University:
California State University, Northridge
Course:
ME 584 | Modeling and Simulation of Dynamic Systems
Academic year:

2010
Views:

173

Pages:

15
Author:

accionox1v

Case Study: Feasibility Study of a Mobile Robot Design chp3 19 Preliminary Design Model • Read Handout 1 • Develop a simplified model of the base and the arm by neglecting the reaction forces that occur at the pivot • When do the reaction forces become significant? => at high accelerations and speeds of the base and the arm chp3 Preliminary Design Model 20 chp3 21 Preliminary Design Model chp3 22 Motion Profiles • Read Handout 2 • Plot the motor force versus time, and motor torque versus time, and determine whether the motor is powerful enough chp3 23 Motion Profiles chp3 24 A More Detailed Model • The simplified model appears feasible • Develop a detailed model, including the reaction forces to see whether they significantly change the results chp3 A More Detailed Model 25 chp3 A More Detailed Model 26 chp3 A More Detailed Model 27 chp3 28 Matlab Simulation Example: Solving Systems of Equations chp3 29 Matlab Simulation Example: Solving Systems of Equations • More on ode45 commands: http://www.mathworks.com/access/helpdesk/help/techdoc/ref/ode45.html chp3 30 Homework 3: chapter 3 • 3.14, 3.21,3.24,3.25,3.31,3.33,3.36 • Case study simulation: – Simulate the detailed model for 10 seconds with initial conditions x0  0, x0  0, 0  100 , 0  0 and for three cases: 1. T = 0, f =0 2. T=370 Nm, f = 0 3. T=0, f = 263 N – For each case, plot state vector versus time – Describe the behavior of the system for each case and discuss the stability of the system chp3 31 Case Study Simulation Model I p  mLx cos   T  mgl sin  or a  bx  c where a  I p ; b   mL cos  ; c  T  mgl sin  (m  M ) x  mL cos   mL sin  2  f or dx  e  g where d  (m  M ); e   mL cos  ; g   mL sin  2  f Solve for x and    2 ag  ec I p  mL sin   f  mL cos  T  mgl sin   x   ad  eb I p m  M   mL cos   mL cos   c b  ag  ec  T  mgl sin  mL cos        a a  ad  eb  Ip Ip    I p  mL sin  2  f  mL cos  T  mgl sin          I m  M  mL cos   mL cos    p chp3 Matlab Simulation tspan  [0 3]; % simulation time vector % State vector  y  [ x x   ]' y 0  [0 0 10 * pi / 180 0]' ; [t , y ]  ode 45(@ secondode, tspan, y 0); % function to be integrated function dy  secondode (t , y ) dy  zeros( 4,1); x  y (:,1); xdot  y (:,2); phi  y (:,3); phidot  y (:,4); % Plot state vector against time figure subplot ( 221) plot (t , x ) ylabel (' x, [ m]' ) xlabel (' t , [ s ]' ) % Define parameters I p  47.5; % kg  m ^ 2 subplot ( 222) plot (t , xdot ) ylabel (' xdot , [ m / s ]' ) xlabel (' t , [ s ]' ) subplot ( 223) plot (t , phi ) ylabel (' phi, [ m]' ) xlabel (' t , [ s ]' ) subplot ( 224) plot (t , phidot ) ylabel (' phidot , [ rad / s ]' ) xlabel (' t , [ s ]' ) L  7 / 8; % m m  40; % kg M  100 ; % kg g  9.81; % m / s ^ 2 T  0; f  0; a  I p; b   m * L * cos( y (3)); c  T  m * g * l * sin( y (3)); d  ( m  M ); e   m * L * cos( y (3)); g   m * L * sin( y (3)) * y ( 4) * y ( 4)  f ; % State vector  y  [ x x   ]'  [ y (1) y ( 2) y (3) y ( 4)]' dy (1)  y ( 2); dy ( 2)  ( a * g  e * c ) /( a * d  e * b); dy (3)  y ( 4); dy ( 4)  c / a  (b / a ) * ( a * g  e * c ) /( a * d  e * b); 32

Feasibility Study of a Mobile Robot Design