Control Engineering Dr Mustafa M Aziz (2010) ________________________________________________________________________________ TRANSFER FUNCTIONS AND BLOCK DIAGRAMS 1. Introduction 2. Transfer Function of Linear Time-Invariant (LTI) Systems 3. Block Diagrams 4. Multiple Inputs 5. Transfer Functions with MATLAB 6. Time Response Analysis with MATLAB 1. Introduction An important step in the analysis and design of control systems is the mathematical modelling of the controlled process
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Transfer Function General with order‚ linear‚ time invariant differential equation an dn(t)dtn+ an-1 dn-1c(t)dtn-1+…a0ct= bmdmrtdtm+bm-1dm-1rtdtm-1+…b0r(t) Where: c (t) is the output r (t) I is the input By taking the Laplace transform of both sides ansn cs+ an-1sn-1 cs+…a0cs+initial condition involving c(t) =bmsmRt+bm-1sm-1Rt+…b0Rs+initial condition involving r(t) If we assume that all initial condition are zero ansn+ an-1sn-1….+…a0cs=bmsm+bm-1sm-1+…b0r(s) Rs-→ bmsm+bm-1sm-1+…b0ansn+
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2001 HADNOUT E.13 - EXAMPLES ON TRANSFER FUNCTIONS‚ POLES AND ZEROS Example 1 Determine the transfer function of the mass-spring-damper system. The governing differential equation of a mass-spring-damper system is given by m x + c x + kx = F . Taking the Laplace transforms of the above equation (assuming zero initial conditions)‚ we have ms 2 X ( s ) + csX ( s ) + kX ( s ) = F ( s )‚ X ( s) 1 ⇒ = . 2 F ( s ) ms + cs + k Equation (1) represents the transfer function of the mass-spring-damper system
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Functions and graphing functions Basics: A function is a rule that changes input into output A relation is any set of ordered pairs A function is defined as a set of ordered pairs in which no two ordered pairs have the same element A function must give exactly one unique output for each input Also called a mapping or simply a map The set of input numbers is called the domain The set of output numbers is called the range The set of all possible outputs is called the co-domain The range is generally
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M. Velas FUNCTIONS OF LEISURE Relation to Increased Production and Consumption The function of leisure is largely determined by the kind and amount of free time and by the ideas of the age. When spare time consists of short breaks between long periods of sustained labor‚ its function is thought of as recreation – relaxing the worker so that he can work more efficiency after the break. When the goals are efficiency of work‚ increased production‚ more power and more wealth‚ the function of leisure
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• Explain the domain and range of a function. Under what circumstances would the domain be something other than all real numbers? Provide an example. Domain: The domain of a function is the set of ‘input’ values; the function must be well defined for these input values. Range: The range of a function is the set of ‘output’ values that result after f is applied to every element of the domain. **The domain will NOT be all real numbers when the horizontal distance from
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Life-time examples: 1. In the Deliotte report‚ it is said 44% of respondents list business intelligence systems as enablers or disruptors that may threaten their business model‚ which makes it second most concerning technology threat. 2. One example of how business intelligence systems have been maximised is at women’s underwear manufacturer Maidenform. Their CIO Bob Russo said recently after implementing BI‚ “Providing targeted information at the right place and time is central to improving the
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CHAPTER 4 : FUNCTIONS AND THEIR GRAPHS 4.1 Definition of Function A function from one set X to another set Y is a rule that assigns each element in X to one element in Y. 4.1.1 Notation If f denotes a function from X to Y‚ we write 4.1.2 Domain and range X is known as the domain of f and Y the range of f. (Note that domain and range are sets.) 4.1.3 Object and image If and ‚ then x and y are known respectively as the objects and images of f. We can write ‚ ‚ . We can represent
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line of attack quickly and smoothly to make the most yards out of each run. Not only do the IRs work to stabilize the hip in these accelerations and decelerations‚ but the muscles also contribute the action of internal rotation‚ such as when the leg crosses the body‚ to alter the direction of movement. IRs also need to be flexible to allow external rotation of the leg‚ when the leg is rotated away from the body beginning from the the heel. You should only move from the hip sockets; do
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[pic] Payroll Management Competence Framework Table of Contents 1. Introduction 3 The Payroll Profession 4 Payroll and the World of Work 5 Overall Objectives of the Payroll Management Competence Framework 6 Enabling Successful Payroll Competence Development 7 The Competence Framework Pyramid 8 Applying the CIPP Competence Framework 9 Evaluation of Payroll Management Competences 2. Payroll
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