Introduction:

Historical Review:

Automatic control systems were first developed over two thousand years ago. The first feedback control device on record is thought to be the ancient Ktesibios‘s water clock in Alexandria, Egypt around the third century B.C. It kept time by regulating the water level in a vessel and, therefore, the water flow from that vessel. This certainly was a successful device as water clocks of similar design were still being made in Baghdad when the Mongols captured the city in 1258 A.D. A variety of automatic devices have been used over the centuries to accomplish useful tasks or simply to just entertain. The latter includes the automata, popular in Europe in the 17th and 18th centuries, featuring dancing figures that would repeat the same task over and over again; these automata are examples of open-loop control. Milestones among feedback, or “closed-loop” automatic control devices, include the temperature regulator of a furnace attributed to Drebbel, circa 1620, and the centrifugal flyball governor used for regulating the speed of steam engines by James Watt in 1788.

In his 1868 paper “On Governors”, J. C. Maxwell (who discovered the Maxwell electromagnetic field equations) was able to explain instabilities exhibited by the flyball governor using differential equations to describe the control system. This demonstrated the importance and usefulness of mathematical models and methods in understanding complex phenomena, and signaled the beginning of mathematical control and systems theory. Elements of control theory had appeared earlier but not as dramatically and convincingly as in Maxwell’s analysis.

Control theory made significant strides in the next 100 years. New mathematical techniques made it possible to control, more accurately, significantly more complex dynamical systems than the original flyball governor. These techniques include developments in optimal control in the 1950s and 1960s, followed by progress in stochastic, robust, adaptive and optimal control methods in the 1970s and 1980s. Applications of control methodology have helped make possible space travel and communication satellites, safer and more efficient aircraft, cleaner auto engines, cleaner and more efficient chemical processes, to mention but a few.

Before it emerged as a unique discipline, control engineering was practiced as a part of mechanical engineering and control theory was studied as a part of electrical engineering, since electrical circuits can often be easily described using control theory techniques. In the very first control relationships, a current output was represented with a voltage control input. However, not having proper technology to implement electrical control systems, designers left with the option of less efficient and slow responding mechanical systems. A very effective mechanical controller that is still widely used in some hydro plants is the governor. Later on, previous to modern power electronics, process control systems for industrial applications were devised by mechanical engineers using pneumatic and hydraulic control devices, many of which are still in use today.

Pneumatics Systems:

Pneumatics is a section of technology that deals with the study and application of pressurized gas to produce mechanical motion.

Pneumatic systems, which are used extensively in industry, and factories, are commonly plumbed with compressed air or compressed inert gases. This is because a centrally located and electrically powered compressor, that powers cylinders and other pneumatic devices through solenoid valves, can often provide motive power in a cheaper, safer, more flexible, and more reliable way than a large number of electric motors and actuators.

Pneumatics also has applications in dentistry, construction, mining, and other areas.

Advantages of pneumatics

Simplicity of design and control—Machines are easily designed using standard cylinders and other components, and operate via simple on-off control.

· Reliability—Pneumatic systems generally have long operating lives and require little maintenance. Because gas is compressible, Equipment is less subject to shock damage. Gas absorbs excessive force, whereas fluid in hydraulics directly transfers force. Compressed gas can be stored, so machines still run for a while if electrical power is lost.

· Safety—there is a very low chance of fire compared to hydraulic oil. Machines are usually overloading safe.

Hydraulic Systems:

A hydraulic drive system is a drive or transmission system that uses pressurized hydraulic fluid to drive hydraulic machinery. The term hydrostatic refers to the transfer of energy from flow and pressure, not from the kinetic energy of the flow.

A hydraulic drive system consists of three parts: The generator (e.g. a hydraulic pump), driven by an electric motor, a combustion engine or a windmill; valves, filters, piping etc. (to guide and control the system); the motor (e.g. a hydraulic motor or hydraulic cylinder) to drive the machinery.

Principle of a hydraulic drive:

Pascal’s law is the basis of hydraulic drive systems. As the pressure in the system is the same, the force that the fluid gives to the surroundings is therefore equal to pressure × area. In such a way, a small piston feels a small force and a large piston feels a large force.

The same principle applies for a hydraulic pump with a small swept volume that asks for a small torque, combined with a hydraulic motor with a large swept volume that gives a large torque. In such a way a transmission with a certain ratio can be built.

Most hydraulic drive systems make use of hydraulic cylinders. Here the same principle is used — a small torque can be transmitted into a large force.

By throttling the fluid between the generator part and the motor part, or by using hydraulic pumps and/or motors with adjustable swept volume, the ratio of the transmission can be changed easily. In case throttling is used, the efficiency of the transmission is limited. In case adjustable pumps and motors are used, the efficiency, however, is very large. In fact, up to around 1980, a hydraulic drive system had hardly any competition from other adjustable drive systems.

