Internal model control

IMC (internal model control) replaces the PID controller completely. Its name derives from the fact that it can be shown that it is effectively the same approach as tuning a PID controller using the IMC tuning method. However, this is only exactly true if there is no deadtime. With deadtime IMC will outperform IMC tuning in a PID controller. 

If the gain is accurate then no further control action is required. If not, then there will be a mismatch between the process and the plant model. This model is used in the same way as the Smith controller, to generate a correction term which, in this scheme, is subtracted from theSP. 

Performance is equivalent to that of the Smith predictor and it too will perform badly if there is significant model error, particularly with deadtime. As with the Smith, higher order models can be used if required. 

Morari and coworkers (Garcia and Morari, Ind. Eng. Chem. Process Des. Dhv. Vol. 21, p. 308, 1982) have used a similar approach in developing Internal Model Control (IMC). The method is useful in that it gives the control engineer a different perspective on the controller design problem. 

The basic idea of IMC is to use a model of the process openloop transfer function in such a way that the selection of the specified closedloop response yields a physically realizable feedback controller. 

In addition, this choice of C(,j will also give perfect control for setpoint disturbances the total transfer function between the setpoint and X is simply unity. 

However, there are two practical problems with this ideal choice of the feedback controller C, y. First, it assumes that the model is perfect More importantly it assumes that the inverse of the plant model Cmo) physically realizable. This is almost never true since most plants have deadtime and/or numerator polynomials that are of lower order than denominator polynomials. 

So if we cannot attain perfect control, what do we do From the IMC perspective we simply break up the controller transfer function C( ) into two parts. The first part is the inverse of. The second part, which Morari calls a filter, is chosen to make the total physically leahzable. As we will show below, this second part turns out to be the closedloop servo transfer function that we defined as S(,j in Eq. (11.64). 

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A recent addition to the model-based tuning correlations is Internal Model Control (Rivera, Morari, and Skogestad, Internal Model Control 4 PID Controller Design, lEC Proc. Des. Dev., 25, 252, 1986), which offers some advantages over the other methods described here. However, the correlations are similar to the ones discussed above. Other plant testing and controller design approaches such as frequency response can be used for more complicated models. 

Internal Model Control was diseussed in relation to robust eontrol in seetion 9.6.3 and Figure 9.19. The IMC strueture is also applieable to neural network eontrol. The plant model GmC) in Figure 9.19 is replaeed by a neural network model and the eontroller C(.v) by an inverse neural network plant model as shown in Figure 10.30. 

The development of "internal model control," a design technique that bridges traditional and robust techniques for designing control systems, has provided the framework for unifying and extending these advances. It is now available in commercially available design software. 

Tune a controller with internal model control relations... 

The controller function will take on a positive pole if the process function has a positive zero. It is not desirable to have an inherently unstable element in our control loop. This is an issue which internal model control will address. 

A more elegant approach than direct synthesis is internal model control (IMC). The premise of IMC is that in reality, we only have an approximation of the actual process. Even if we have the correct model, we may not have accurate measurements of the process parameters. Thus the imperfect model should be factored as part of the controller design. 

Internal model control Extension of direct synthesis. Controller design includes an internal approximation process function. 

In theory, the internal model control methods discussed for SISO systems in Chap. 11 can be extended to multivariable systems (see the paper by Garcia and Morari in lEC Process Design and Development, Vol. 24, 1985, p. 472). 

When thermodynamics or physics relates secondary measurements to product quality, it is easy to use secondary measurements to infer the effects of process disturbances upon product quality. When such a relation does not exist, however, one needs a solid knowledge of process operation to infer product quality from secondary measurements. This knowledge can be codified as a process model relating secondary to primary measurements. These strategies are within the domain of model-based control Dynamic Matrix Control (DMC), Model Algorithmic Control (MAC), Internal Model Control (IMC), and Model Predictive Control (MPC—perhaps the broadest of model-based control strategies). 

Figure 9.1 Basic internal model control (IMC) structure...

Several process control design methods, such as the Generic Model Control (GMC) [41], the Globally Linearizing Control (GLC) [37], the Internal Decoupling Control (IDC) [7], the reference system synthesis [8], and the Nonlinear Internal Model Control (NIMC) [29], are based on input-output linearization. 

M.A. Henson and D.E. Seborg. An internal model control strategy for nonlinear systems. AIChE Journal, 37 1065-1081, 1991. 

Figure 4 illustrates the operation of an internal model control system (5) designed to use Pd as a manipulated variable to minimize the variance of the purity error APp while optimizing Y. As shown in the figure, the effect of the change in Pd at the time point k-1 is subtracted from the measured output variable (i.e., the purity error) at the time point k in order to determine an estimate of ADk, i.e.,... 

Figure 4. Internal model control representation of a minimum variance control method for product purity with simultaneous optimization of product yield.

The configuration of a back-propagation neural network and its use as an internal model controller (IMC). 

Model predictive control was conceived for multivariable systems with changing objectives and constraints. In simpler situations, a PID controller tuned according to internal model control (IMC) principles [8] can deliver equal performance with much less effort. 

Keywords Freeze drying, moving boundary, non linear distributed parameter systems, model based predictive control, internal model control. 

I ARTTwo Laplace-lX)niain Dynamics aiicl Contfol 9.5.2 Internal Model Control... 

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