Derivation of the Dc motor differential equationsUnder typical operating conditions, the torque generated by a DC motor is directly proportional to the cumrent passing through itT-kaiwhere kis a proportionality constant determined by the characteristics of the specific motor. This relationship fails for large values of i.When the armature ratates, z generates a back electromotive force (back EMF) that opposes the applied valtage. In the circuit diagram, this is represented by a mator symbol. The voltage drop dua to the back EMF, denoted e, isproportional to the rotational velocity af the armaturee-kpwhere k, is a constant of proportionality. Ta derive the relationship between the current i and the motor shaftt angular position 0. yau can apply KirchhofT's voltage law and Nowton's second law in terms of torques acting on themotor shaft. Kirchhoff's voltage law implies that the sum at the vatage drops across the circuit must equal tha applied voltage:iR +(1)where v is the electric potential applied to the motor. In the absence af other applied torques, the equation aft motion can be derived by balancing the inertia of the motor shaft (Jõ) with the applied torque (7) and mictionalresistance (kJõ-T-RUsing the linear relationship batwoen torque and curent, this is equivalent to:Jõ + Bồ -i(2)Exerolce. In this axercise, you will compute transfer functions of the DC motor system. Assume that the system starts at rest (i-i-0-0-0). Also, assume that the applied voltage is a function of time v-ve).(a) Compute the Laplace transform af the voltage conservation equation (1) and apply the initial condiions Type your result below in terms af the defined symbolic variables.Pro-tip: When you write a symbolic equatian, you assign the whole aquation to a MATLAB variable using the assignment aperator"-" (singie equals). The equals sign in the symbolic equation is written using "--" (doubleequals). For exampie:syms y blineartay* use these sysbolic variablessyns LRke Bknsyms Theta ISV* write your laplace transform equation here* Constants* Laplace donaln varlables%checkEgn1(egn1)(b) Compute the Laplace transform of the equation of motion (2) and apply the initial condions. Type your answer below in tems of the defined symbolic variables.* write your laplace transform equation hereegn2 - NaN,IcheckEgn2(egn2)(0) Salve for the angular displacement transfer funcion Gs)esusing your results from (a) and (D).* write your transfer function hereThetaoverv - Na,XcheckThetaoverv( Thetadverv)(d) Solve for tha angular velocity transter function liswhere 2 is the Laplace transform of the angular velocity a) -).* write your transfer function hereOnegaoverv - NaN;Xcheckonegaoverv(Onegaoverv)

1. You can compute Laplace transform using the symbolic toolbox of MATLAB. If you want to compute…

Under typical operating condtons, the torgue generatad by a DC motor is dractly proportional to he cument passing through where sa proportionality constant datermined by the charactaristics of the specitie motor. This reiationshp tais tor large values of i When the armature ratates, generates a back electromotive force (back EMF) hat opcposas the applied vatage. In the circut dagram, tis is rapresentad by a motor symbol. The votage drop due to the back EMF, danoted ei proportional ohe rtational velocity of the amatre e- where isa constart ot proportionaity. To derive the reiationstip betwean he cument i and the motor shat angular position e. you can apply Kirchnots voitage law and Nowtoris second law in terms of torgues acting on the motor shat. Kirchhofs voltage law imples that the sum of the voltage drops across the cirout must equal he applied voitage: where vis the electie potantal applied to the motor. In he absance of oher applied torques, the equation af motion can be deived by balancing the inarta of the motor shat J) wn ne appled torque (T)and tronal resistance ( Jõ=T-B Using the inear relationship batwoen torgue and aumant, his is equivalent to: (2 LExeroice. in this exarcisa, you will compute transter tunctions of the DC motor systam. Assume that the system starts at rest (i-i-0-0-0, Asa, assume hat the appliad voltage is a tunction of time -. (a) Compute the Laplace transtom of the vatage consenvation equation (1) and apply the inital conditons. Type your resut balow in tems of he defined symbole varabies Pro-tp When you wta a symbolc equaton, you assign the whole aquation to a MATLAB varatie using the assignment operator- (singie equas). The equas sign in the symbolic eguaton is w equais. For exampie riten using "" (double wyy rtey