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Fig: Principle of hydraulic drive system

Nowadays, electric drive systems using electric servo-motors can be controlled in an excellent way and can easily compete with rotating hydraulic drive systems. Hydraulic cylinders are, in fact, without competition for linear forces. For these cylinders, hydraulic systems will remain of interest and if such a system is available, it is easy and logical to use this system for the rotating drives of the cooling systems, also.

Advantages of hydraulics:

· Liquid (as a gas is also a ‘fluid’) does not absorb any of the supplied energy.

· Capable of moving much higher loads and providing much higher forces due to the incompressibility.

· The hydraulic working fluid is basically incompressible, leading to a minimum of spring action. When hydraulic fluid flow is stopped, the slightest motion of the load releases the pressure on the load; there is no need to “bleed off” pressurized air to release the pressure on the load.

Thermal Systems:

In spacecraft design, the Thermal Control System (TCS) has the function to keep all the spacecraft parts within acceptable temperature ranges during all mission phases, withstanding the external environment, which can vary in a wide range as the spacecraft is exposed to deep space or to solar or planetary flux, and rejecting to space the internal heat dissipation of the spacecraft itself.

The thermal control is essential to guarantee the optimum performance and success of the mission, because if a component encounters a temperature which is too high or to low, it could be damaged or its performance could be severely affected. Thermal control is also necessary to keep specific components (such as optical sensors, atomic clocks, etc.) within a specified temperature stability requirement, to ensure that they perform as efficiently as possible.

The thermal control subsystem can be composed both of passive and of active items and works in two ways:

Protects the equipment from too hot temperatures, either by thermal insulation from external heat fluxes (such as the Sun or the planetary infrared and albedo flux), or by proper heat removal from internal sources (such as the heat dissipated by the internal electronic equipment).

Protects the equipment from too cold temperatures, by thermal insulation from external sinks, by enhanced heat absorption from external sources, or by heat release from internal sources.

Passive Thermal Control System (PTCS) items include:

· multi-layer insulation (MLI), which protects the spacecraft from excessive solar or planetary heating as well as from excessive cooling when exposed to deep space

· coatings that change the thermo-optical properties of external surfaces

· thermal fillers to improve the thermal coupling at selected interfaces (for instance on the thermal path between an electronic unit and its radiator)

· thermal washers to reduce the thermal coupling at selected interfaces

· thermal doublers to spread on the radiator surface the heat dissipated by equipment

· mirrors (secondary surface mirrors, SSM, or optical solar reflectors, OSR) to improve the heat rejection capability of the external radiators and at the same time to reduce the absorption of external solar fluxes

· radioisotope heater units (RHU), used by some planetary and exploratory missions to produce and store electrical power for TCS purposes

Active Thermal Control System (ATCS) items include:

· thermostatically controlled resistive electric heaters to keep the equipment temperature above its lower limit during the mission cold phases

· fluid loops to transfer the heat dissipated by equipment to the radiators. They can be:

· single-phase loops, controlled by a pump

· two-phase loops, composed of heat pipes (HP), loop heat pipes (LHP) or capillary pumped loops (CPL)

· louvers (which change the heat rejection capability to space as a function of temperature)

· thermoelectric coolers

Systems in Series:

When two or more systems are in series, they can be combined into a single representative system, with a transfer function that is the product of the individual systems.

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If we have two systems, f(t) and g(t), we can put them in series with one another so that the output of system f(t) is the input to system g(t). Now, we can analyze them depending on whether we are using our classical or modern methods.

If we define the output of the first system as h(t), we can define h(t) as:

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Now, we can define the system output y(t) in terms of h(t) as:

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We can expand h(t):

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But, since convolution is associative, we can re-write this as:

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Our system can be simplified therefore as such:

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Series Transfer Functions:

If two or more systems are in series with one another, the total transfer function of the series is the product of all the individual system transfer functions.

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In the time domain we know that:

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But, in the frequency domain we know that convolution becomes multiplication, so we can re-write this as:

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We can represent our system in the frequency domain as:

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Systems in Parallel:

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Blocks may not be placed in parallel without the use of an added. Blocks connected by an adder as shown above have a total transfer function of:

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Since the Laplace transform is linear, we can easily transfer this to the time domain by converting the multiplication to convolution:

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Analogous Mechanical and Electrical Components:

It is possible to make electrical and mechanical systems using analogs.  An analogous electrical and mechanical system will have differential equations of the same form.  There are two analogs that are used to go between electrical and mechanical systems.  The analogous quantities are given below.

Analogous Quantity:

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To see the analogies more clearly, examine the following table that shows the constitutive relationships for the various analogous quantities.  The entries for the mechanical analogs are formed by substituting the analogous quantities into the equations for the electrical elements.  For example the electrical version of Ohm’s law is e=iR.  The Mechanical I analog stipulates that e is replaced by v, i by f and R by 1/B, which yields v=f/B.

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