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# Zine Making/Selling or giving copies to people \_\_NOEDITSECTION\_\_ \_\_NOTOC\_\_ ### `<span style="font-size:x-small; color:dimgray;">`{=html}Presentation`</span>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ```...
# Acoustics/Fundamentals of Acoustics ![](Acoustics_Fundamentals_of_Acoustics.jpg "Acoustics_Fundamentals_of_Acoustics.jpg") ## Introduction Sound is an oscillation of pressure transmitted through a gas, liquid, or solid in the form of a traveling wave, and can be generated by any localized pressure variation in a m...
# Acoustics/Fundamentals of Room Acoustics ![](Acoustics_fundamentals_of_room_acoustics.JPG "Acoustics_fundamentals_of_room_acoustics.JPG") ## Introduction Three theories are used to understand room acoustics : 1. The modal theory 2. The geometric theory 3. The theory of Sabine ## The modal theory This theory ...
# Acoustics/Fundamentals of Psychoacoustics ![](Acoustics_Psychoacoustics.jpg "Acoustics_Psychoacoustics.jpg") Due to the famous principle enounced by Gustav Theodor Fechner, the sensation of perception doesn't follow a linear law, but a logarithmic one. The perception of the intensity of light, or the sensation of w...
# Acoustics/Sound Speed ![](Acoustics_Sound_Speed.jpg "Acoustics_Sound_Speed.jpg") The **speed of sound** *c* (from Latin *celeritas*, \"velocity\") varies depending on the medium through which the sound waves pass. It is usually quoted in describing properties of substances (e.g. Sodium\'s Speed of Sound is listed u...
# Acoustics/Flow-induced Oscillations of a Helmholtz Resonator ![](Acoustics_flow_induced.JPG "Acoustics_flow_induced.JPG") ## Introduction The importance of flow excited acoustic resonance lies in the large number of applications in which it occurs. Sound production in organ pipes, compressors, transonic wind tunne...
# Acoustics/Active Control ![](Acoustics_active_control.JPG "Acoustics_active_control.JPG") ## Introduction The principle of active control of noise, is to create destructive interferences using a secondary source of noise. Thus, any noise can theoretically disappear. But as we will see in the following sections, on...
# Acoustics/Rotor Stator interactions ![](Acoustics_RotorStatorInteractions_2.JPG "Acoustics_RotorStatorInteractions_2.JPG") An important issue for the aeronautical industry is the reduction of aircraft noise. The characteristics of the turbomachinery noise are to be studied. The rotor/stator interaction is a predomi...
# Acoustics/Car Mufflers ![](Acoustics_car_muflers.JPG "Acoustics_car_muflers.JPG") ## Introduction A car muffler is a component of the exhaust system of a car. The exhaust system has mainly 3 functions: 1. Getting the hot and noxious gas from the engine away from the vehicle 2. Reduce exhaust emission 3. At...
# Acoustics/Sonic Boom ![](Acoustics_sonic_boom.JPG "Acoustics_sonic_boom.JPG") !Warplane passing the sound barrier. A **sonic boom** is the audible component of a shock wave in air. The term is commonly used to refer to the air shocks caused by the supersonic flight of military aircraft or passenger transports such...
# Acoustics/Sonar **SONAR** (**so**und **n**avigation **a**nd **r**anging) is a technique that uses sound propagation under water to navigate or to detect other vessels. There are two kinds of sonar: active and passive. ## History The French physicist Paul Langevin, working with a Russian émigré electrical engineer,...
# Acoustics/Interior Sound Transmission ## Introduction to NVH Noise is characterized by frequency (20--20 kHz), level (dB) and quality. Noise may be undesirable in some cases, i.e. road NVH yet may be desirable in other cases, i.e. powerful sounding engine. Vibration is defined as the motion sensed by the body, mai...
# Acoustics/Anechoic and reverberation rooms ![](Acoustics_anechoic_reverberation.JPG "Acoustics_anechoic_reverberation.JPG") ## Introduction Acoustic experiments often require to realise measurements in rooms with special characteristics. Two types of rooms can be distinguished: anechoic rooms and reverberation roo...
