the relative gain array technique due to BRISTOL 36. This approach can be illustrated by considering the process shown in Fig. 7.74 which has two inputs and two outputs. The procedure is as follows ... 

The two larger numbers (i.e. 0.75) indicate the recommended control loop configuration (i.e. that with the smaller amount of interaction) which is constructed by coupling C2 with A/Vl and C, with Mv2 (Fig. 7.776). 

Starting from the pre-powerstroke state myosin complex with ADP and Pi tightly bound (summarized structure in Table I), the M.D.Pi is in rapid equilibrium with an actin-bound state on the microsecond-millisecond time scale. This is very dependent on ionic strength (Furch et al., 2000 White and Taylor, 1976) and is therefore probably a non-stereo-specific weak binding state and is controlled by the ionic interactions between loop 2 and the N-terminus of actin. Other ionic interactions may also be involved. This loose association between actin and myosin probably does not alter the overall conformation of myosin. 

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