# ;control theory; مبادئ علم السيطرة ((نظرية))



## حسن هادي (30 أغسطس 2007)

الاخوة الاعزاء /تحية طيبة نقدم لكم موضوعا في علم السيطرة والتحكم وذلك بعد مواضيع التوربينات ومحطات القدرة الحرارية والنووية اذ اننا نلاحظ ان عملية التحكم تعتبر عمليةجوهرية وتدخل في تشعبات الاختصاصات الهندسية كون علم السيطرة يعد من المواضيع المشركة لمختلف الاقسام الهندسية كل ينظر له من زاويته الخاصة *هذا وتقبلوا تحياتي اخوكم حسن *
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## حسن هادي (30 أغسطس 2007)

For control theory in psychology and sociology, see control theory (sociology).
*Control theory* is an interdisciplinary branch of engineering and mathematics, that deals with the behavior of dynamical systems. The desired output of a system is called the _reference_. When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system.
الروابط فعالة مع التقدير*


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## حسن هادي (30 أغسطس 2007)

Overview
Control theory is

theory, that deals with the behavior of dynamical systems
interdiscipinary subfield of science with orgininated in engineering and mathematics, and evolved into social science like psychology and sociology
* An example*

Consider an automobile's cruise control, which is a device designed to maintain a constant vehicle speed. The output variable of the system is vehicle speed. The input variable is the engine's throttle position which influences engine torque output.
A simple way to implement cruise control is to lock the throttle position when the driver engages cruise control. However, on hilly terrain, the vehicle will slow down going uphill and accelerate going downhill. This type of controller is called an *open-loop controller* because there is no direct connection between the output of the system and its input.
In a *closed-loop control* system, a *feedback controller* monitors the vehicle's speed and adjusts the throttle as necessary to maintain the desired speed. This feedback compensates for disturbances to the system, such as changes in slope of the ground or wind speed.

*[History*

Although control systems of various types date back to antiquity, a more formal analysis of the field began with a dynamics analysis of the centrifugal governor, conducted by the physicist James Clerk Maxwell in 1868 entitled _On Governors_[1]. This described and analyzed the phenomenon of "hunting," in which lags in the system can lead to overcompensation and unstable behavior. This generated a flurry of interest in the topic, during which Maxwell's classmate Edward John Routh generalized the results of Maxwell for the general class of linear systems. Independently, Adolf Hurwitz analyzed system stability using differential equations in 1877. This result is called the Routh-Hurwitz Criterion.
A notable application of dynamic control was in the area of manned flight. The Wright Brothers made their first successful test flights on December 17, 1903 and were distinguished by their ability to control their flights for substantial periods (more so than the ability to produce lift from an airfoil, which was known). Control of the airplane was necessary for safe flight.
By World War II, control theory was an important part of fire-control systems, guidance systems, and electronics. The Space Race also depended on accurate spacecraft control. However, control theory also saw an increasing use in fields such as economics and sociology.


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## حسن هادي (30 أغسطس 2007)

من خلال موسوعة الويكيبيديا نقدم هذا الموضوع بروابطه واليكم الروابط ذات المواضيع الممتعة تاريخيا ً*
*********************************************************************************
People in systems and control
_Main article: People in systems and control_
A lot of active and historical figures made significant contribution to control theory, for example:

Richard Bellman (1920-1984), developed dynamic programming since the 1940s.
Harold S. Black (1898-1983), invented the negative feedback amplifier in the 1930s.
Alexander Lyapunov (1857-1918) in the 1890s marks the beginning of stability theory.
Harry Nyquist (1889-1976), developed the Nyquist stability criterion for feedback systems in the 1930s.
John R. Ragazzini (1912-1988) introduced digital control and the z-transform in the 1950s.
Norbert Wiener (1894-1964) coined the term Cybernetics in the 1940s.


