MIMO control

Introduction The model-based contfol strategy that has been most widely applied in the process industries is model predictive control (MFC). It is a general method that is especially well-suited for difficult multiinput, multioutput (MIMO) control problems where there are significant interactions between the manipulated inputs and the controlled outputs. Unlike other model-based control strategies, MFC can easily accommodate inequahty constraints on input and output variables such as upper and lower limits or rate-of-change limits. 

This chapter is organized in the following way. First, the general model of the CSTR process, based on first principles, is derived. A linearized approximate model of the reactor around the equilibrium points is then obtained. The analysis of this model will provide some hints about the appropriate control structures. Decentralized control as well as multivariable (MIMO) control systems can be designed according to the requirements. 

A distillation column provides a good example of multiple input/multiple output (MIMO) control and illustrates well the qualitative methodology involved in determining a suitable control strategy for a process. The first requirement is to decide the primary objective of the process, i.e. what is its principal purpose Let us suppose that, for the column shown in Fig. 7.9, it is required to produce an overhead product D of a particular specification xD without attempting to control... 

The input/output data-based predictive controller based on the identified model is designed and applied to a MIMO control problem for the SMB process. We use the input/output data-based prediction model in the MPC algorithm. The QP method is used to obtain the control input Ufby minimizing the objective function defined as... 

CA McNabb and SJ Qin. Projection based MIMO control performance monitoring - I. Covariance monitoring in state space. J. Process Control, 13 739-759, 2003. 

Depending on how many controlled outputs and manipulated inputs we have in a chemical process, we can distinguish the control configurations as either single-input, single-output (SISO) or multiple-input, multiple-output (MIMO) control systems. 

Discuss the design questions related to a MIMO control system. 

Determine the number of controlled and manipulated variables for the flash drum (Example 23.1) assuming steady-state operation. Why are the results different from those of Example 23.1 State the danger involved when we consider steady-state models to design a MIMO control system. 

For multiple-input-multiple-output (MIMO) control algorithms, these variables are written in bold type to denote that they are vectors of variables (e.g., u is a vector of manipulated variables). 

There have been relatively few studies of multi-variable controllers for continuous crystallizers. Most studies of MIMO control algorithms are based on linear state-space models of the form... 

Naturally, the type of controller plays an important role. In this chapter we limit the analysis to classical PID controllers. These form over 90% of the control loops in industry. As mentioned, from a plantwide control viewpoint multi-SISO controllers are the most adapted. Naturally, we do not exclude more sophisticated MIMO control systems, as DMC or Model Based Control systems, but these are typically applied to stand-alone complex units, as FCC reactors, complex distillation units in refining, etc. Hence, the controllability analysis presented here aims more to get a conceptual insight in the dynamics of a process related to its design than to offer a high-performance control solution. 

In a multi-input multi-output (MIMO) control system (Fig. 12.14), there are several controlled variables (vector y) that should be kept on set-points (vector r) faced to disturbances (vector d) by means of appropriate manipulated variables (vector u). The feedback controller K provides the algorithm that will ensure the link between the manipulated (inputs) and controlled (outputs) variables. In this chapter we will consider a decentralised control system that makes use of multi-SISO control loops, which means that a single controlled variables is controlled by a single manipulated variable. This arrangement is typical for plantwide control purposes. However, there will be interactions between different loops. These Interactions can be detrimental, or can bring advantages. Therefore, the assessment of interactions is a central issue in the analysis of MIMO systems. 

A MIMO control system must be configured for the retrofitted column. To compute the RGA, a linearized model, in the steady state, relates the changes in the designated outputs, T, L, and Li, to those of the manipulated variables, gi, Q2, and S ... 

This section starts by presenting the outline of the methodology. It follows the description of a case study and the plantwide control problem. Possible control structures, as well as the effect of recycles are evaluated by linear MIMO controllability analysis, both at steady state and in the frequency domain. The comparison of design alternatives is performed by closed loop simulation. This procedure allows the designer to choose the final flowsheet, as well as the appropriate control strategy. 

C.T. Kiranoudis, G.V. Bafas, and Z.B. Marouhs, MIMO control of conveyor-belt drying chambers. Drying Technol., 13(l/2) 73-97,1995. 

In previous chapters, we have emphasized control problems that have only one controlled variable and one manipulated variable. These problems are referred to as single-input, single-output (SISO), or single-loop, control problems. But in many practical control problems, typically a number of variables must be controlled, and a number of variables can be manipulated. These problems are referred to as multiple-input, multiple-output (MIMO) control problems. For almost all important processes, at least two variables must be controlled product quahty and throughput. 

Several examples of processes with two controlled variables and two manipulated variables are shown in Fig. 18.1. These examples illustrate a characteristic feature of MIMO control problems, namely, the presence of process interactions, that is, each manipulated variable can affect both controlled variables. Consider the in-line blending system shown in Fig. 18.1a. Two streams containing species A and B, respectively, are to be blended to produce a product stream with mass flow rate w and composition x, the mass fraction of A. Adjusting either manipulated flow rate, Wj or wb, affects both w and x. 

A schematic representation of several SISO and MIMO control applications is shown in Fig. 18.2. For convenience, it is assumed that the number of manipulated variables is equal to the number of controlled variables. 

Table 18.1 shows the single-loop ITAE settings, and Fig. 18.5 shows simulation results for set-point changes for each controlled variable. The ITAE settings provide satisfactory set-point responses for either control loop when the other controller is in manual (solid line). However, when both controllers are in automatic, the control loop interactions produce very oscillatory responses especially mxB (dashed line). McAvoy (1981) has discussed various approaches for improving the performance of the multiloop controllers. See Exercise 18.1 for a similar MIMO control problem where the loops also exhibit oscillations. 

The SVA and RGA methods can be used as a way to screen subsets of the possible manipulated variables (MVs) and controlled variables (CVs) for a MIMO control system. Because these analyses are based on the steady-state gain matrix, it is recommended that promising combinations of MVs and CVs be identified and then investigated in more detail using simulation and dynamic analysis. The two steps shown below can be used to identify promising subsets of MVs and CVs, recognizing that for multiloop control the number of MVs should equal the number of CVs (a square system). 

In this chapter we have considered control problems with multiple inputs (manipulated variables) and multiple outputs (controlled variables), with the main focus on using a set of single-loop controllers (multiloop control). Such MIMO control problems are more difficult than SISO control problems because of the presence of process interactions. Process interactions can produce undesirable control loop interactions for multiloop... 

Additional information on statistically-based CPM is available in a tutorial (MacGregor, 1988), survey articles (Piovoso and Hoo, 2002 Kourti, 2005), and books (Box and Luceno, 1997 Huang and Shah, 1999 Cinar et al., 2007). Extensions to MIMO control problems, including MPC, have also been reported (Huang et al., 2000 Qin and Yu, 2007 Cinar et al., 2007). 

Employ MIMO control for highly interactive processes. 

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