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

See similar textbooks

Related questions

Question

Derivation of the Dc motor differential equations
Under typical operating conditions, the torque generated by a DC motor is directly proportional to the cumrent passing through it
T-kai
where kis a proportionality constant determined by the characteristics of the specific motor. This relationship fails for large values of i.
When the armature ratates, z generates a back electromotive force (back EMF) that opposes the applied valtage. In the circuit diagram, this is represented by a mator symbol. The voltage drop dua to the back EMF, denoted e, is
proportional to the rotational velocity af the armature
e-kp
where k, is a constant of proportionality. Ta derive the relationship between the current i and the motor shaftt angular position 0. yau can apply KirchhofT's voltage law and Nowton's second law in terms of torques acting on the
motor shaft. Kirchhoff's voltage law implies that the sum at the vatage drops across the circuit must equal tha applied voltage:
iR +
(1)
where v is the electric potential applied to the motor. In the absence af other applied torques, the equation aft motion can be derived by balancing the inertia of the motor shaft (Jõ) with the applied torque (7) and mictional
resistance (k
Jõ-T-R
Using the linear relationship batwoen torque and curent, this is equivalent to:
Jõ + Bồ -i
(2)
Exerolce. In this axercise, you will compute transfer functions of the DC motor system. Assume that the system starts at rest (i-i-0-0-0). Also, assume that the applied voltage is a function of time v-ve).
(a) Compute the Laplace transform af the voltage conservation equation (1) and apply the initial condiions Type your result below in terms af the defined symbolic variables.
Pro-tip: When you write a symbolic equatian, you assign the whole aquation to a MATLAB variable using the assignment aperator"-" (singie equals). The equals sign in the symbolic equation is written using "--" (double
equals). For exampie:
syms y b
lineartay
* use these sysbolic variables
syns LRke Bkn
syms Theta ISV
* write your laplace transform equation here
* Constants
* Laplace donaln varlables
%checkEgn1(egn1)
(b) Compute the Laplace transform of the equation of motion (2) and apply the initial condions. Type your answer below in tems of the defined symbolic variables.
* write your laplace transform equation here
egn2 - NaN,
IcheckEgn2(egn2)
(0) Salve for the angular displacement transfer funcion Gs)
es
using your results from (a) and (D).
* write your transfer function here
Thetaoverv - Na,
XcheckThetaoverv( Thetadverv)
(d) Solve for tha angular velocity transter function lis
where 2 is the Laplace transform of the angular velocity a) -).
* write your transfer function here
Onegaoverv - NaN;
Xcheckonegaoverv(Onegaoverv)

Expert Solution

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Recommended textbooks for you

Computer Networking: A Top-Down Approach (7th Edi…

Computer Engineering

ISBN:

9780133594140

Author:

James Kurose, Keith Ross

Publisher:

PEARSON

Computer Organization and Design MIPS Edition, Fi…

Computer Engineering

ISBN:

9780124077263

Author:

David A. Patterson, John L. Hennessy

Publisher:

Elsevier Science

Network+ Guide to Networks (MindTap Course List)

Computer Engineering

ISBN:

9781337569330

Author:

Jill West, Tamara Dean, Jean Andrews

Publisher:

Cengage Learning

Computer Networking: A Top-Down Approach (7th Edi…

Computer Engineering

ISBN:

9780133594140

Author:

James Kurose, Keith Ross

Publisher:

PEARSON

Computer Organization and Design MIPS Edition, Fi…

Computer Engineering

ISBN:

9780124077263

Author:

David A. Patterson, John L. Hennessy

Publisher:

Elsevier Science

Network+ Guide to Networks (MindTap Course List)

Computer Engineering

ISBN:

9781337569330

Author:

Jill West, Tamara Dean, Jean Andrews

Publisher:

Cengage Learning

Concepts of Database Management

Computer Engineering

ISBN:

9781337093422

Author:

Joy L. Starks, Philip J. Pratt, Mary Z. Last

Publisher:

Cengage Learning

Prelude to Programming

Computer Engineering

ISBN:

9780133750423

Author:

VENIT, Stewart

Publisher:

Pearson Education

Sc Business Data Communications and Networking, T…

Computer Engineering

ISBN:

9781119368830

Author:

FITZGERALD

Publisher:

WILEY

SEE MORE TEXTBOOKS