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## حسن هادي (30 أغسطس 2007)

Classical control theory: the closed-loop controller
To avoid the problems of the open-loop controller, control theory introduces feedback. A *closed-loop controller* uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs (e.g. voltage applied to an electric motor) have an effect on the process outputs (e.g. velocity or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is used as input to the process, closing the loop.
Closed-loop controllers have the following advantages over open-loop controllers:

disturbance rejection (such as unmeasured friction in a motor)
guaranteed performance even with model uncertainties, when the model structure does not match perfectly the real process and the model parameters are not exact
unstable processes can be stabilized
reduced sensitivity to parameter variations
improved reference tracking performance
In some systems, closed-loop and open-loop control are used simultaneously. In such systems, the open-loop control is termed *feedforward* and serves to further improve reference tracking performance.
A common closed-loop controller architecture is the PID controller.
The output of the system _y(t)_ is fed back to the reference value _r(t)_, through a sensor measurement. The controller _C_ then takes the error _e_ (difference) between the reference and the output to change the inputs _u_ to the system under control _P_. This is shown in the figure. This kind of controller is a closed-loop controller or feedback controller.
This is called a single-input-single-output (_SISO_) control system; _MIMO_ (i.e. Multi-Input-Multi-Output) systems, with more than one input/output, are common. In such cases variables are represented through vectors instead of simple scalar values. For some distributed parameter systems the vectors may be infinite-dimensional (typically functions).






If we assume the controller _C_ and the plant _P_ are linear and time-invariant (i.e.: elements of their transfer function _C(s)_ and _P(s)_ do not depend on time), the systems above can be analysed using the Laplace transform on the variables. This gives the following relations:










Solving for _Y_(_s_) in terms of _R_(_s_) gives:



The term



is referred to as the *transfer function* of the system. The numerator is the forward gain from _r_ to _y_, and the denominator is one plus the loop gain of the feedback loop. If



, i.e. it has a large norm with each value of _s_, then _Y(s)_ is approximately equal to _R(s)_. This means simply setting the reference controls the output.


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## حسن هادي (30 أغسطس 2007)

Topics in control theory

*Stability*

*Stability* (in control theory) often means that for any bounded input over any amount of time, the output will also be bounded. This is known as BIBO stability (see also Lyapunov stability). If a system is BIBO stable then the output cannot "blow up" (i.e., become infinite) if the input remains finite. Mathematically, this means that for a causal linear continuous-time system to be stable all of the poles of its transfer function must

lie in the closed left half of the complex plane if the Laplace transform is used (i.e. its real part is less than or equal to zero)
OR

lie on or inside the unit circle if the Z-transform is used (i.e. its modulus is less than or equal to one)
In the two cases, if respectively the pole has a real part strictly smaller than zero or a modulus strictly smaller than one, it is asymptotically stable: the variables of an asymptotically stable control system always decrease from their initial value and do not show permanent oscillations, which are instead present if a pole has a real part exactly equal to zero (or a modulus equal to one). If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable: in this case it has non-repeated poles along the vertical axis (i.e. their real and complex component is zero). Oscillations are present when poles with real part equal to zero have an imaginary part not equal to zero.
Differences between the two cases are not a contradiction. The Laplace transform is in Cartesian coordinates and the Z-transform is in circular coordinates, and it can be shown that

the negative-real part in the Laplace domain can map onto the interior of the unit circle
the positive-real part in the Laplace domain can map onto the exterior of the unit circle
If the system in question has an impulse response of
_x_[_n_] = 0.5_n__u_[_n_] and considering the Z-transform (see this example), it yields



which has a pole in _z_ = 0.5 (zero imaginary part). This system is BIBO (asymptotically) stable since the pole is _inside_ the unit circle.
However, if the impulse response was
_x_[_n_] = 1.5_n__u_[_n_] then the Z-transform is



which has a pole at _z_ = 1.5 and is not BIBO stable since the pole has a modulus strictly greater than one.
Numerous tools exist for the analysis of the poles of a system. These include graphical systems like the root locus , Bode plots or the Nyquist plots.


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## م/محمد لطفي (30 أغسطس 2007)

جزاك الله خيرا


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## حسن هادي (31 أغسطس 2007)

م/محمد لطفي قال:


> جزاك الله خيرا


 
بارك الله بك يا م/محمد وتقبل تحياتي


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## حسن هادي (31 أغسطس 2007)

Controllability and observability
Controllability and observability are main issues in the analysis of a system before deciding the best control strategy to be applied. Controllability is related to the possibility of forcing the system into a particular state by using an appropriate control signal. If a state is not controllable, then no signal will ever be able to stabilize the system. Observability instead is related to the possibility of "observing", through output measurements, the state of a system. If a state is not observable, the controller will never be able to correct the closed-loop behaviour if such a state is not desirable.
From a geometrical point of view, looking at the states of each variable of the system to be controlled, every "bad" state of these variables must be controllable and observable to ensure a good behaviour in the closed-loop system. That is, if one of the eigenvalues of the system is not both controllable and observable, this part of the dynamics will remain untouched in the closed-loop system. If such an eigenvalue is not stable, the dynamics of this eigenvalue will be present in the closed-loop system which therefore will be unstable. Unobservable poles are not present in the transfer function realization of a state-space representation, which is why sometimes the latter is preferred in dynamical systems analysis.
Solutions to problems of uncontrollable or unobservable system include adding actuators and sensors.

