Digital Control Systems [MEE 4003] - Kckong.info

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1.1. PROBLEM DEFINITION 3 (a) (b) (c) (d) Figure 1.2: Examples of controlled systems. (a): a robot arm, (b): a helicopter; (c): an active suspension, (d): an air conditioning system [Example 1-1] The systems in Fig. 1.2 are examples of controlled systems. The robot arm in (a) is a tracking control system, because the reference of the robot joint is time-varying in general. On the other hand, the remaining systems are all regulation systems. For example, once the desired height of a helicopter is set, the rotor speed is automatically controlled to maintain the height. For (c) and (d), find the reason why they are regulation systems. Disturbance Disturbance is an undesired input that affects the performance of the overall control system. Disturbance includes an environmental change, an external force, a change in system parameter, etc. 1.1.3 System System is a set of interacting components forming an integrated whole. Every system has input(s) and output(s). Most systems share common characteristics, including: • Systems have structure, defined by components and their composition, Digital Control Systems, Sogang University Kyoungchul Kong
1.1. PROBLEM DEFINITION 4 • Systems have behavior, which involves inputs, processing and outputs of material, energy, information, or data, • Systems have interconnectivity: the various parts of a system have functional as well as structural relationships to each other, • Systems may have some functions or groups of functions Plant A plant in control theory is the combination of process and actuator. In particular, a plant is the system to be controlled. 1.1.4 Signal A signal is any time-varying or spatial-varying quantity. In the physical world, any quantity measurable through time or over space can be considered as a signal. More generally, any set of human information or machine data can also be considered as a signal. Such information or machine data must all be part of systems existing in the physical world. [Example 1-2] Examples of signals follow. • Motion: The motion of a particle through some space can be considered as a signal, or can be represented by a signal. In general the position signal is a 3- vector signal. If orientation is considered, it is a 6-vector signal. • Sound: Since a sound is a vibration of a medium (such as air), a sound signal is related to the pressure value of air. A microphone converts sound pressure at some place to a function of time, generating a voltage signal that is proportional to the sound signal. Sound signals can be sampled to a discrete set of time points. For example, compact discs (CDs) contain discrete signals representing sound, recorded at 44,100 samples per second. • Images: A picture or image consists of a brightness or color signal, a function of a two-dimensional location. A 2D image can have a continuous spatial domain, as in a traditional photograph or painting; or the image can be discretized in space, as in a raster scanned digital image. Color images are typically represented as a combination of images in three primary colors, so that the signal is vectorvalued with dimension three. • Videos: A video signal is a sequence of images. A point in a video is identified by its two-dimensional position and by the time at which it occurs, so a video signal has a three-dimensional domain. Analog video has one continuous domain Digital Control Systems, Sogang University Kyoungchul Kong
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