Electrical Engineering

Control Systems Electronics

continuous time signalIt does this with the aid of input devices such as sensors, that respond in some way to this information and then uses electrical energy in the form of an output action to control a physical process or perform some type of mathematical operation on the signal.

But electronic control systems can also be regarded as a process that transforms one signal into another so as to give the desired system response. Then we can say that a simple electronic system consists of an input, a process, and an output with the input variable to the system and the output variable from the system both being signals.

There are many ways to represent a system, for example: mathematically, descriptively, pictorially or schematically. Electronic systems are generally represented schematically as a series of interconnected blocks and signals with each block having its own set of inputs and outputs.

As a result, even the most complex of electronic control systems can be represented by a combination of simple blocks, with each block containing or representing an individual component or complete sub-system. The representing of an electronic system or process control system as a number of interconnected blocks or boxes is known commonly as “block-diagram representation”.

Block Diagram Representation of a Simple Electronic System

Electronic Systems have both inputs and outputs with the output or outputs being produced by processing the inputs. Also, the input signal(s) may cause the process to change or may itself cause the operation of the system to change. Therefore the input(s) to a system is the “cause” of the change, while the resulting action that occurs on the systems output due to this cause being present is called the “effect”, with the effect being a consequence of the cause.

In other words, an electronic system can be classed as “causal” in nature as there is a direct relationship between its input and its output. Electronic systems analysis and process control theory are generally based upon this Cause and Effect analysis.

discrete time signalSo for example in an audio system, a microphone (input device) causes sound waves to be converted into electrical signals for the amplifier to amplify (a process), and a loudspeaker (output device) produces sound waves as an effect of being driven by the amplifiers electrical signals.

But an electronic system need not be a simple or single operation. It can also be an interconnection of several sub-systems all working together within the same overall system.

Our audio system could for example, involve the connection of a CD player, or a DVD player, an MP3 player, or a radio receiver all being multiple inputs to the same amplifier which in turn drives one or more sets of stereo or home theatre type surround loudspeakers.

But an electronic system can not just be a collection of inputs and outputs, it must “do something”, even if it is just to monitor a switch or to turn “ON” a light. We know that sensors are input devices that detect or turn real world measurements into electronic signals which can then be processed. These electrical signals can be in the form of either voltages or currents within a circuit. The opposite or output device is called an actuator, that converts the processed signal into some operation or action, usually in the form of mechanical movement.

Types of Electronic System

Electronic systems operate on either continuous-time (CT) signals or discrete-time (DT) signals. A continuous-time system is one in which the input signals are defined along a continuum of time, such as an analogue signal which “continues” over time producing a continuous-time signal.

But a continuous-time signal can also vary in magnitude or be periodic in nature with a time period T. As a result, continuous-time electronic systems tend to be purely analogue systems producing a linear operation with both their input and output signals referenced over a set period of time.

series block diagramFor example, the temperature of a room can be classed as a continuous time signal which can be measured between two values or set points, for example from cold to hot or from Monday to Friday. We can represent a continuous-time signal by using the independent variable for time t, and where x(t) represents the input signal and y(t) represents the output signal over a period of time t.

Generally, most of the signals present in the physical world which we can use tend to be continuous-time signals. For example, voltage, current, temperature, pressure, velocity, etc.

On the other hand, a discrete-time system is one in which the input signals are not continuous but a sequence or a series of signal values defined in “discrete” points of time. This results in a discrete-time output generally represented as a sequence of values or numbers.

Generally a discrete signal is specified only at discrete intervals, values or equally spaced points in time. So for example, the temperature of a room measured at 1pm, at 2pm, at 3pm and again at 4pm without regards for the actual room temperature in between these points at say, 1:30pm or at 2:45pm.

However, a continuous-time signal, x(t) can be represented as a discrete set of signals only at discrete intervals or “moments in time”. Discrete signals are not measured versus time, but instead are plotted at discrete time intervals, where n is the sampling interval. As a result discrete-time signals are usually denoted as x(n) representing the input and y(n) representing the output.

Then we can represent the input and output signals of a system as x and y respectively with the signal, or signals themselves being represented by the variable, t, which usually represents time for a continuous system and the variable n, which represents an integer value for a discrete system as shown.

Interconnection of Systems

One of the practical aspects of electronic systems and block-diagram representation is that they can be combined together in either a series or parallel combinations to form much bigger systems. Many larger real systems are built using the interconnection of several sub-systems and by using block diagrams to represent each subsystem, we can build a graphical representation of the whole system being analysed.

When subsystems are combined to form a series circuit, the overall output at y(t) will be equivalent to the multiplication of the input signal x(t) as shown as the subsystems are
cascaded together.

Series Connected System

For a series connected continuous-time system, the output signal y(t) of the first subsystem, “A” becomes the input signal of the second subsystem, “B” whose output becomes the input of the third subsystem, “C” and so on through the series chain giving A x B x C, etc.

Then the original input signal is cascaded through a series connected system, so for two series connected subsystems, the equivalent single output will be equal to the multiplication of the systems, ie, y(t) = G1(s) x G2(s). Where G represents the transfer function of the subsystem.

Note that the term “Transfer Function” of a system refers to and is defined as being the mathematical relationship between the systems input and its output, or output/input and hence describes the behaviour of the system.

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