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Eng: Mohammed Hussein1Republic of YemenTHAMAR UNIVERSITYFaculty of Computer Science&Information SystemLecturer, and Researcher atThamar UniversityBy Eng: Mohammed Hussein
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History18th Century James Watt’s centrifugal governor for the speed control of a steamengine.1920s Minorsky worked on automatic controllers for steering ships.1930s Nyquist developed a method for analyzing the stability of controlled systems1940s Frequency response methods made it possible to design linear closed-loopcontrol systems1950s Root-locus method due to Evans was fully developed1960s State space methods, optimal control, adaptive control and1980s Learning controls are begun to investigated and developed.Present and on-going research fields. Recent application of modern control theoryincludes such non-engineering systems such as biological, biomedical, economic andsocio-economic systems???????????????????????????????????2 Eng: Mohammed Hussein
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Introduction to Control SystemsObjectives We will describe a general process for designing a control system. A control system consisting of interconnected components is designed toachieve a desired purpose. To understand the purpose of a control system, it is useful to examineexamples of control systems through the course of history. These earlysystems incorporated many of the same ideas of feedback that are in usetoday. Modern control engineering practice includes the use of control designstrategies for improving manufacturing processes, the efficiency of energyuse, advanced automobile control, including rapid transit, among others. The iterative nature of design allows us to handle the design gap effectivelywhile accomplishing necessary tradeoffs in complexity, performance, and costin order to meet the design specifications.3 Eng: Mohammed Hussein
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Introduction A study of control involves developing a mathematical model for eachcomponent of the control system. A system is a set of self-contained processes under study. A control system by definition consists of the system to be controlled -called the plant - as well as the system which exercises control over theplant, called the controller.A controller could be either human, or anartificial device.The controller is said to supply a signal to the plant, calledthe input to the plant (or the control input), in order to produce a desiredresponse from the plant, called the output from the plant.When referringto an isolated system, the terms input and output are used to describe thesignal that goes into a system, and the signal that comes out of a system,respectively.4 Eng: Mohammed Hussein
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Example of control system If we select the car to be the plant, then the driver becomes thecontroller, who applies an input to the plant in the form of pressingthe gas pedal if it is desired to increase the speed of the car.Thespeed increase can then be the output from the plant.5 Eng: Mohammed Hussein
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IntroductionSystem – An interconnection of elements and devices for a desired purpose.Control System – An interconnection of components forming a systemconfiguration that will provide a desired response.Process – The device, plant, or systemunder control. The input and outputrelationship represents the cause-and-effect relationship of the process.6 Eng: Mohammed Hussein
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IntroductionMultivariable Control SystemOpen-Loop Control Systemsutilize a controller or controlactuator to obtain the desiredresponse.Closed-Loop ControlSystems utilizes feedback tocompare the actual output tothe desired output response.7 Eng: Mohammed Hussein
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Plan of study Information, picture and video for system Math Apply in Matlab Using simulink and output of system Response of the human ear (20 Hz to 20 KHz, sensitive to changesto signal levels rather than absolute values, for animal can be morethen human ).8 Eng: Mohammed Hussein
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A Simple Feedback Control Example9 Eng: Mohammed Hussein
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Hardware elements Series R Model series resistor Series C Model series capacitor Series L Model series inductor Library Ladders Filters sublibrary of the Physical library DescriptionThe Series R,C,L blocks models described in the blockdialog box, in terms of its frequency-dependent S-parameters.10 Eng: Mohammed Hussein
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Series RLC Series RLC Branch Implement series RLC branch Library Elements DescriptionThe Series RLC Branch block implements a single resistor,inductor, or capacitor, or a series combination of these. Use theBranch type parameter to select elements you want to includein the branch.11 Eng: Mohammed Hussein
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Signal A signal is a function that conveys information about the behavioror attributes of some phenomenon. The IEEETransactions on Signal Processing definition as: The term "signal" includes, among others, audio, video,speech, image, communication, geophysical, sonar, radar, medical andmusical signals. There are types of signal such as:1. Discrete-time and continuous-time signals2. Analog and digital signals12 Eng: Mohammed Hussein
