Internal Model Control IMC

in equation (9.112) the model is exaet, i.e. CmCv) = G(s) and the disturbanee D(s) and noise A (.v) are both zero, then B(s) is also zero and the eontrol system is effeetively open-loop. This is the eondition when there is no uneertainty. However, if CmCv) 7 G(s), and D(s) and A (.v) are not zero, then B(s) expresses the uneertainty of the proeess. 

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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. 

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. 

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...

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. 

A set of Internal Model Control (IMC) tuning rules were established by Rivera, Morari, and Skogestad for a first-order plus dead time (FOPDT) open-loop process response that simply involves the adjustment of the proportional gain in the controller, K, for tuning. The integral time constant, 7, is set equal to the first-order time constant, TFO, for PI controllers (Table 10.5). 

It is therefore necessary to develop control-relevant techniques for characterizing nonlinearity. Through use of the Optimal Control Structure (OCS) approach [5], Stack and Doyle have shown that measures, such as Eq. (1), may still be applied but to a controlrelevant system structure. In the OCS approach, the necessary conditions for an optimal control trajectory given a process and performance objective are analyzed as an independent system. The nonlinearity of these equations determine the control-relevant nonlinearity. The OCS has been used to determine the control-relevance of certain commonly-exhibited nonlinear behaviors [6]. Using nonlinear internal model control (IMC) structures, similar analysis has been performed on Hammerstein and Wiener systems with polynomial nonlinearities to examine the role of performance objectives on the controlrelevant nonlinearity [7]. Though not applied to the examples in section 5, these controlrelevant analysis techniques have been shown to be beneficial and remain an active research area. 

II Single-loop PID control with compensation for difficult dynamics (e.g., Smith predictors for time-delays), again with appropriate loop pairing for multivariable processes. Alternatively, the use of explicitly model-based control strategies like direct synthesis control. Internal Model Control (IMC), or Model Predictive Control (MPC) may be appropriate ... 

The Internal Model Control (IMC) framework was used in [3] to identify and analyze factors that limit achievable closed-loop performance. The top diagram in Fig. 1 shows a standard feedback structure, which with the addition and subtraction of the controller output passed through a plant model, Gm, gives the equivalent IMC structure shown in the accompanying diagram. The classical controller, C, and IMC controller, Gc, may be readily shown to be related as follows ... 

Figure 1 Classical and Internal Model Control (IMC) structures.

The combination of the nonlinear estimator (28a,b) with the nonlinear controller (Eq. 17) yields the measurement-driven controller in internal model control (IMC) form ... 

A more comprehensive model-based design method. Internal Model Control IMC), was developed by Morari and coworkers (Garcia and Morari, 1982 Rivera et al., 1986). The IMC method, like the DS method, is based on an assumed process model and leads to analytical expressions for the controller settings. These two design methods are closely related and produce identical controllers if the design parameters are specified in a consistent manner. However, the IMC approach has the advantage that it allows model uncertainty and tradeoffs between performance and robustness to be considered in a more systematic fashion. 

When a cascade control system is tuned after installation, the secondary controller should be tuned first with the primary controller in the manual mode. Then the primary controller is transferred to automatic, and it is tuned. The relay auto-tuning technique presented in Chapter 12 can be used for each control loop. If the secondary controller is retuned for some reason, usually the primary controller must also be retuned. Alternatively, Lee et al. (1998) have developed a tuning method based on Direct Synthesis where both loops are tuned simultaneously. When there are limits on either controller (saturation constraints), Brosilow and Joseph (2002) have recommended design modifications based on the Internal Model Control (IMC) approach. 

ABSTRACT In this paper the Internal Model Control (IMC) approach for marine autopilot system is presented. The inversion by feedback techniques are employed for reahzation of inversion such nonlinear characteristics as saturation of rudder angle and rudder rate. The extension of the model and inverse model to a nonlinear form enabled to achieve a significant improvement in the control performance. 

In the ship autopilot systems there are also adopted internal model control (IMC). The difference between the IMC and single-loop systems lies in better prediction capabilities of the IMC approach. 

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