*[edit] Control specifications*

Several different control strategies have been devised in the past years. These vary from extremely general ones (PID controller), to others devoted to very particular classes of systems (especially robotics or aircraft cruise control).
A control problem can have several specifications. Stability, of course, is always present: the controller must ensure that the closed-loop system is stable, regardless of the open-loop stability. A poor choice of controller can even worsen the stability of the open-loop system, which must normally be avoided. Sometimes it would be desired to obtain particular dynamics in the closed loop: i.e. that the poles have



, where



is a fixed value strictly greater than zero, instead of simply ask that _R__e_[λ] < 0.
Another typical specification is the rejection of a step disturbance; including an integrator in the open-loop chain (i.e. directly before the system under control) easily achieves this. Other classes of disturbances need different types of sub-systems to be included.
Other "classical" control theory specifications regard the time-response of the closed-loop system: these include the *rise time* (the time needed by the control system to reach the desired value after a perturbation), *peak overshoot* (the highest value reached by the response before reaching the desired value) and others (settling time, quarter-decay). Frequency domain specifications are usually related to robustness (see after).
Modern performance assessments use some variation of integrated tracking error (IAE,ISA,CQI).


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## حسن هادي (31 أغسطس 2007)

*[ Model identification and robustness*

_Main article: System identification_
A control system must always have some *robustness* property. A robust controller is such that its properties do not change much if applied to a system slightly different from the mathematical one used for its synthesis. This specification is important: no real physical system truly behaves like the series of differential equations used to represent it mathematically. Typically a simpler mathematical model is chosen in order to simplify calculations, otherwise the true system dynamics can be so complicated that a complete model is impossible.

*[edit] System identification*

The process of determining the equations that govern the model's dynamics is called system identification. This can be done off-line: for example, executing a series of measures from which to calculate an approximated mathematical model, typically its transfer function or matrix. Such identification from the output, however, cannot take account of unobservable dynamics. Sometimes the model is built directly starting from known physical equations: for example, in the case of a mass-spring-damper system we know that



. Even assuming that a "complete" model is used in designing the controller, all the parameters included in these equations (called "nominal parameters") are never known with absolute precision; the control system will have to behave correctly even when connected to physical system with true parameter values away from nominal.
Some advanced control techniques include an "on-line" identification process (see later). The parameters of the model are calculated ("identified") while the controller itself is running: in this way, if a drastic variation of the parameters ensues (for example, if the robot's arm releases a weight), the controller will adjust itself consequently in order to ensure the correct performance.

*[edit] Analysis*

Analysis of the robustness of a SISO control system can be performed in the frequency domain, considering the system's transfer function and using Nyquist and Bode diagrams. Topics include *phase margin* and *amplitude margin*. For MIMO and, in general, more complicated control systems one must consider the theoretical results devised for each control technique (see next section): i.e., if particular robustness qualities are needed, the engineer must shift his attention to a control technique including them in its properties.

*[edit] Constraints*

A particular robustness issue is the requirement for a control system to perform properly in the presence of input and state constraints. In the physical world every signal is limited. It could happen that a controller will send control signals that cannot be followed by the physical system: for example, trying to rotate a valve at excessive speed. This can produce undesired behavior of the closed-loop system, or even break actuators or other subsystems. Specific control techniques are available to solve the problem: model predictive control (see later), and anti-wind up systems. The latter consists of an additional control block that ensures that the control signal never exceeds a given threshold.