# Acoustics/Basic Room Acoustic Treatments ![](Acoustics_basic_room_acoustic_treatments.JPG "Acoustics_basic_room_acoustic_treatments.JPG") ## Introduction Many people use one or two rooms in their living space as \"theatrical\" rooms where theater or music room activities commence. It is a common misconception that...
# Acoustics/Human Vocal Fold ![](Acoustics_human_vocal_fold.JPG "Acoustics_human_vocal_fold.JPG") ## Physiology of vocal fold The human vocal fold is a set of lip-like tissues located inside the larynx, and is the source of sound for humans and many animals. The larynx is located at the top of the trachea. It is ma...
# Acoustics/How an Acoustic Guitar Works ![](Acoustics_how_an_acoustic_guitar_works.JPG "Acoustics_how_an_acoustic_guitar_works.JPG") What are sound vibrations that contribute to sound production? First of all, there are the strings. Any string that is under tension will vibrate at a certain frequency. The weight and...
# Acoustics/Basic Acoustics of the Marimba ![](Acoustics_basic_acoustics_marimba.JPG "Acoustics_basic_acoustics_marimba.JPG") ## Introduction Like a xylophone, a marimba has octaves of wooden bars that are struck with mallets to produce tones. Unlike the harsh sound of a xylophone, a marimba produces a deep, rich to...
# Acoustics/Bessel Functions and the Kettledrum ![](Acoustics_bessel_ketteldrum.JPG "Acoustics_bessel_ketteldrum.JPG") ## Introduction In class, we have begun to discuss the solutions of multidimensional wave equations. A particularly interesting aspect of these multidimensional solutions are those of bessel functio...
# Acoustics/Acoustics in Violins For a detailed anatomy of the violin, please refer to Atelierla Bussiere. ![](Violin_front_view.jpg "Violin_front_view.jpg")![](backview.jpg "backview.jpg") ## How does a violin make sound? ### General concept When a violinist bows a string, which can produce vibrations with abunda...
# Acoustics/Microphone Technique ![](Acoustics_microphone_technique.JPG "Acoustics_microphone_technique.JPG") ## General technique 1. A microphone should be used whose frequency response will suit the frequency range of the voice or instrument being recorded. 2. Vary microphone positions and distances until yo...
# Acoustics/Microphone Design and Operation ![](Acoustics_microphone_design_and_operation.JPG "Acoustics_microphone_design_and_operation.JPG") ## Introduction Microphones are devices which convert pressure fluctuations into electrical signals. There are two main methods of accomplishing this task that are used in th...
# Acoustics/Acoustic Loudspeaker ![](Acoustics_loudspeakers.JPG "Acoustics_loudspeakers.JPG") The purpose of the acoustic transducer is to convert electrical energy into acoustic energy. Many variations of acoustic transducers exist, although the most common is the moving coil-permanent magnet transducer. The classic...
# Acoustics/Sealed Box Subwoofer Design A sealed or closed box baffle is the most basic but often the cleanest sounding sub-woofer box design. The sub-woofer box in its most simple form, serves to isolate the back of the speaker from the front, much like the theoretical infinite baffle. The sealed box provides simple ...
# Acoustics/Bass-Reflex Enclosure Design ```{=html} <div style="float:right;margin:0 0 1em 1em;"> ``` ![](Bassreflex-Gehäuse_(enclosure).png "Bassreflex-Gehäuse_(enclosure).png") ```{=html} </div> ``` Bass-reflex enclosures improve the low-frequency response of loudspeaker systems. Bass-reflex enclosures are also cal...
# Acoustics/Polymer-Film Acoustic Filters ```{=html} <center> ``` ![](Acoustics_polymer_film_acoustic_filters.JPG "Acoustics_polymer_film_acoustic_filters.JPG") ```{=html} </center> ``` ## Introduction Acoustic filters are used in many devices such as mufflers, noise control materials (absorptive and reactive), and ...
# Acoustics/Noise in Hydraulic Systems ```{=html} <center> ``` ![](Acoustics_noise_in_hydraulic_systems.JPG "Acoustics_noise_in_hydraulic_systems.JPG") ```{=html} </center> ``` ## Noise in Hydraulic Systems Hydraulic systems are the most preferred source of power transmission in most of the industrial and mobile equ...
