Gp4_Chapter 2 - EE2010 Systems and Control (Chapter 2)...

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EE2010 Systems and Control (Chapter 2) 2-1 Static and Dynamic System System is static (also called memoryless) if output is a function of the input at the present time only, i.e., y ( t ) = K × u ( t ) Example is a resistor, V ( t ) = i ( t ) × R. Output of a dynamic system (also called non-zero memory) at time t depends on past or future values of the input u in addition to the present time, i.e., y ( t ) = f {…, u ( t + 1), u ( t ), u ( t 1), …} Examples include, Capacitors, Inductors, Basic System Properties t d i C t V 0 ) ( 1 ) ( dt t di L t V ) ( ) (
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EE2010 Systems and Control (Chapter 2) 2-2 An important characteristic of dynamic systems is that output signal must be continuous Consider battery charging in a mobile phone (a simple RC circuit): For V c ( t ) to change in a step manner when switch is closed, i ( t ) needs to be infinite. However, current in circuit must be finite because voltage source is finite. Therefore V c ( t ) must be continuous since Likewise, current flowing in an inductor must be continuous because dt t dV C t i c ) ( ) ( dt t dV c ) ( dt t dV c ) ( dt t di L t V L L ) ( ) (
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EE2010 Systems and Control (Chapter 2) 2-3 Causal and Non-Causal System System is causal or non-anticipatory if the output signal, y ( t 0 ), at t = t 0 , depends only on values of the input, u ( t ), for t t 0 Causality implies that the system does not respond to an input event until that event actually occurs, i.e., the response to an event beginning at t = t 0 is non-zero only for t t 0 All static/memoryless systems are causal since the output depends only on the current value of the input. All naturally occurring systems are causal or appear to be causal
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EE2010 Systems and Control (Chapter 2) 2-4 Engineering applications, whose independent variable is not time, may be non-causal, e.g., an image processing software Linear and Non-linear Systems Linear systems satisfy the properties of Additivity: y ( t ) = f { x 1 ( t ) + x 2 ( t )} = f { x 1 ( t )} + f { x 2 ( t )} Scaling: If y ( t ) = f { x ( t )}, then y ( t ) = f { x ( t )}
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EE2010 Systems and Control (Chapter 2) 2-5 Examples: Vending machine is a linear system: Put in twice as much money, get twice as much drinks. Humans are non-linear systems: Quiz mark is 60 if student studies 1 hour per day. With twice as much effort, may only score 80 marks. Superposition Principle Recall how circuits with multiple independent current/voltage sources are analyzed in EG1108. Two independent sources, E and I . What is voltage across 6 resistor, V r ?
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Systems and Control (Chapter 2) 2-6 1. “Kill” current source (let I = 0), find V r 1 2. “Kill” voltage source (set E = 0), find V r 2 3. Sum solutions, i.e., V r = V r 1 + V r 2 Suppose a linear system is perturbed by n independent input signals, x i ( t ) ( i = 1,…, n ). System output, y ( t
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This note was uploaded on 07/11/2011 for the course ECE 2010 taught by Professor Tankaychen during the Spring '11 term at National University of Singapore.

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Gp4_Chapter 2 - EE2010 Systems and Control (Chapter 2)...

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