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Unformatted text preview: Systems System Properties DE Model Definition Maths Models Analysis & Design Block Diag Definition of Systems I A system is an entity or process that manipulates one or more signals to accomplish a particular task, thereby yielding new signals. For example, I Capacitor : Input is charge/current, output is voltage I Robot : Input is applied torque, output is position of end effector (joints) I Car : Input is pressure on accelerator, output is speed I Vending machine : Input is money, output is cola I Heart : Input is electrical stimuli, output is blood flowrate I System is commonly viewed as a “black box” with p inputs and q output terminals. y q (n) x p (n) Continuous System y 1 (t) y 2 (t) y q (t) x 1 (t) x 2 (t) x p (t) Discrete System y 1 (n) y 2 (n) x 1 (n) x 2 (n) Output signals represent the influence of the system on the environment Input signals represent how environment influences the system i.e. message/instruction from the environment EE2010 Systems & Control Notes WW Tan Chapter 1 Page 1 Systems System Properties DE Model Definition Maths Models Analysis & Design Block Diag Example How signals are transformed by systems System x ( t ) y ( t ) x ( t ) and y ( t ) are elementary signals or its combination. I Anger person feels after receiving slap Time Input/Output Signal 0 0 Input Signal : Slap model ed as impulse function δ (t) System : Person Output Signal : Anger represented mathematical y as Keat U(t) I Car speed when accelerator is floored Time Input/Output Signal 0 0 Output signal : Car speed, [K o K o eat ] U(t) Input signal : Pressure on accelerator, K i U(t) System : Car EE2010 Systems & Control Notes WW Tan Chapter 1 Page 2 Systems System Properties DE Model Definition Maths Models Analysis & Design Block Diag Mathematical Models of Systems A system model is an idealised mathematical equation that predicts how the system would behave. I When the mathematical representation is compared to the physical system, they must agree to an acceptable level of accuracy. Time Input/Output Signal 0 0 Input Signal : Slap model ed as impulse function δ (t) "Model" of a Person Output of model : Anger represented mathematical y as Keat U(t) Actual output signal Types of model : I Integrodifferential equations + + V(t) V(t) i(t) i(t) C L Capacitor Inductor V ( t ) = 1 C Z ∞ i ( τ ) d τ V ( t ) = L di ( t ) dt EE2010 Systems & Control Notes WW Tan Chapter 1 Page 3 Systems System Properties DE Model Definition Maths Models Analysis & Design Block Diag I Impulse representation (Introduced in EE2009) I The impulse response , h ( t ), is output signal of a system when input signal is δ ( t ). I For a general input signal, u ( t ), the output signal can be derived by convolution ....
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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.
 Spring '11
 TanKayChen

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