*[edit] Main control strategies*

Every control system must guarantee first the stability of the closed-loop behavior. For linear systems, this can be obtained by directly placing the poles. Non-linear control systems use specific theories (normally based on Aleksandr Lyapunov's Theory) to ensure stability without regard to the inner dynamics of the system. The possibility to fulfill different specifications varies from the model considered and the control strategy chosen. Here a summary list of the main control techniques is shown:

*[edit] PID controllers*

_Main article: PID controller_
The *PID controller* is probably the most-used feedback control design, being the simplest one. "PID" means Proportional-Integral-Derivative, referring to the three terms operating on the error signal to produce a control signal. If _u(t)_ is the control signal sent to the system, _y(t)_ is the measured output and _r(t)_ is the desired output, and tracking error _e_(_t_) = _r_(_t_) − _y_(_t_), a PID controller has the general form



The desired closed loop dynamics is obtained by adjusting the three parameters _K__P_, _K__I_ and _K__D_, often iteratively by "tuning" and without specific knowledge of a plant model. Stability can often be ensured using only the proportional term. The integral term permits the rejection of a step disturbance (often a striking specification in process control). The derivative term is used to provide damping or shaping of the response. PID controllers are the most well established class of control systems: however, they cannot be used in several more complicated cases, especially if MIMO systems are considered.

*[edit] Direct pole placement*

_Main article: State space (controls)_
For MIMO systems, pole placement can be performed mathematically using a State space representation of the open-loop system and calculating a feedback matrix assigning poles in the desired positions. In complicated systems this can require computer-assisted calculation capabilities, and cannot always ensure robustness. Furthermore, all system states are not in general measured and so observers must be included and incorporated in pole placement design.

*[edit] Optimal control*

_Main article: Optimal control_
Optimal control is a particular control technique in which the control signal optimizes a certain "cost index": for example, in the case of a satellite, the jet thrusts needed to bring it to desired trajectory that consume the least amount of fuel. Two optimal control design methods have been widely used in industrial applications, as it has been shown they can guarantee closed-loop stability. These are Model Predictive Control (*MPC*) and Linear-Quadratic-Gaussian control (*LQG*). The first can more explicitly take into account constraints on the signals in the system, which is an important feature in many industrial processes. However, the "optimal control" structure in MPC is only a means to achieve such a result, as it does not optimize a true performance index of the closed-loop control system. Together with PID controllers, MPC systems are the most widely used control technique in process control.

*[edit] Adaptive control*

_Main article: Adaptive control_
Adaptive control uses on-line identification of the process parameters, or modification of controller gains, thereby obtaining strong robustness properties. Adaptive controls were applied for the first time in the aerospace industry in the 1950s, and have found particular success in that field.

*[edit] Intelligent control*

_Main article: Intelligent control_
Intelligent control use various AI computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, evolutionary computation and genetic algorithms to control a dynamic system

*[edit] Non-linear control systems*

_Main article: Non-linear control_
Processes in industries like robotics and the aerospace industry typically have strong non-linear dynamics. In control theory it is sometimes possible to linearize such classes of systems and apply linear techniques: but in many cases it can be necessary to devise from scratch theories permitting control of non-linear systems. These normally take advantage of results based on Lyapunov's theory. Differential geometry has been widely used as a tool for generalizing well-known linear control concepts to the non-linear case, as well as showing the subtleties that make it a more challenging problem.


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## حسن هادي (31 أغسطس 2007)

*Controller (control theory)*

*From Wikipedia, the free encyclopedia*


Jump to: navigation, search
In control theory, a *controller* is a device which monitors and affects the operational conditions of a given dynamic system. The operational conditions are typically referred to as output variables of the system which can be affected by adjusting certain input variables. For example, the heating system of a house can be equipped with a thermostat (controller) for sensing air temperature (output variable) which can turn on or off a furnace or heater when the air temperature becomes too low or too high.
In this example, the thermostat is the controller and directs the activities of the heater. The heater is the processor that warms the air inside the house to the desired temperature (setpoint). The air temperature reading inside the house is the feedback. And finally, the house is the environment in which the heating system operates.
The notion of *controllers* can be extended to more complex systems. In the natural world, individual organisms also appear to be equipped with *controllers* that assure the homeostasis necessary for survival of each individual. Both human-made and natural systems exhibit collective behaviors amongst individuals in which the *controllers* seek some form of equilibrium.

