In this chapter the prerequisites for control design is discussed: a defined objective, a set of available actions and a model that could be interrogated to establish which of the available actions would best move the system towards meeting the objective. Now we add more structure to the concepts to put forward a possible design methodology. In this methodology, central use is made of a system model.

In automatic control, a device called a controller issues commands that are physically connected to a process with the intention to influence the behaviour of the process in a particular way. The commands that will be issued by the controller in a particular set of circumstances are completely determined by the designer of the controller. Thus, automatic control can be seen to be completely pre-determined at the design stage.

Frequency response methods have a physical explanation that is readily understandable without any mathematics. In addition, the methods are design oriented, link easily between practical results and differential equation methods, and have been proven to work well in many practical design situations. The 'home territory' for frequency response methods has traditionally been in servomechanism, process control and aerospace applications, and they have been rather resistant to applications outside these areas.

There is no unifying feature present in nonlinear systems except the absence of linearity. For a nonlinear system, it is generally meaningless to speak of global behaviour. Approaches to the analysis of nonlinear systems include: Lyapunov's second or direct method, Lyapunov's first method, describing function method, sector bound methods. The most powerful tools for analysis and design of control systems operate only on linear models. It is therefore, potentially, very attractive when undertaking the design of a controller for a nonlinear system to replace the nonlinear system model by a linear approximation. Thus, linearisation amounts to a local approximation of differentiable functions by derivatives and is only valid for small perturbations.

This paper discusses control system design for industrial process control. In a typical industrial process, the online available measurements will usually be rather peripheral to the variables that are needed for control or that relate to 'customer satisfaction' (in the widest sense). For example, it is all too easy to measure the (unimportant) temperature of the flames inside a heating furnace but all too difficult to measure or even estimate, as a function of time, the internal temperature contours of a massive object that is being heated. Important (to the customer) product variables, (say) the clarity of plate, glass or the texture and taste of a food product, are typically difficult to define and even more difficult to measure online.

This chapter concentrates on establishing the mainstream structure of the state space approach. This chapter also establishes state-variable techniques for the representation and analysis of both continuous time and discrete time systems with an analogous development for the two cases. Canonical forms are introduced for the structural insight that they create and it is also indicated how canonical forms may be useful in control system design.

The term optimisation is often used very loosely in general speech, but in control theory it has a precise meaning: the action of finding the best possible solution as defined by an unambiguous criterion. Time-optimal control and linear quadratic optimisation are also discussed in this chapter.

This paper discusses H_∞ approach by specifically taking into account modelling uncertainty, and doing so in a worst-case sense, allow complex control design problems to be solved in a theoretically rigorous way while guaranteeing robustness of the implemented solutions over a pre-specified range of model incorrectness or (equivalently) of process variability. Here, we review the linear spaces that underlie much of the modern operator-based control theory with particular emphasis on the theory underlying H_∞ approach. Some of the H_∞ control design methodology is then introduced in very simple terms to establish the basic principles.

During the period of early industrial development, control was not identified as anything significant since the main preoccupations were with wider basic issues. For instance, the main problems in the early coal industry were with explosions, roof falls, carbon monoxide poisoning and dust-borne diseases. Once these problems had been largely solved, control systems technology came into play, for instance, in the design of remotely operated coal cutters. Present-day coal mine managers are now preoccupied with logistics, reliability, information and maintenance. The evolutionary pattern-mechanisation/automation and control/organisation and logistics-can be discerned in almost every industry. Thus, automatic control was scarcely needed until mechanisation had produced the devices and processes that needed to be controlled, and, in fact, it was the requirements of telephony that drove Nyquist (1932), Black (1934), Bode (1945) and co-workers to develop their frequency response and feedback techniques that were to have such wide applicability much later. Control theory rests on a very substantial mathematical foundation that gives rigour to mathematical representations of dynamical systems and underpins all the approaches to systems analysis and multivariable controller design.