Given a representative model of a process, 'What-If' investigations can be made via simulation, to answer operational questions such as safety related issues and to provide for operator training. However, this approach is not suitable for real-time automatic control. Within the context of automatic control, the inverse problem is considered, i.e. given the current states of the process, what actions should be taken to achieve desired specifications. Depending on the form of the plant model, different control strategies can be developed. The attraction of adopting a model based approach to controller development is illustrated in the block diagram shown in Figure 2.
Figure 2. Ideal Model Based Control
By regarding the blocks to be mathematical operators, it can be seen that if an accurate model of the process is available, and if its inverse exists, then process dynamics can be cancelled by the inverse model. As a result, the output of the process will always be equal to the desired output. In other words, model based control design has the potential to provide perfect control. Hence, the first task in the implementation of modern control is to obtain a model of the process to be controlled. However, given that there are constraints on process operations; that all models will contain some degree of error and that all models may not be invertible, perfect control is very difficult to realise. These are the issues that modern control techniques aim to address, either directly or indirectly.
In the process industries, black box models are normally used for controller synthesis because the ill-defined nature of the processes makes mechanistic model development very costly. For process design purposes, precise characterisation is important. However, for the purposes of control strategy specification, controller design and control system analysis, models that can replicate the dynamic trends of the target processes are usually sufficient. Black box models have been found to be suitable in this respect and can be used to predict the results of taking certain actions.
Linear transfer functions and time-series descriptions are popular model forms used in control systems design. This is because of the wealth of knowledge that has been built up in linear systems theory. Increasingly, however, controllers are being designed using nonlinear time-series as well as neural network based models in recognition of the nonlinearities that pervade real world applications. The following sections briefly discuss the various algorithms that may arise from model based controller designs.
The ubiquitous three-term Proportional+Integral+Derivative (PID) controller accounts for more than 80% of installed automatic feedback control devices in the process industries. In the past, these have been tuned using frequency response techniques or empirically derived rules-of-thumb. The modern approach is to determine the settings of the PID controller based upon a model of the process. The settings are chosen so that the controlled response adhere to user specifications. A typical criterion is that the controlled response should have a quarter decay ratio. Alternatively, it may be desired that the controlled response follow a defined trajectory or that the closed loop has certain stability properties [e.g. Warwick and Rees, 1988].
It can be easily shown that a Proportional+Integral controller is optimal for a first order linear process without time-delays. Similarly, the PID controller is optimal for a second order linear process without time-delays. In practice, process characteristics are nonlinear and can change with time. Thus the linear model used for initial controller design may not be applicable when process conditions change or when the process is operated at another region.
One solution is to have a series of stored controller settings, each pertinent to a specific operating zone. Once it is detected that the operating regime has changed, the appropriate settings are switched in. This strategy, called parameter- or gain-scheduled control, has found favour in applications to processes where the operating regions are changed according to a preset and constant pattern. In applications to continuous systems, however, the technique is not so effective.
A more elegant technique is to implement the controller within an adaptive framework. Here the parameters of a linear model are updated regularly to reflect current process characteristics [Warwick et al, 1987; Willis and Tham, 1989a]. These parameters are in turn used to calculate the settings of the controller as shown schematically in Fig. 3.
Figure 3. Simplified Schematic of the Structure of Adaptive Controllers
The settings of the controller can be updated continuously according to changes in process characteristics. Such devices are therefore called auto-tuning/adaptive/self-tuning controllers. In some formulations, the controller settings are directly identified. A faster algorithm results because the model building stage has been avoided. Currently, many commercial auto-tuning PID controllers available from major control and instrumentation manufacturers. The simplest forms are those based upon the use of linear time-series models Some PID controllers are also auto-tuned using pattern recognition methods [Bristol, 1977]. For example, the Foxboro EXACT controller changes its settings to maintain a user defined response pattern. A good review of auto-tuning PID controllers is given in Astrom and Hagglund .