# Acoustics/Noise from Cooling Fans ```{=html} <center> ``` ![](Acoustics_noise_from_cooling_fans.JPG "Acoustics_noise_from_cooling_fans.JPG") ```{=html} </center> ``` ## Proposal As electric/electronic devices get smaller and functional, the noise of cooling device becomes important. This page will explain the orig...
# Acoustics/Piezoelectric Transducers ```{=html} <center> ``` ![](Acoustics_piezoelectric_transducers.JPG "Acoustics_piezoelectric_transducers.JPG") ```{=html} </center> ``` # Introduction Piezoelectricity from the Greek word \"piezo\" means pressure electricity. Certain crystalline substances generate electric char...
# Acoustics/Generation and Propagation of Thunder **Thunder** is the sound made by lightning. Depending on the nature of the lightning and distance of the listener, thunder can range from a sharp, loud crack to a long, low rumble (brontide). The sudden increase in pressure and temperature from lightning produces rapid...
# New Zealand History/Introduction ## Introduction to A Concise New Zealand History This is a concise textbook on New Zealand history, designed so it can be read by virtually anyone wanting to find out more about New Zealand history. The textbook covers the time span of human settlement in New Zealand. It includes:...
# New Zealand History/The Colonial Government New ## The Colonial Government !The Colonial New Zealand flag After New Zealand was annexed by Britain, it was initially set up as a dependency of New South Wales. However, by 1841, New Zealand was made a colony in its own right. As a colony, it inherited political pract...
# New Zealand History/Famous New Zealanders ## Famous New Zealanders !Sir Edmund Hillary in Poland, 2004. **Edmund Hillary** On the 29th of May 1953, New Zealander Edmund Hillary became the first person to reach the summit of Mount Everest with Nepalese climber Tenzing Norgay (the summit at the time was 29,028 fee...
# Speech-Language Pathology/Stuttering/Print version # Core Stuttering Behaviors # Incidence and Prevalence of Stuttering # Development of Childhood Stuttering # Neurology of Stuttering # Genetics of Stuttering # Physiology, Psychology, and Personality of Stutterers # Belief-Related Changes in Stuttering # Stre...
# Transportation Economics/Decision Making **Decision Making** is the process by which one alternative is selected over another. Decision making generally occurs in the planning phases of transportation projects, but last minute decision making has been shown to occur, sometimes successfully. Several procedures for ma...
# Transportation Economics/Modeling *All forecasts are wrong; some forecasts are more wrong than others.* - anonymous **Modeling** is a means for representing reality in an abstracted way. Your mental models are your **world view**: your outlook on life, and the world. The world view is your *internal model of how th...
# Transportation Economics/Data There are a variety of types of transportation data used in analysis. Some are listed below: - Infrastructure Status - Traffic Counts - Travel Behavior Inventory - Land Use Inventory - Truck/Freight Demand - External/Internal Demand (by Vehicle Type) - Special Generators ...
# Transportation Economics/Land Use Forecasting **Land use forecasting** undertakes to project the distribution and intensity of trip generating activities in the urban area. In practice, land use models are demand driven, using as inputs the aggregate information on growth produced by an aggregate economic forecastin...
# Transportation Economics/Evaluation A **benefit-cost analysis** (BCA)[^1] is often required in determining whether a project should be approved and is useful for comparing similar projects. It determines the stream of quantifiable economic benefits and costs that are associated with a project or policy. If the benef...
# UK Constitution and Government/Print version *Note: current version of this book can be found at <http://en.wikibooks.org/wiki/UK_Constitution_and_Government>* Remember to click \"refresh\" to view this version. ```{=html} <div style="font-family:verdana; margin-left='8%'; margin-right='8%'; text-align: justify;...
# UK Constitution and Government/Normans ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=left> ``` ```{=html} <t...
# UK Constitution and Government/Plantagenets ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=left> ``` ```{=htm...
# UK Constitution and Government/Houses of Lancaster and York ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=le...
# UK Constitution and Government/House of Tudor ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=left> ``` ```{=h...
# UK Constitution and Government/House of Stuart and the Commonwealth ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td ...
# UK Constitution and Government/House of Hanover ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=left> ``` ```{...
# UK Constitution and Government/Houses of Saxe-Coburg-Gotha and Windsor ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <...
# UK Constitution and Government/Constitution ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=left> ``` ```{=htm...