*[edit] Types of control*

In control theory there are two basic types of control. These are feedforward and feedback. The input to a feedback controller is the same as what it is trying to control - the controlled variable is "fed back" into the controller. The thermostat of a house is an example of a feedback controller. This controller relies on measuring the controlled variable, in this case the temperature of the house, and then adjusting the output, whether or not the heater is on. However, feedback control usually results in intermediate periods where the controlled variable is not at the desired setpoint. With the thermostat example, if the door of the house were opened on a cold day, the house would cool down. After it fell below the desired temperature (setpoint), the heater would kick on, but there would be a period when the house was colder than desired.
Feedforward control can avoid the slowness of feedback control. With feedforward control, the disturbances are measured and accounted for before they have time to affect the system. In the house example, a feedforward system may measure the fact that the door is opened and automatically turn on the heater before the house can get too cold. The difficulty with feedforward control is that the effect of the disturbances on the system must be perfectly predicted, and there must not be any surprise disturbances. For instance, if a window were opened that was not being measured, the feedforward-controlled thermostat might still let the house cool down.
To achieve the benefits of feedback control (controlling unknown disturbances and not having to know exactly how a system will respond to disturbances) _and_ the benefits of feedforward control (responding to disturbances before they can affect the system), there are combinations of feedback and feedforward that can be used.
Some examples of where feedback and feedforward control can be used together are dead-time compensation, and inverse response compensation. Dead-time compensation is used to control devices that take a long time to show any change to a change in input, for example, change in composition of flow through a long pipe. A dead-time compensation control uses an element (also called a Smith predictor) to predict how changes made now by the controller will affect the controlled variable in the future. The controlled variable is also measured and used in feedback control. Inverse response compensation involves controlling systems where a change at first affects the measured variable one way but later affects it in the opposite way. An example would be eating candy. At first it will give you lots of energy, but later you will be very tired. As can be imagined, it is difficult to control this system with feedback alone, therefore a predictive feedforward element is necessary to predict the reverse effect that a change will have in the future.

*[edit] Types of controllers*

Most control systems in the past were implemented using mechanical systems or solid state electronics. Pneumatics were often utilized to transmit information and control using pressure. However, most modern control systems in industrial settings now rely on computers for the controller. Obviously it is much easier to implement complex control algorithms on a computer than using a mechanical system.
For feedback controllers there are a few simple types. The most simple is like the thermostat that just turns the heat on if the temperature falls below a certain value and off it exceeds a certain value (on-off control).
Another simple type of controller is a proportional controller. With this type of controller, the controller output (control action) is proportional to the error in the measured variable.
The error is defined as the difference between the current value (measured) and the desired value (setpoint). If the error is large, then the control action is large. Mathematically:
_c_(_t_) = _K__c_ * _e_(_t_) + _c__s_
In the above equation, _e_(_t_) represents the error, _K__c_ represents the controller's gain, and _c__s_ represents the steady state control action necessary to maintain the variable at the steady state when there is no error.
The gain _K__c_ will be positive if an increase in the input variable requires an increase in the output variable (direct-acting control), and it will be negative if an increase in the input variable requires a decrease in the output variable (reverse-acting control). A typical example of a direct-acting system is controlling flow of cooling water - if the temperature increases, the flow must be increased to maintain the desired temperature. Conversely, a typical example of a reverse-acting system is controlling flow of steam for heating - if the temperature increases, the flow must be decreased to maintain the desired temperature.
Although proportional control is simple to understand, it has drawbacks. The largest problem is that for most systems it will never entirely remove error. This is because when error is 0 the controller only provides the steady state control action so the system will settle back to the original steady state (which is probably not the new set point that we want the system to be at). To get the system to operate near the new steady state, the controller gain, Kc, must be very large so the controller will produce the required output when only a very small error is present. Having large gains can lead to system instability or can require physical impossibilities like infinitely large valves.
Alternates to proportional control are proportional-integral (PI) control and proportional-integral-derivative (PID) control. PID control is commonly used to implement closed-loop control.
Open-loop control can be used in systems sufficiently well-characterized as to predict what outputs will necessarily achieve the desired states. For example, the rotational velocity of an electric motor may be well enough characterized for the supplied voltage to make feedback unnecessary.
Drawbacks of open-loop control is that it requires perfect knowledge of the system (i.e. one knows exactly what inputs to give in order to get the desired output), and it assumes there are no disturbances to the system.