Theoretically, all model based controllers can be operated in an adaptive mode [e.g. Hang et al, 1993]. Nevertheless, there are instances when the adaptive mechanism may not be fast enough to capture changes in process characteristics due to system nonlinearities. Under such circumstances, the use of a nonlinear model may be more appropriate for PID controller design. Nonlinear time-series, and recently neural networks, have been used in this context. A nonlinear PID controller may also be automatically tuned using an appropriate strategy, by posing the problem as an optimisation problem. This may be necessary when the nonlinear dynamics of the plant are time-varying. Again, the strategy is to make use of controller settings most appropriate to the current characteristics of the controlled process. A self-tuning PID controller based on the use of a nonlinear neural net model has been reported by Montague and Willis (1993).
PID type controllers do not perform well when applied to systems with significant time-delays. Perhaps the best known technique for controlling systems with large time-delays is the 'Smith predictor'. It overcomes the debilitating problems of delayed feedback by using predicted future states of the output for control. Currently, some commercial controllers have Smith predictors as programmable blocks. There are, however, many other model based control strategies have dead-time compensation properties. If there is no time-delay, these algorithms usually collapse to the PID form. Predictive controllers can also be embedded within an adaptive framework and a typical adaptive predictive control structure is shown in Fig. 4.
Figure 4. Simplified Schematic of Adaptive Predictive Controllers
The, by now, classical Generalised Minimum Variance (GMV) controller is an example of this philosophy [Clarke and Gawthrop, 1975]. GMV control minimises the squared weighted difference between the desired value and the predicted output while penalising excessive control effort. The prediction horizon is the time-delay of the system, and this is a fixed parameter. GMV control, however, cannot effectively cope with variable time-delays and process constraints. This led to the development of long-range predictive controllers, e.g. the Generalised Predictive Controller (GPC) and Dynamic Matrix Control (DMC) [Clarke et al, 1987; Cutler and Ramaker, 1979; Wilkinson et al, 1990, 1991a,b]. The control problem is formulated in a manner similar to that adopted in the GMV approach. The differences are that the model is used to provide predictions of the output over a range of time-horizons into the future. Usually the range is between the smallest and largest expected delays. This alleviates the problem of varying time-delays and hence enhances robustness. Calculation of the control signal is essentially an optimisation problem. Here, economic objectives as well as process constraints can be included in the problem formulation. Examples of process constraints are the limits to liquid flows in fixed sized piping, allowable temperatures and pressures in process units, emissions to atmosphere, etc. Nowadays, the phrase 'predictive control' refers to the application of long-range predictive controllers. Again, predictive controllers may be designed using linear or nonlinear models.
Thus far, we have only considered the case where the is one manipulated input and one controlled output; single-input single-output (SISO) systems. With most processes, there are many variables that have to be regulated. The chemical reactor is a typical example where level, temperature and pressure have to kept at design values, that is there are at least three control loops; a multi-loop system. If the actions of one controller affect other loops in the system, then control-loop interaction is said to exist. If each controller has been individually tuned to provide maximum performance, then depending on the severity of the interactions system instability may occur when all the loops are closed. SISO controllers, whether adaptive, linear or nonlinear strategies, may therefore not be applicable to such processes. Models used in the design of SISO controllers do not contain information about the effects of loop interactions. Thus, they cannot be expected to perform well. For a multiloop strategy to work, individual SISO controllers are usually detuned (made less sensitive), resulting in sluggish performances for some or all loops.
Ideally, multivariable controllers should be applied to systems where interactions occur. As opposed to multi-loop control, multivariable controllers take into account loop interactions and their de-stabilising effects. Fortunately, it is a relatively trivial task to modify model based controllers to accommodate multivariable systems. By regarding loop interactions as feed-forward disturbances, they can be easily included in the model description. This simple augmentation leads to multivariable linear decoupling controllers [Jones and Tham, 1987; Tham, 1985; Tham et al, 1991b; Vagi et al, 1991], as well as nonlinear neural network based multivariable control algorithms [Willis et al, 1991e]. Following SISO designs, multivariable controllers that can provide time-delay compensation and handle process constraints can also be developed with relative ease. By incorporating suitable numerical procedures to build the model on-line, adaptive multivariable control strategies result.
