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Unformatted text preview: EE 200L  Foundations of Electrical Engineering Systems Homework 1  Solutions 1. Systems with memory: Heating a container of water  The input is the amount of heat via the stove burner. The output is the temperature of water. The instantaneous heat is not the only factor affecting the temperature of water. The amount of time is it applied also affects the temperature. Another example is a vending machine. The machine ‘remembers’ the value of coins put in for a until it dispenses the product and change then resets itself. 2. Non linear systems: A car engine  the input is the amount of fuelair mixture regulated via the gas pedal. The response is the acceleration of the car. Depressing the pedal by a factor k more does not increase the acceleration by a factor of k. The phenomenon is nonuniform. In particular, the property of homogeneity or superposition has to be violated for a system to be nonlinear. Nonlinear systems are ubiquitous in nature! Typically, at the very least, they all exhibit a deadzone or saturation effect. 1 3. (a) GramSchimdt algorithm for v 1 , v 2 , v 3 : u 1 = 1 1 2 2 u 2 = v 2 h u 1 , v 2 i h u 1 , u 1 i u 1 = 1 1 1  1 + 0 + 0 2 + 0 1 + 1 + 0 + 4 + 4 1 1 2 2 = 1 . 1 . 1 1 . 8 . 2 u 3 = v 3 h u 1 , v 3 i h u 1 , u 1 i u 1 h u 2 , v 3 i h u 2 , u 2 i u 2 = 5 3 2 4 6  5 + 3 + 0 + 8 + 12 10 1 1 2 2  5 . 5 + 0 . 3 + 2 3 . 2 + 1 . 2 2 . 9 1 . 1 . 1 1 . 8 . 2 = 5 3 2 4 6  2 . 8 2 . 8 5 . 6 5 . 6 ...
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 Fall '08
 ZADEH
 Electrical Engineering, Linear Algebra, Addition, Vector Space, additive inverse, aj ψi

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