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## حسن هادي (31 أغسطس 2007)

مبدأ التغذية الرجوعية ((العكسية ))للاشارة /

For the superhero, see Feedback (Dark Horse Comics).
For the list of albums named "Feedback", see Feedback (album).
*Feedback* is the signal that is looped back to control a system within itself. This loop is called the feedback loop. A control system usually has input and output to the system; when the output of the system is fed back into the system as part of its input, it is called the "feedback."
In cybernetics and control theory, *feedback* is a process whereby some proportion of the output signal of a system is passed (fed back) to the input. This is often used to control the dynamic behavior of the system. Examples of feedback can be found in most complex systems, such as engineering, architecture, economics, and biology
*******************
Types of feedback


 


Figure 1: Ideal feedback model. The feedback is negative if B < 0


_Main articles: Negative feedback, positive feedback, and bipolar feedback_
Feedback may be negative, which tends to reduce output (but in amplifiers, stabilizes and linearizes operation), positive, which tends to increase output, or bipolar, which can either increase or decrease output. Systems which include feedback are prone to _hunting_, which is oscillation of output resulting from improperly tuned inputs of first positive then negative feedback. Audio feedback typifies this form of oscillation.

*[edit] Electro mechanics*


Tactile feedback.
*[edit] In electronic engineering*

The processing and control of feedback is engineered into many electronic devices and may also be embedded in other technologies.
The most common general-purpose controller is a proportional-integral-derivative (PID) controller. Each term of the PID controller copes with time. The proportional term handles the present state of the system, the integral term handles its past, and the derivative or slope term tries to predict and handle the future.
If the signal is inverted on its way round the control loop, the system is said to have _negative feedback_; otherwise, the feedback is said to be _positive_. Negative feedback is often deliberately introduced to increase the stability and accuracy of a system, as in the feedback amplifier invented by Harold Stephen Black. This scheme can fail if the input changes faster than the system can respond to it. When this happens, the negative feedback signal begins to act as positive feedback, causing the output to oscillate or _hunt_. Positive feedback is usually an unwanted consequence of system behaviour.
With mechanical devices, hunting can be severe enough to destroy the device.
Harry Nyquist was an electrical engineer who contributed the Nyquist plot for determining the stability of feedback systems.

*[edit] In mechanical engineering*

In ancient times, the float valve was used to regulate the flow of water in Greek and Roman water clocks; similar float valves are used to regulate fuel in a carburetor and also used to regulate tank water level in the flush toilet.
The windmill was enhanced in 1745 by blacksmith Edmund Lee who added a fantail to keep the face of the windmill pointing into the wind. In 1787 Thomas Mead regulated the speed of rotation of a windmill by using a centrifugal pendulum to adjust the distance between the bedstone and the runner stone (i.e. to adjust the load).
The use of the centrifugal governor by James Watt in 1788 to regulate the speed of his steam engine was one factor leading to the Industrial Revolution. Steam engines also use float valves and pressure release valves as mechanical regulation devices. A mathematical analysis of Watt's governor was done by James Clerk Maxwell in 1868.
The Great Eastern was one of the largest steamships of its time and employed a steam powered rudder with feedback mechanism designed in 1866 by J.McFarlane Gray. Joseph Farcot coined the word servo in 1873 to describe steam powered steering systems. Hydraulic servos were later used to position guns. Elmer Ambrose Sperry of the Sperry Corporation designed the first autopilot in 1912. Nicolas Minorsky published a theoretical analysis of automatic ship steering in 1922 and described the PID controller.
Internal combustion engines of the late 20th century employed mechanical feedback mechanisms such as vacuum advance but mechanical feedback was replaced by electronic engine management systems once small, robust and powerful single-chip microcontrollers became affordable.

*[edit] In economics and finance*

A system prone to hunting (oscillating) is the stock market, which has both positive and negative feedback mechanisms. This is due to cognitive and emotional factors belonging to the field of behavioral finance. For example,

When stocks are rising (a bull market), the belief that further rises are probable gives investors an incentive to buy (positive feedback, see also stock market bubble); but the increased price of the shares, and the knowledge that there must be a peak after which the market will fall, ends up deterring buyers (negative feedback).
Once the market begins to fall regularly (a bear market), some investors may expect further losing days and refrain from buying (positive feedback), but others may buy because stocks become more and more of a bargain (negative feedback).
George Soros used the word "reflexism" to describe feedback in the financial markets and developed an investment theory based on this principle.
The conventional economic equilibrium model of supply and demand supports only ideal linear negative feedback and was heavily criticized by Paul Ormerod in his book "The Death of Economics" which in turn was criticized by traditional economists. This book was part of a change of perspective as economists started to recognise that Chaos Theory applied to nonlinear feedback systems including financial markets.