Using an on-line parameter estimation algorithm to identify the parameters of the model, the parameters of most linear model based controllers can be adjusted in line with changes in process characteristics. Although great strides have been made in resolving the implementation issues of adaptive systems, for one reason or other, many practitioners are still not confident about the long term integrity of the adaptive mechanism. This concern has led to another contemporary topic in modern control engineering; robust control.
Robust control involves, firstly, quantifying the uncertainties or errors in a 'nominal' process model, due to nonlinear or time-varying process behaviour for example. If this can be accomplished, we essentially have a description of the process under all possible operating conditions. The next stage involves the design of a controller that will maintain stability as well as achieve specified performance over this range of operating conditions. A controller with this property is said to be 'robust' [Morari and Zafiriou, 1989].
A sensitive controller is required to achieve performance objectives. Unfortunately, such a controller will also be sensitive to process uncertainties and hence suffer from stability problems. On the other hand, a controller that is insensitive to process uncertainties will have poorer performance characteristics in that controlled responses will be sluggish. The robust control problem is therefore formulated as a compromise between achieving performance and ensuring stability under assumed process uncertainties. Uncertainty descriptions are at best very conservative, whereupon performance objectives will have to be sacrificed. Moreover, the resulting optimisation problem is frequently not well posed. Thus, although robustness is a desirable property, and the theoretical developments and analysis tools are quite mature, application is hindered by the use of daunting mathematics and the lack of a suitable solution procedure.
Nevertheless, underpinning the design of robust controllers is the so called 'internal model' principle. It states that unless the control strategy contains, either explicitly or implicitly, a description of the controlled process, then either the performance or stability criterion, or both, will not be achieved. The corresponding 'internal model control' design procedure encapsulates this philosophy and provides for both perfect control and a mechanism to impart robust properties (see Fig. 5).
Figure 5. Schematic of Internal Model Control Strategy
If the process model is invertible, then the controller is simply the inverse of the model. If the model is accurate and there is no disturbance, then perfect control is achieved if the filter is not present. This also implies that if we know the behaviour of the process exactly, then feedback is not necessary! The primary role of the low-pass filter is to attenuate uncertainties in the feedback, generated by the difference between process and model outputs and serves to moderate excessive control effort. The strategy and the concept that it embraces are clearly very powerful. Indeed, the internal model principle is the essence of model based control and all model based controllers can be designed within its framework.
As mentioned previously, there are cases when adaptive linear control schemes would not perform well when faced with a highly nonlinear process. This is because the adaptive mechanism may not be fast enough to track changes in process characteristics. Appropriately designed nonlinear controllers would therefore be expected to perform better. The use of neural network model based controllers has already been mentioned. Another emerging field is that of nonlinear controller designed based on mechanisitc models via the use of differential geometric concepts [Brockett, 1976; Kravaris and Kantor, 1990]. The aim of the design is similar to the use of Taylor series expansion to linearise the nonlinear model prior to application of linear model based controller designs. However, instead of providing local linearisation, contemporary nonlinear control strategies aim to provide 'global' linearisation over the space spanned by the states of the process; Globally Linearising Control (GLC). Global linearisation is achieved by a pre-compensator, designed such that the relationship between the inputs to the pre-compensator and the process output is linear. Linear control techniques can then be applied to the pseudo linear plant. A schematic of this strategy is shown in Fig. 6.
Figure 6. Schematic of Globally Linearising Control
Globally linearising control is a relatively new development and much research is being still being carried out to investigate the applicability of the technique [e.g. McColm et al, 1994]. McLellan et al  provide a review of nonlinear controller designs based upon mechanistic models. An interesting development that avoids the requirement of mechanistic models, is to use neural networks models instead. Neural network models are transformed into an equivalent state-space representation, and the GLC is designed based upon this state-space model [Peel et al, 1994].