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Types of Waveforms (periodic) Signals16 Eng: Mohammed Hussein
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Waveforms (Aperiodic) Signal17 Eng: Mohammed Hussein
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Types of Waveforms (Aperiodic) Signals18 Eng: Mohammed Hussein
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Why we use these signals? Based on these Signals we can create complex Signals. Sinusoid, unit step and exponential are used to approximatebasically more complex signals. They help us to predict and analysis as we take the signals as inputto the system such as filters, high pass, low pass, band pass, etcfilters and see what the output is.19 Eng: Mohammed Hussein
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How we can digitize audio signal? Basic steps:1. Conversion to electronic form using microphone (analog signal )2. Sampling the analog signal based on PAM or PCM.3. Quantization using Analog to Digital converter20 Eng: Mohammed Hussein
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Digitizing audio signalAnalog signalPAM signal (Sampling )Quantized signal21 Eng: Mohammed Hussein
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Pulse Code Modulation (PCM)Eng: Mohammed Hussein22
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Discrete-time and continuous-time signals A discrete-time signal is quantities that defined only on a discreteset of times.A simple source for a discrete time signal isthe sampling of a continuous signal, approximating the signal by asequence of its values at particular time instants. A continuous-time real signal is any real-valued (or complex-valued) function which is defined at every time t in an interval, mostcommonly an infinite interval.23 Eng: Mohammed Hussein
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Analog and digital signals The figure shows a digital signal that results from approximatingan analog signal by its values at particular time instants. Digitalsignals are discrete and quantized, while analog signals possessneither property.24 Eng: Mohammed Hussein
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Direct current (DC) Direct current (DC) is the unidirectional flow of electric charge. Directcurrent is produced by sources such as batteries, thermocouples, solarcells, and commutator-type electric machines of the dynamo type. The electric charge flows in a constant direction, distinguishing itfrom Alternating current (AC). A term formerly used for directcurrent was galvanic current.The abbreviationsAC and DC are often usedto mean simply alternating and direct, as when theymodify current or voltage.Direct Current (red curve). The horizontal axismeasures time; the vertical, current or voltage.Types of direct current.25 Eng: Mohammed Hussein
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DC signals It does not change over time.26 Eng: Mohammed Hussein
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Voltage or Current over time27 Eng: Mohammed Hussein
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Amplifier An amplifier is a device for increasing the power of a signal by use of anexternal energy source. In an electronic amplifier, the input "signal" is usually a voltage or acurrent. Amplifiers may be classified in a variety of ways depending on theirapplication, the frequency range they cover, or the active devices used.Ideally an amplifier increases the power of a signal without otherwisealtering it; practical amplifiers have finite distortion and noise which theyinvariably add to the signal. DC integrated amplifier DC(Direct Coupled) using no capacitors in the audio path. Integrated = Power amplifier and Pre-amplifier integrated together in onebox.31 Eng: Mohammed Hussein
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Sensor A device that converts signals from one type toanother (for example, a light signal in photonsto a DC signal in amperes) is a transducer, atransformer, or a sensor. However, none ofthese amplify power. A sensor (also called detector) is a converterthat measures a physical quantity and converts itinto a signal which can be read by an observeror by an (today mostly electronic) instrument.33 Eng: Mohammed Hussein
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Decibel (dB) The decibel (dB) is a logarithmicunit that indicates the ratio of a physicalquantity (usually power or intensity)relative to a specified or impliedreference level.A ratio in decibels isten times the logarithm to base 10 ofthe ratio of two power quantities. An example scale showing powerratios x and amplitude ratios √x and dBequivalents 10 log10 x.34 Eng: Mohammed Hussein
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Mechanical power Power in mechanical systems is the combination of forces andmovement. In particular, power is the product of a force on an objectand the objects velocity, or the product of a torque on a shaft and theshafts angular velocity. Mechanical power is also described as the time derivative of work.In mechanics, the work done by a force F on an object that travelsalong a curve C is given by the line integral: where x defines the path C and v is the velocity along this path.Thetime derivative of the equation for work yields the instantaneouspower,35 Eng: Mohammed Hussein
