MIMO process

It is a general control strategy for MIMO processes with inequality constraints on input and output variables. 

With the dimension of multivariable MFC systems ever increasing, the probability of dealing with a MIMO process that contains an integrator or an unstable unit also increases. For such units FIR models, as used by certain traditional commercial algorithms such as dynamic matrix control (DMC), is not feasible. Integrators or unstable units raise no problems if state-space or DARMAX model MFC formulations are used. As we will discuss later, theory developed for MFC with state-space or DARMAX models encompasses all linear, time-invariant, lumped-parameter systems and consequently has broader applicability. 

A multiple-input/multiple-output (MIMO) process has two or more inputs and two or more outputs. A two-input/two-output system is shown schematically in Figure 15.69. Note that both Cj and C2 affect both y, and y2- When both inputs affect both outputs, the process is referred to as a coupled process. MIMO processes are frequently encountered in the chemical processing industries. 

This section considers the application of PID controllers to coupled MIMO processes. A key issue when applying PID controllers to MIMO systems is deciding which manipulated variable should be used to control which controlled variable. This is referred to as choosing the manipu-lated/controlled variable pairings [(c, y) pairings] or the control configuration. The factors that affect the choice of (c, y) pairings are analyzed here. 

Figure 15.70 shows two single-loop PID controllers applied to a two-input/two-output process (2 X 2 system). Applying single-loop PID controllers to a MIMO process is called decentralized... 

The recommended tuning procedure for a single PID loop can be extended to tuning the singleloop PID controllers applied for decentralized control of a MIMO process. The first step in tuning... 

Assume that it is required to tune PI controllers on a 2 x 2 MIMO process. The ATV results are used to select the controller gain and reset time based on, for example, Zeigler-Nichols tuning. Then, a single tuning factor, Fj, is applied to the tuning parameters for both control loops ... 

What is a MIMO process, and in what sense is the design of a control system for a MIMO process different from that for a SISO process ... 

The presence of multiple controlled outputs and multiple manipulated inputs creates a situation that we have not confronted so far There are more than one possible control configurations for a MIMO process. In this chapter we develop a concise methodology for the development of all feasible control systems for (1) single processing units and (2) processes composed of more than one interacting units. 

Why do we claim that there are a large number of control configurations for a MIMO process Find the number of alternative loop configurations for a process with N controlled variables and M manipulations, where M> N. 

The interaction among the control loops of a MIMO process... 

The production of intermediate chemicals requires more manifold types of production processes. Similar to the production of basic chemicals, chemical reactions are typically accompanied by separation processes such that most of these reactions can be categorized as SIMO or MIMO processes. Because intermediate chemicals are required for the production of final chemical products in huge quantities, they are usually produced by continuously operated plants. Typically, the production plants are specialized to perform a specific reaction and, hence, are single-purpose plants. 

Final chemical products are typically produced on multi-purpose plants which are designed for a specific product family. Such production processes are usually convergent. The composition of raw materials to produce a final chemical is called a recipe. Multipurpose plants are capable to handle multiple recipes, i.e. reactants and products handled vary in both type and quantity. These processes can be mainly categorized as MISO or MIMO processes. 

Figure 21.1 shows the block diagram for a multiple-input, multiple-output (MIMO) process to be controlled by two single-loop controllers. Having closed one of the loops (yi — ,), the controller in the second loop, which manipulates 2 based on the feedback of y2, must be tuned. A desirable feature of the process, as seen by this controller, is to have the effective process gain remain invariant, regardless of the action of the other control loop. 

Figure 21.1 MIMO process with one control loop.

When this ratio is close to unity, the given controller is relatively insensitive to interaction. Computing this ratio for the MIMO process in Figine 21.1 ... 

Considering the same MIMO process in Figure 21.1, y2 is expressed in terms of u and U2. 

The MIMO processes can be two dimensional (the simplest MIMO case), as in the following simple example ... 

Multiple-Input, Multiple-Output (MIMO) Processes Summary... 

MULTIPLE-INPUT, MULTIPLE-OUTPUT (MIMO) PROCESSES... 

Consider an MIMO process with r MVs and m CVs. Denote the current values of u and y as u k) and y k). The objective is to calculate the optimum set point ygp for the next control calculation (at A + 1) and also to determine the corresponding steady-state value of u, Usp. This value is used as the set point for u for the next control calculation. 

The development of an extended predictive control for SISO and MIMO plants is presented. This work develops a new tuning strategy that is reliable for a broad class of SISO and MIMO processes and provides better performance than the move suppressed dynamic matrix controllers. The application of this strategy is demonstrated through practical real plant applications with good control performance. The EPC algorithm for SISO and MIMO plants provides a well-conditioned controller that is capable of fast closed-loop response. 

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