1.1 Describing Systems ECE 5800 Western Michigan University Fall 2012

1.1 The nature of Systems A System is an entity isolated from an environment with entry points called Inputs and exits into the environment call Outputs. System Input x(t) Output z(t) State y(t) environment Zeroth order system

Properties

Properties Continued

Dynamic System Dynamic systems have memory, delays, time advances, derivatives, and integrals. state

V S (t)V R2 (t) V S (t)V R2 (t)

Example 1.1 Show LtSpice and MatLab Example.

Time Driven Models The solution to example

Example 1.2 The RC circuit is driven by a time signal. The output is the voltage is across the capacitor. The derivation of the output voltage is shown. V S (t)V R2 (t)

MATLAB Solution %Example 1.2 %ECE 5800 %John Stahl clc; clear all; % Constants pi = ; % n = 1000; t = 0:1/n:60e-3-1/n; % Solution Vs = 2 + 1*sin(2*pi*60*t); Vo = -2*exp(-100*t) *sin(2*pi*60*t) *cos(2*pi*60*t)+2; % figure(1) plot(t,Vo,'r'); title('ECE 5800 Example 1.2') xlabel('time') ylabel('volts')

LTSpice Solution

Control Systems Open loop control Plant: subsystem with a relationship we want to have a prescribed output. Controller: a subsystem with alters the behavior of the plant. Controller Plant Reference signal

Control Systems Closed loop control Feedback: a signal giving the controller the response of the plant to the reference signal. Disturbance: a signal which alters the behavior of the plant. Controller Plant