This study source was downloaded by 100000838733379 from CourseHero com on 11 09 2022 03 13 04 GMT 06 00 https www coursehero com file 86296454 ECE11L CRUZ CARLOUI Group2 Lab 2pdf SOUTHERN LUZON STATE UNIVERSITY COLLEGE OF ENGINEERING ECE DEPARTMENT ECE11 FEEDBACK AND CONTROL SYSTEMS LABORATORY LABORATORY NO 2 Mathematical Modeling of Physical Systems GROUP 2 Brian Aaron R Bermudez Bethrina Ira A Carreon Carloui R Cruz Nathaniel B Delos Reyes Camille Y Dequito Cristel Joyce M Esmerna BSECE III GG TUE 7 30 10 30 AM DATE OF PERFORMANCE March 18 2021 DATE OF SUBMISSION March 23 2021 ENGR KRIS BRYAN G NAYNES INSTRUCTOR RATING This study source was downloaded by 100000838733379 from CourseHero com on 11 09 2022 03 13 04 GMT 06 00 https www coursehero com file 86296454 ECE11L CRUZ CARLOUI Group2 Lab 2pdf 2 Page I OBJECTIVES 1 To learn how to represent the mathematical models of physical systems in MATLAB able to grasp the learnings to solve such models which is used in design and analysis of control systems 2 To familiarize oneself with the functions of MATLAB on representing the mathematical modeling of physical systems such as mass spring system model were using the Linear or nonlinear ordinary differential equation as well as more advance applications 3 To perform Exercises 1 and 2 by creating scripts with appropriate MATLAB codes and function by providing screenshots of the results II INTRODUCTORY INFORMATION In further studying the control system the mathematical modeling is integral to learn such as to be able to model a dynamic system in mathematical terms and analyze their characteristics A mathematical model of a system is defined as a set of equations that represents the dynamics of the system MATLAB offers convenient commands and function to obtain results that can be used in analysis and design purposes Mathematical models may assume many different forms Depending on the particular system and the particular circumstances one mathematical model may be better suited than other models Physical modeling includes interconnected components For example in mechanical system deriving differential equations for combination of masses springs and dampers to assembled to obtain the system model This can assume that a suitable approximation will be depending on their behavior which is mathematically described by ordinary differential equations These equations are in general are often linearized about an operating point for analysis and design purposes III PROCEDURES A Read and analyze the lecture provided for this laboratory experiment Familiarize oneself with the mass spring system model given in the manual which describe the uses equation such as ODE on representing models B Open MATLAB application and practice script writing with different functions and codes for representing the mathematical modeling of physical systems such as in mass spring and damper system which uses differential equations C Perform Exercises 1 and 2 by writing the codes for each condition D Run or execute the script and check if the results meet the given conditions E Copy and paste the script s and attach screenshots of the results in the Data and Results part This study source was downloaded by 100000838733379 from CourseHero com on 11 09 2022 03 13 04 GMT 06 00 https www coursehero com file 86296454 ECE11L CRUZ CARLOUI Group2 Lab 2pdf 3 Page IV DATA AND RESULTS Exercise 1 1 Plot the position and the speed in separate graphs 2 Change the value of r to 2 and 3 3 Superpose the results and compare with the linear case r 1 and plot all three cases in the same plot window Please use different figures for velocity and displacement Exercise 2 Consider the mechanical system depicted in the figure The input is given by and the output is given by Determine the differential equation governing the system response such that forcing function f t 1 Let m 10 k 1 and b 0 5 Show that the peak amplitude of the output is about 1 8 MATLAB Commands Exercise 1 For r 1 function dXdt mass spring t X flow rate M 750 Kg B 30 Nsec m Fa 300 N K 15 N m r 1 dX dt dXdt 1 1 X 2 dXdt 2 1 B M X 2 K M X 1 r Fa M end For r 2 function dXdt mass spring2 t2 X2 flow rate MR2 750 Kg BR2 30 Nsec m FaR2 300 N This study source was downloaded by 100000838733379 from CourseHero com on 11 09 2022 03 13 04 GMT 06 00 https www coursehero com file 86296454 ECE11L CRUZ CARLOUI Group2 Lab 2pdf 4 Page KR2 15 N m r2 2 dX dt dXdt 1 1 X2 2 dXdt 2 1 BR2 MR2 X2 2 KR2 MR2 X2 1 r2 FaR2 MR2 end For r 3 function dXdt mass spring3 t3 X3 flow rate MR3 750 Kg BR3 30 Nsec m FaR3 300 N KR3 15 N m r3 3 dX dt dXdt 1 1 X3 2 dXdt 2 1 BR3 MR3 X3 2 KR3 MR3 X3 1 r3 FaR3 MR3 end For plotting commands X0 0 0 initial speed and position t X ode45 mass spring 0 200 X0 t2 X2 ode45 mass spring2 0 200 X0 t3 X3 ode45 mass spring3 0 200 X0 figure subplot 321 plot t X 1 xlabel Time ylabel Position grid on title Mass Spring System at r 1 subplot 322 plot t X 2 xlabel Time ylabel Speed grid on title Mass Spring System at r 1 subplot 323 plot t2 X2 1 xlabel Time ylabel Position grid on title Mass Spring System at r 2 subplot 324 plot t2 X2 2 This study source was downloaded by 100000838733379 from CourseHero com on 11 09 2022 03 13 04 GMT 06 00 https www coursehero com file 86296454 ECE11L CRUZ CARLOUI Group2 Lab 2pdf 5 Page xlabel Time ylabel Speed grid on title Mass Spring System at r 2 subplot 325 plot t3 X3 1 xlabel Time ylabel Position grid on title Mass Spring System at r 3 subplot 326 plot t3 X3 2 xlabel Time ylabel Speed grid on title Mass Spring System at r 3 Exercise 2 For f t 1 function dXdt mechanical system t X flow rate M 10 Kg B 0 5 Nsec m Fa 1 N K 1 N m r 1 dX dt dXdt 1 1 X 2 dXdt 2 1 B M X 2 K M X 1 r Fa M end For the transfer function differential equation of the system num 1 den 10 0 5 1 sys tf num den step sys For plotting commands X0 0 0 initial speed and position t X ode45 mechanical system 0 200 X0 figure plot t X This study source was downloaded by 100000838733379 from CourseHero com on 11 09 2022 03 13 04 GMT 06 00 https www coursehero com file 86296454 ECE11L CRUZ CARLOUI Group2 Lab 2pdf 6 Page xlabel Time ylabel Amplitude title Time Response grid on Results Exercise 1 This study source was downloaded by 100000838733379 from CourseHero com on 11 09 2022 03 13 04 GMT 06 00 https www coursehero com file 86296454 ECE11L CRUZ …