# Signal and Systems Concepts

Several concepts from linear control/systems theory are collected in nearly alpha­betical order [1-4]. All of which might have not been used in this book; however, they would be very useful in general for aerospace science and engineering applications.

C1 CONTROL SYSTEM: A "DYNAMICAL SYSTEM” CONCEPT

A system is something that can be studied as a whole. It is a collection of parts, subsystems, or components that function in unison to enable the system to carry out an assigned functional role. An airplane is a complex and sophisticated dynamic system in this sense. Systems may consist of subsystems that are interesting in their own right (Chapter 6). They may exist in an environment that consists of other similar systems. Systems are generally understood to have an internal state, inputs from an environment, and methods for manipulating the environment or themselves. Since cause and effect can flow in both directions of a system and environment, interesting systems often possess feedback. The idea behind dynamic systems theory is studying, understanding, and estimating the long-term behavior of a system that changes in time. The characterization of this behavior consists in knowing the conditions of a system. Some examples of these are (1) the system has a periodic behavior, (2) it recurrently returns to a given set, (3) it goes to all the possible sets that cover its space, (4) it never leaves a given set, and (5) its components interact with each other as desired.

Although there is a clear distinction between the so-called ‘‘classical’’ (frequency domain-based) and ‘‘modern’’ (time domain/optimal control) concepts and theories, we do not want/need to invoke these distinctions here. These are matters of the past and of a bygone era! Even today we need to use tools or techniques available easily for analysis and design of systems/control systems. The point is that with the great progress in computing technology (HW memory, speed, HW/SW parallelization) we can easily use any of the classical or modern tools with greater ease and flexibility than we could do two decades ago. And we believe that we need to use Bode diagrams and transfer functions to have the frequency domain feel and interpretation as well as state-space and time-domain analysis for optimization and direct time – history visualization and interpretation of control system performance. Hence, we should use both approaches in an integrated way to achieve the best design with the best performance. We should perhaps call this a hybrid approach rather than classical or modern. Also, since even this hybrid approach would further be augmented using ‘‘soft computing’’ (based on artificial neural networks, fuzzy logic/modeling, genetic algorithms, and approximate reasoning), we would like to consider the entire gamut of control system analysis, design, and validation methods as the ‘‘general theory of control systems.’’ The main reason for this is that we should make recourse to all or several such composite (classical, modern, and soft) approaches and tools for analysis, design, and validation of complex and sophisticated control systems: fly­by-wire aircraft, spacecraft, missiles, UVAs, MAVs, huge powerful computing network systems, and integrated electrical power grids/systems.