Decoupling control loops

The NI [4] is a useful tool to analyse the stability of the control loop pairings determined using the relative gain analysis. If a manipulated variable is to be used to control an output variable, then the loop must not become unstable in dynamic situations. The NI can be used to prove that a 2 x 2 matrix is stable however, when n 2 (if there are more than two input-output variables being paired) the NI can only be used to prove that the control loop is definitely not stable. Then, for the steady-state matrix G described in Equation 9.7, where each element in 6 is rational and open-loop stable [3], the system will definitely be imstable if the NI is negative, i.e. if 

The NI will detect instability introduced by closing the other control loops. Remember that the NI does not prove the control system is stable when there are n 2 variables a negative NI only proves that the system is definitely not stable. 

The NI should not be used for systems with time delays (dead time). Grosdidier et. al. [5] provides a detailed explanation on how to use the index for systems containing dead time. Dynamic simulation should always be used to test the stability of a system if the NI is positive. 

There are some basic rules that should be followed to obtain optimal pairing in control loops  

RGA rule 1. Pair the input and output variables that have positive RGA elements that are closest to 1.0. 

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Thus, the equivalent completely decoupled control loops can be represented by the block diagram in Fig. 7.76. 

Fig. 7.76. Equivalent decoupled control loops corresponding to the system illustrated in...

Ideally, manipulated variables are coupled to controlled variables on a one-to-one basis, i.e. mi controls y, m2 controls y2, etc., for ease of control. Since interactions do occur often between control loops, it is these controller interactions that need to be decoupled. SVD is a matrix technique useful in determining whether it is sttucturaUy impossible to apply decoupling to a system [3]. When the sets of equations in the steady-state gain matrices are nearly singular, the problem is ill conditioned and it may not be possible to decouple control-loop interactions. 

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. 

After proper pairing of manipulated and controlled variables, we still have to design and tune the controllers. The simplest approach is to tune each loop individually and conservatively while the other loop is in manual mode. At a more sophisticated level, we may try to decouple the loops mathematically into two non-interacting SISO systems with which we can apply single loop tuning procedures. Several examples applicable to a 2 x 2 system are offered here. 

Most of the evaluation boards of such ESR-sensitive parts are shipped out to customers with only aluminum electrolytic or tantalum capacitors at their outputs. But what really happens is that the customer happily connects the eval board (rather expectantly) into his or her system, and completely forgets there are a bunch of ceramic capacitors all over the system board (for local decoupling at different points). In effect, the switcher can lose that valuable zero in its control loop and break into oscillations (see Figure 3-5). More so if the connecting leads are short. 

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... 

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. 

The decoupling structure is depicted in Figure 11. The global transfer matrix is diagonal. It is clear that the decoupling, as stated, is not always possible, as the transfer function of the different blocks should be stable and physically feasible. If it is possible, the new input variable u will control the concentration and U2 will control the temperature, and both control loops could be tuned independently. Sometimes, a static decoupling is more than enough. 

Multivariable controls (MVCs) are particularly well suited for controlling highly interactive fractionators where several control loops need to be simultaneously decoupled. MVCs can simultaneously consider all the process lags, and apply safety constraints and economic optimization factors in determining the required manipulations to the process. The technique of multivariable control requires the development of dynamic models based on fractionator testing and data collection. Multivariable control applies the dynamic models and historical information to predict future fractionator characteristics. For towers that are subject to many constraints, towers that have severe interactions, and towers with complex configurations, multivariable control can be a valuable tool. 

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

The base case and three alternatives were evaluated by controllability analysis [7, 8], firstly at steady-state. The conclusion is that the loops Q2 (reboiler duty) -1, and SS2 (side-stream flow)-I2 are more interactive than the loop controlling I3 with D2, D4 or Q4. The use of D4 offers the best decoupling of loops. In the base case and alternative B the effect of the variables belonging to S4 on I3 is enhanced by closing the other loops, while in alternatives A and C this effect is hindered. However, at this point there is not a clear distinction between the base case and alternatives. A dynamic controllability analysis is needed. 

Figure 1. Schematic of closed loop, decoupled control system.

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. 

If Au = 1, then m2 does not affect yi and the control loop between yi and mi does not interact with the loop of y2 and m2. In this case we have completely decoupled loops. 

When the designer is confronted with two strongly interacting loops, he or she introduces in the control system special new elements called decouplers. The purpose of decouplers is to cancel the interaction effects between the two loops and thus render two noninteracting control loops. Let us now study how we can design the decouplers for a process with two strongly interacting loops. 

The block diagram of the process with two feedback control loops and two decouplers is given in Figure 24.7b. 

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. 

Bristol s relative-gain array initiated an extensive and vigorous research effort in interaction and decoupling of control loops. There is a large number of papers with applications of Bristol s array, as well as several theoretical treatments. Today it has been shown that if dynamic interaction is important Bristol s method may lead to the wrong couplings. The following paper demonstrates this point ... 

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... 

Bode diagram, 330-31, 334-37 frequency response, 323-24 interacting capacities, 197-200 noninteracting capacities, 194-96 pulse transfer function, 619 Multiple-input multiple-output system, 20 discrete-time model, 586 discrete transfer function, 612 input-output model, 83-85, 163-68 linearization, 121-26 transfer-function matrix, 164, 166 Multiple loop control systems, 394-409 Multiplexer, 560, 564 Multivariable control systems, 461-62 alternative configurations, 467-84 decoupling of loops, 503-8 design questions, 461-62 interaction of loops, 487-94 selection of loops, 494-503 Multivariable process (see Multiple-input multiple-output system)... 

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