# UK Constitution and Government/Sovereign ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=left> ``` ```{=html} ...
# UK Constitution and Government/Parliament ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=left> ``` ```{=html}...
# UK Constitution and Government/Government ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=left> ``` ```{=html}...
# UK Constitution and Government/Judiciary ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=left> ``` ```{=html} ...
# UK Constitution and Government/Devolved Administrations ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=left> ...
# UK Constitution and Government/Elections ### `<font size=1 color=dimgray>`{=html}Presentation`</font>`{=html} ```{=html} <table height=1 border=1 style="border-collapse:collapse; border-color:LightSkyBlue; background-color:AliceBlue;" width="100%"> ``` ```{=html} <tr> ``` ```{=html} <td align=left> ``` ```{=html} ...
# Control Systems/Introduction ## This Wikibook This book was written at **Wikibooks**, a free online community where people write open-content textbooks. Any person with internet access is welcome to participate in the creation and improvement of this book. Because this book is continuously evolving, there are no fi...
# Control Systems/System Identification ## Systems Systems, in one sense, are devices that take input and produce an output. A system can be thought to **operate** on the input to produce the output. The output is related to the input by a certain relationship known as the **system response**. The system response usu...
# Control Systems/Digital and Analog ## Digital and Analog There is a significant distinction between an **analog system** and a **digital system**, in the same way that there is a significant difference between analog and digital data. This book is going to consider both analog and digital topics, so it is worth tak...
# Control Systems/System Metrics ## System Metrics When a system is being designed and analyzed, it doesn\'t make any sense to test the system with all manner of strange input functions, or to measure all sorts of arbitrary performance metrics. Instead, it is in everybody\'s best interest to test the system with a se...
# Control Systems/System Modeling ## The Control Process It is the job of a control engineer to analyze existing systems, and to design new systems to meet specific needs. Sometimes new systems need to be designed, but more frequently a controller unit needs to be designed to improve the performance of existing syste...
# Control Systems/Transforms ## Transforms There are a number of transforms that we will be discussing throughout this book, and the reader is assumed to have at least a small prior knowledge of them. It is not the intention of this book to teach the topic of transforms to an audience that has had no previous exposur...
# Control Systems/Transfer Functions ## Transfer Functions A **Transfer Function** is the ratio of the output of a system to the input of a system, in the Laplace domain considering its initial conditions and equilibrium point to be zero. This assumption is relaxed for systems observing transience. If we have an inpu...
# Control Systems/Poles and Zeros ## Poles and Zeros **Poles** and **Zeros** of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes infinite and zero respectively. The values of the poles and the zeros of a system determine whether the system is st...
# Control Systems/State-Space Equations ## Time-Domain Approach The \"Classical\" method of controls (what we have been studying so far) has been based mostly in the transform domain. When we want to control the system in general, we represent it using the Laplace transform (Z-Transform for digital systems) and when ...
# Control Systems/Linear System Solutions ## State Equation Solutions The state equation is a first-order linear differential equation, or (more precisely) a system of linear differential equations. Because this is a first-order equation, we can use results from Ordinary Differential Equations to find a general solut...
# Control Systems/Time Variant System Solutions ## General Time Variant Solution The state-space equations can be solved for time-variant systems, but the solution is significantly more complicated than the time-invariant case. Our time-variant state equation is given as follows: $$x'(t) = A(t)x(t) + B(t)u(t)$$ We ...
# Control Systems/Digital State Space ## Digital Systems Digital systems, expressed previously as difference equations or Z-Transform transfer functions, can also be used with the state-space representation. All the same techniques for dealing with analog systems can be applied to digital systems with only minor chan...
# Control Systems/Eigenvalues and Eigenvectors ## Eigenvalues and Eigenvectors The eigenvalues and eigenvectors of the system matrix play a key role in determining the response of the system. It is important to note that only square matrices have eigenvalues and eigenvectors associated with them. Non-square matrices ...
# Control Systems/Standard Forms ## Companion Form A **companion form** contains the coefficients of a corresponding characteristic polynomial along one of its far rows or columns. For example, one companion form matrix is: $$\begin{bmatrix} 0 & 0 & 0 & \cdots & 0 & -a_0 \\ 1 & 0 & 0 & \cdots ...