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Electrical power The instantaneous electrical power P delivered to a component isgiven by: where: P(t) is the instantaneous power, measuredin watts (joules per second). V(t) is the potential difference (or voltage drop) across thecomponent, measured in volts. I(t) is the current through it, measured in amperes If the component is a resistor with time-invariant voltage to current ratio, then:36 Eng: Mohammed Hussein
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Mechanical advantageThe law of the lever The lever is a movable bar that pivots on a fulcrum attached to orpositioned on or across a fixed point.The lever operates by applyingforces at different distances from the fulcrum, or pivot. As the lever pivots on the fulcrum, points farther from this pivot movefaster than points closer to the pivot.The power into and out of thelever must be the same, so forces applied to points farther from thepivot must be less than when applied to points closer in. If a and b are distances from the fulcrum to pointsA and B and ifforce FA applied toA is the input force and FB exerted at B is theoutput, the ratio of the velocities of pointsA and B is given by a/b, sothe ratio of the output force to the input force, or mechanicaladvantage, is given by37 Eng: Mohammed Hussein
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Mechanical advantage- Speed ratio The requirement for power input to an ideal mechanism to equal poweroutput provides a simple way to compute mechanical advantage fromthe input-output speed ratio of the system. Power is the product of force and velocity.The power input to a geartrain with a torqueTA applied to the drive pulley which rotates at anangular velocity of ωA is P=TA ωA. Because the power flow is constant, the torque TB and angularvelocity ωB of the output gear must satisfy the relation This shows that for an ideal mechanism the input-output speed ratioequals the mechanical advantage of the system.38 Eng: Mohammed Hussein
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Complex Numbers Where σ is the real part and ῳ is the imaginary part. The basic imaginary unit is equal tothe square root of -1.This is represented in MATLAB by either of two letters: i or j. The variable x is assigned a complex number with a real part of 2 and an imaginary part of3. Another way to create a complex number is using the complex function. A complex function G(s),a function of s,has a real part and an imaginary part This function combines two numeric inputs into a complex output, making the first inputreal and the second imaginary. You can separate a complex number into its real and imaginary parts using the real andimag functions.x = 2 + 3i;x = rand(3) * 5;y = rand(3) * -8;z = complex(x, y);zr = real(z);zi = imag(z);39 Eng: Mohammed Hussein
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I.C.=0. (initial condition =0).40 Eng: Mohammed Hussein
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Laplace transform method The Laplace transform method is an operational method that can be usedadvantageously for solving linear differential equations. By use of Laplace transforms,we can convert many common functions, such as sinusoidal functions, dampedsinusoidal functions, and exponential functions, into algebraic functions of a complexvariable s. Operations such as differentiation and integration can be replaced byalgebraic operations in the complex plane.Thus, a linear differential equation can betransformed into an algebraic equation in a complex variable s. If the algebraicequation in s is solved for the dependent variable, then the solution of the differentialequation (the inverse Laplace transform of the dependent variable) may be found byuse of a Laplace transform table or by use of the partial-fraction expansion technique. An advantage of the Laplace transform method is that it allows the use of graphicaltechniques for predicting the system performance without actually solving systemdifferential equations.Another advantage of the Laplace transform method is that,when we solve the differential equation, both the transient component and steady-state component of the solution can be obtained simultaneously.45 Eng: Mohammed Hussein
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Laplace Function F = F(s)=>L = L(t), If F = F(s),laplace returns a function of t.where t is the symbolic variable inF. L = laplace(F,t) makes L a functionof t instead of the default s. Here Lis returned as a scalar symbol. L = laplace(F,w,z) makes L afunction of z and F a function of winstead of the default variables sand t, respectively.46 Eng: Mohammed Hussein
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Inverse Laplace F = ilaplace(L is the inverseLaplace transform of the scalarsymbolic object L is applied to afunction of s and returns afunction of t. If L = L(t), ilaplace returns afunction of x. F = ilaplace(L,y) makes F afunction of y instead of thedefault t. F = ilaplace(L,y,x) takes F to bea function of x and L a functionof y instead of the defaultvariables t and s, respectively.47 Eng: Mohammed Hussein