*[edit] In nature*

Bipolar feedback is present in many natural and human systems. Feedback is usually bipolar—that is, positive and negative—in natural environments, which, in their diversity, furnish synergic and antagonistic responses to the output of any system.
In biological systems such as organisms, ecosystems, or the biosphere, most parameters must stay under control within a narrow range around a certain optimal level under certain environmental conditions. The deviation of the optimal value of the controlled parameter can result from the changes in internal and external environments. A change of some of the environmental conditions may also require change of that range to change for the system to function. The value of the parameter to maintain is recorded by a reception system and conveyed to a regulation module via an information channel.
Biological systems contain many types of regulatory circuits, both positive and negative. As in other contexts, _Positive_ and _negative_ don't imply consequences of the feedback have good or bad final effect. A negative feedback loop is one that tends to slow down a process, while the positive feedback loop tends to accelerate it.
Feedback and regulation are self related. The negative feedback helps to maintain stability in a system in spite of external changes. It is related to homeostasis. Positive feedback amplifies possibilities of divergences (evolution, change of goals); it is the condition to change, evolution, growth; it gives the system the ability to access new points of equilibrium.
For example, in an organism, most positive feedback provide for fast autoexcitation of elements of endocrine and nervous systems (in particular, in stress responses conditions) and play a key role in regulation of morphogenesis, growth, and development of organs, all processes which are in essence a rapid escape from the initial state. Homeostasis is especially visible in the nervous and endocrine systems when considered at organism level.
The mirror neurons are part of a social feedback system, when an observed action is ´mirrored´ by the brain - like a self performed action.
Feedback is also central to the operations of genes and gene regulatory networks. repressor (see Lac repressor) and activator proteins are used to create genetic operons, which were identified by Francois Jacob and Jacques Monod in 1961 as _feedback loops_.
Any self-regulating natural process involves feedback and is prone to hunting. A well known example in ecology is the oscillation of the population of snowshoe hares due to predation from lynxes.
In zymology, feedback serves as regulation of activity of an enzyme by its direct product(s) or downstream metabolite(s) in the metabolic pathway (see Allosteric regulation).
There is an ice-albedo positive feedback loop whereby melting snow exposes more dark ground (of lower albedo), which in turn absorbs heat and causes more snow to melt. This is part of the evidence of the danger of global warming.
Compare with: feed-forward.


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## حسن هادي (31 أغسطس 2007)

تمنياتنا ان نكون قد اوصلنا افكار الموضوع بتسلسل مشاركاته الى المستوى المطلوب /وبامكانكم اخوتي متابعة الروابط المتداخلة مع تحياتي :6:


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## شكرى محمد نورى (31 أغسطس 2007)

الأخ حسن هادي .

جزيل الشكر والتقدير وماقصرت يا مبدع .

اعانك الله على المجهود الذي بذلته ويسر خطاك .

البغدادي .


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## حسن هادي (31 أغسطس 2007)

شكرى محمد نورى قال:


> الأخ حسن هادي .
> 
> جزيل الشكر والتقدير وماقصرت يا مبدع .
> 
> ...


 
حياك الله يا مشرفنا العزيز وتقبل منا كل المودة والتقدير *


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## عراااااقي (31 أغسطس 2007)

رااائع جدااا


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## حسن هادي (3 سبتمبر 2007)

تحياتنا لكل الاخوة الاعضاء مع التقدير:6:


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## حبيب جاسم (3 نوفمبر 2007)

Thanks for the nice information,please if somebody help me to get the following book (Schaum Series ,theory & problem feed back & control system.


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## fomari6 (29 ديسمبر 2007)

Dear Mr. Hasan
Thank you for these satisfying explaination .I am looking for books in control desigin system by using simulink,for mechanical application .

if you have links ,PDFs,or any useful media kindly send it me .


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## محمد القاضى1 (29 ديسمبر 2007)

طب انا ان شاء الله فى اولى ميكانيكا عايز اعرف اذا كنت ها درس الحاجات الجميله دى ول لا


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## مهندس احمد غازى (14 مارس 2008)

شكراااااااااااااااااااااااااااااااااااااااااااا


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## رائد احمد (12 مايو 2008)

شكرا جزيلا استاذ حسن


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