# Control Systems/MIMO Systems ## Multi-Input, Multi-Output Systems with more than one input and/or more than one output are known as **Multi-Input Multi-Output** systems, or they are frequently known by the abbreviation **MIMO**. This is in contrast to systems that have only a single input and a single output (SISO)...
# Control Systems/Realizations ## Realization **Realization** is the process of taking a mathematical model of a system (either in the Laplace domain or the State-Space domain), and creating a physical system. Some systems are not realizable. An important point to keep in mind is that the Laplace domain representati...
# Control Systems/Gain ## What is Gain? **Gain** is a proportional value that shows the relationship between the magnitude of the input to the magnitude of the output signal at steady state. Many systems contain a method by which the gain can be altered, providing more or less \"power\" to the system. However, increa...
# Control Systems/Block Diagrams When designing or analyzing a system, often it is useful to model the system graphically. **Block Diagrams** are a useful and simple method for analyzing a system graphically. A \"block\" looks on paper exactly what it means: ## Systems in Series When two or more systems are in serie...
# Control Systems/Feedback Loops ## Feedback A **feedback loop** is a common and powerful tool when designing a control system. Feedback loops take the system output into consideration, which enables the system to adjust its performance to meet a desired output response. When talking about control systems it is impo...
# Control Systems/Signal Flow Diagrams ## Signal-flow graphs **Signal-flow graphs** are another method for visually representing a system. Signal Flow Diagrams are especially useful, because they allow for particular methods of analysis, such as **Mason\'s Gain Formula**. Signal flow diagrams typically use curved li...
# Control Systems/Bode Plots ## Bode Plots A Bode Plot is a useful tool that shows the gain and phase response of a given LTI system for different frequencies. Bode Plots are generally used with the Fourier Transform of a given system. center\|framed\|An example of a Bode magnitude and phase plot set. The Magnitude ...
# Control Systems/Stability ## Stability When a system is unstable, the output of the system may be infinite even though the input to the system was finite. This causes a number of practical problems. For instance, a robot arm controller that is unstable may cause the robot to move dangerously. Also, systems that are...
# Control Systems/State-Space Stability ## State-Space Stability If a system is represented in the state-space domain, it doesn\'t make sense to convert that system to a transfer function representation (or even a transfer matrix representation) in an attempt to use any of the previous stability methods. Luckily, the...
# Control Systems/Discrete Time Stability ## Discrete-Time Stability The stability analysis of a discrete-time or digital system is similar to the analysis for a continuous time system. However, there are enough differences that it warrants a separate chapter. ## Input-Output Stability ### Uniform Stability An LTI...
# Control Systems/Routh-Hurwitz Criterion ## Stability Criteria The Routh-Hurwitz stability criterion provides a simple algorithm to decide whether or not the zeros of a polynomial are all in the left half of the complex plane (such a polynomial is called at times \"Hurwitz\"). A Hurwitz polynomial is a key requireme...
# Control Systems/Jurys Test ## Routh-Hurwitz in Digital Systems Because of the differences in the Z and S domains, the Routh-Hurwitz criteria can not be used directly with digital systems. This is because digital systems and continuous-time systems have different regions of stability. However, there are some methods...
# Control Systems/Root Locus ## The Problem Consider a system like a radio. The radio has a \"volume\" knob, that controls the amount of gain of the system. High volume means more power going to the speakers, low volume means less power to the speakers. As the volume value increases, the poles of the transfer functio...
# Control Systems/Nyquist Stability Criteria ## Nyquist Stability Criteria The **Nyquist Stability Criteria** is a test for system stability, just like the Routh-Hurwitz test, or the Root-Locus Methodology. However, the Nyquist Criteria can also give us additional information about a system. Routh-Hurwitz and Root-Lo...
# Control Systems/Controllability and Observability ## System Interaction In the world of control engineering, there are a slew of systems available that need to be controlled. The task of a control engineer is to design controller and compensator units to interact with these pre-existing systems. However, some syste...
# Control Systems/System Specifications ## System Specification There are a number of different specifications that might need to be met by a new system design. In this chapter we will talk about some of the specifications that systems use, and some of the ways that engineers analyze and quantify technical systems. ...
# Control Systems/State Feedback ## State Observation The state space model of a system is the model of a single plant, not a true feedback system. The feedback mechanism that relates *x\'* to *x* is a representation of the mechanism internal to the plant, where the state of the plant is related to its derivative. As...