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MATLAB SIMULINK To start the Simulink software, you must first start the MATLAB®technical computing environment.You can then start the Simulinksoftware in two ways: On the toolbar, click the Simulink icon. Enter the simulink command at the MATLAB prompt.48 Eng: Mohammed Hussein
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MATLAB SIMULINK components49 Eng: Mohammed Hussein
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Elements in simulink Simulink/Gain: Element-wise gain (y = K.*u) or matrixgain (y = K*u or y = u*K). Simulink/Constant: Output the constant specified by theConstant value parameter. If Constant value is a vector andInterpret vector parameters as 1-D is on, treat the constant value asa 1-D array. Otherwise, output a matrix with the same dimensions asthe constant value. Simulink/Transfer Fcn:The numerator coefficient canbe a vector or matrix expression.The denominator coefficient mustbe a vector.The output width equals the number of rows in thenumerator coefficient.You should specify the coefficients indescending order of powers of s.50 Eng: Mohammed Hussein
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Elements in simulink Simulink/SineWave: Output a sine wave:O(t) = Amp*Sin(Freq*t+Phase) + BiasSine type determines the computational technique used.The parameters in the two typesare related through:Samples per period = 2*pi / (Frequency * Sample time)Number of offset samples = Phase * Samples per period / (2*pi)Use the sample-based sine type if numerical problems due to running for large times (e.g.overflow in absolute time) occur. Simulink/Add:Add or subtract inputs. Specify one of the following:1) string containing + or - for each input port, | for spacer between ports (e.g. ++|-|++).2) scalar, >= 1, specifies the number of input ports to be summed.When there is only one input port, add or subtract elements over all dimensions orone specified dimension. The Scope block displays its input with respect to simulation time.51 Eng: Mohammed Hussein
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Getting Started with Simulinkالوعالج حرارة لقياس نظام52 Eng: Mohammed Hussein
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First Order Dynamic System The Mass block represents an ideal mechanical translational mass53 Eng: Mohammed Hussein
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First Order Dynamic System model54 Eng: Mohammed Hussein
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Second Order Dynamic System55 Eng: Mohammed Hussein
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Second Order Dynamic System model56 Eng: Mohammed Hussein
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PID and Second Order DynamicSystem model58 Eng: Mohammed Hussein
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Change in PID change the results of system59 Eng: Mohammed Hussein
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Auto control: Response time&Parameters60 Eng: Mohammed Hussein
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Open-loop bode plot of the system61 Eng: Mohammed Hussein
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System Results and error62 Eng: Mohammed Hussein
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K=1 Here is the Imaginary Axis. when you have your systemresult poles after theAxis,you would have unstablesystem. Also Step Response is stableStep Response is stable63 Eng: Mohammed Hussein
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Changing K controller value When we change k=6 which is near to Imaginary Axis, we haveunstable system that represented in Step Response figure.64 Eng: Mohammed Hussein
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(a) Automobilesteering controlsystem.(b) The driver usesthe differencebetween the actualand the desireddirection of travelto generate acontrolled adjustmentof the steering wheel.(c) Typical direction-of-travel response.Examples of Modern Control Systems71 Eng: Mohammed Hussein
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Examples of Modern Control Systems72 Eng: Mohammed Hussein
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Examples of Modern Control Systems73 Eng: Mohammed Hussein
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Examples of Modern Control Systems74 Eng: Mohammed Hussein
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Examples of Modern Control Systems75 Eng: Mohammed Hussein
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Examples of Modern Control Systems76 Eng: Mohammed Hussein
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Examples of Modern Control Systems77 Eng: Mohammed Hussein
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Examples of Modern Control Systems78 Eng: Mohammed Hussein
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Examples of Modern Control SystemsA Robot Balanced on a BallTohoru gakuin universityRobot development engineering lab79 Eng: Mohammed Hussein
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The Future of Control Systems80 Eng: Mohammed Hussein
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The Future of Control Systems81 Eng: Mohammed Hussein
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