# Control Systems/Estimators and Observers ## Estimators and Observers A problem arises in which the internal states of many systems cannot be directly observed, and therefore state feedback is not possible. What we can do is try to design a separate system, known as an **observer** or an **estimator** that attempts ...
# Control Systems/Eigenvalue Assignment for MIMO Systems The design of control laws for MIMO systems are more extensive in comparison to SISO systems because the additional inputs ($q > 1$) offer more options like defining the Eigenvectors or handling the activity of inputs. This also means that the feedback matrix *K...
# Control Systems/Controllers and Compensators ## Controllers There are a number of different standard types of control systems that have been studied extensively. These controllers, specifically the P, PD, PI, and PID controllers are very common in the production of physical systems, but as we will see they each car...
# Control Systems/Polynomial Design ## Polynomial Design A powerful tool for the design of controller and compensator systems is **polynomial design**. Polynomial design typically consists of two separate stages: 1. Determine the desired response of the system 2. Adjust your system to match the desired response. ...
# Control Systems/Adaptive Control ## Adaptive Controllers What we\'ve been studying up till this point are fixed systems, that is systems that do not change over time. However, real-world applications and experience tells us that the environment can change over time: New noise can be added to a signal, the signal qu...
# Control Systems/State Machines ## State Machines Digital computers have a lot more power and flexibility to offer than processing simple difference equations like the kind that we have been looking at so far in our discrete cases. Computer systems are capable of handling much more complicated digital control tasks,...
# Control Systems/Nonlinear Systems ## Nonlinear General Solution A nonlinear system, in general, can be defined as follows: $$x'(t) = f(t, t_0, x, x_0)$$ $$x(t_0) = x_0$$ Where *f* is a nonlinear function of the time, the system state, and the initial conditions. If the initial conditions are known, we can simpli...
# Control Systems/Common Nonlinearities There are some nonlinearities that happen so frequently in physical systems that they are called \"Common nonlinearities\". These common nonlinearities include Hysteresis, Backlash, and Dead-zone. ## Hysteresis Continuing with the example of a household thermostat, let\'s say ...
# Control Systems/Noise Driven Systems ## Noise-Driven Systems Systems frequently have to deal with not only the control input *u*, but also a random noise input *v*. In some disciplines, such as in a study of electrical communication systems, the noise and the data signal can be added together into a composite input...
# Control Systems/Digital Control Systems ## Digital Systems Digital systems, expressed previously as difference equations or Z-Transform transfer functions can also be used with the state-space representation. Also, all the same techniques for dealing with analog systems can be applied to digital systems, with only ...
# Control Systems/Discrete-Time Stability ## Discrete-Time Stability The stability analysis of a discrete-time or digital system is similar to the analysis for a continuous time system. However, there are enough differences that it warrants a separate chapter. ## Input-Output Stability ### Uniform Stability An LTI...
# Control Systems/System Delays ## Delays A system can be built with an inherent **delay**. Delays are units that cause a time-shift in the input signal, but that don\'t affect the signal characteristics. An **ideal delay** is a delay system that doesn\'t affect the signal characteristics at all, and that delays the ...
# Control Systems/Sampled Data Systems ## Ideal Sampler In this chapter, we are going to introduce the ideal sampler and the **Star Transform**. First, we need to introduce (or review) the **Geometric Series** infinite sum. The results of this sum will be very useful in calculating the Star Transform, later. Conside...
# Control Systems/Z Transform Mappings ## Z Transform Mappings There are a number of different mappings that can be used to convert a system from the complex Laplace domain into the Z-Domain. None of these mappings are perfect, and every mapping requires a specific starting condition, and focuses on a specific aspect...
# Control Systems/Physical Models ## Physical Models This page will serve as a refresher for various different engineering disciplines on how physical devices are modeled. Models will be displayed in both time-domain and Laplace-domain input/output characteristics. The only information that is going to be displayed h...
# Control Systems/Transforms Appendix ## Laplace Transform When we talk about the Laplace transform, we are actually talking about the version of the Laplace transform known as the **unilinear Laplace Transform**. The other version, the **Bilinear Laplace Transform** (not related to the Bilinear Transform, below) is ...