analytical dynamics 2 projects

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DEADLINE IS STRICT 46 HRS FROM NOW , EVEN AN HR MORE , I WILL NOT BE ABLE TO PAYUSE OF MATLAB IS MUST

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Please i need you to make to project , one for me and one for my friend... A paper that includes an equation of motion U might look for a crane or pendulum or any other applications that includes equations of motion? We have to solve it in Maple or Matlab (very important) Also you have to analyze and make sure that his work is correct or not ... These are some references you can look at them to find such a papers Please see the attached other two files l. VOL. 18, NO. 4, pp. 1-9. July 2016 1 REFERENCES wn by eri- I by for still - the Lent. eler- ofile satu- city, gan for avers uses 1. Abdel-Rahman, E., A. Nayfeh, and Z. Masoud, “Dynamics and control of cranes: A review." I. Vibr. Control, Vol. 9. No. 7. pp. 863_908 (2003). 2. Singhose, W., "Command shaping for flexible sys- tems: A review of the first 50 years." Int. J. Precis Eng. Manuf., Vol. 10, No. 4, pp. 153-168 (2009). 3. Vaughan. I. A. Yano, and W. Singhose, Com- parison of robust input shapers.” I Sound Vibra... Vol. 315, No. 4. pp. 797-815 (2008). 4. Masoud, Z., A. Nayfeh, and D. Mook. "Cargo pendulation reduction of ship-mounted cranes. Nonlinear Dyn, Vol. 35. No. 3. pp. 299–311 (2004). 5. Masoud, Z. A Nayfeh, and N Nayfeh. "Sway reduction on quay-side container cranes using delayed feedback controller: Simulations and experi- ments." I Vibr. Control, Vol. 11, No. 8. pp. 1103-1122 (2005). 6. Schaub. H. "Rate-based ship-mounted crane payload pendulation control system, Control Eng Practice, Vol. 16, No. I. pp. 132-145 (2008). 7. Cho, S K. and H. H. Lee. "A fuzzy-logic antiswing controller for three-dimensional overhead cranes, ISA Trans, Vol. 41, No. 2. pp. 235-243 (2002). 8. Liu, D. I Yi, D. Zhao, and W. Wang. "Adaptive sliding mode fuzzy control for a two-dimensional overhead crane." Mechatronics, Vol. 15, No. 5. pp. 505-522 (2005). 9. Omar, H and A. Nayfeh, "Gantry cranes gain scheduling feedback control with friction compen- sation," I Sound Vibr., Vol. 281, No. 1, pp. 1-20 (2005) 10. Singer, N and W. Seering. “Preshaped command inputs to reduce system vibrations, I Dyn. Syst. Meas Control-Trans ASME, Vol. 112, No. 1, pp. 76-82 (1990) 11. Smith. O. I M., Feedback Control Systems, McGraw-Hill, New York (1958). 12. Starr G., "Swing-free transport of suspended objects with a path-controlled robot manipulator, I Dyn Syst. Meas Control-Trans ASME, VOL. 107, No. 1, pp. 97-100 (1985) 13. Strip. D. Swing-free transport of suspended objects: A general treatment," IEEE Trans Robotics Automation, Vol. 5. No. 2. pp. 234 236 (1989). 14. Singhose, W. and L. Pao, "A comparison of input shaping and time-optimal flexible-body control, Control Eng Practice, Vol. 5, No. 4, pp. 459-467 (1997) 15. Jolevski, D. and O. Bego. "Input shaping of the synchronous generator for reduction of self-induced rofile hani- ctural at the posed accel- esults of an d the ile is at the ne of mon sin is The ach is more plicit oller. rofile erent 15 Chinese Automatic Control Society and Wiley Publishing Asia Pty Ltd 29. 30. 31. 1 N I Оч- mand generation for flexible systems by input shaping and command smoothing," AIAA J. Guid, Control Dyn., Vol. 33, No. 6, pp. 1697-1707 (2010). 17. Daqaq, M. and Z. Masoud, “Nonlinear input -shaping controller for quay-side container cranes," Nonlinear Dyn., Vol. 45, No. 1-2, pp. 149-170 (2006). 18. Hu, Q. I. and G. F. Ma, “Flexible spacecraft vibration suppression using pwpf modulated input command and sliding mode control,” Asian J. Control, Vol. 9, No. 1, pp. 20-29 (2007). 19. Kang, C. G. and J. H. Kwak, “On a simplified resid- ual vibration ratio function for input shaping con- trol,” Asian J. Control, Vol. 16, No. 1, pp. 277–283 (2014). 20. Vaughan, J., A. Yano, and W. Singhose, “Per- formance comparison of robust negative input shapers, Proc. 2008 Amer. Control Conf., Seattle WA, pp. 3257-3262 (2008). 21. Moriyasu, S. and Y. Okuyama, "Surge propagation of pwm-inverter and surge voltage on the motor," Trans. Inst. Elec. Eng. Japan D, Vol. 119, pp. 508–514 (1999). 22. Ogasawara, S. and H. Akagi, "Modeling and damp- ing of high-frequency leakage currents in pwm inverter-fed ac motor drive systems,” IEEE Trans. Ind. Appl., Vol. 32, No. 5, pp. 1105–1114 (1996). 23. Narang, A., B. K. Gupta, E. P. Dick, and D. K. Sharma, "Measurement and analysis of surge dis- tribution in motor stator windings,” IEEE Trans. Energy Convers., Vol. 4, No. 1, pp. 126-134 (1989). 24. Doughty, R. L. and F. P. Heredos, “Cost-effective motor surge capability,” IEEE Trans. Ind. Appl., Vol. 33, No. 1, pp. 167–176 (1997). 25. Ahmad, M. A., R. M. T. R. Ismail, M. S. Ramli, N. M. Abd Ghani, and N. Hambali, “Investigations of feed-forward techniques for anti-sway control of 3-d gantry crane system,” IEEE Symp. Ind. Electron. Applicat., ISIEA 2009, Kuala Lumpur, Malaysia, pp. 265-270 (2009). 26. Singer, N., W. Singhose, and W. Seering, "Compari- son of filtering methods for reducing residual vibra- tion," Eur. J. Control, Vol. 5, No. 2, pp. 208–218 (1999). 27. Feddema, J., C. Dohrmann, and G. Parker, “A com- parison of maneuver optimization and input shaping filters for robotically controlled slosh-free motion of an open container of liquid," Proc. 1997 Amer. EX © 2015 Chinese Automatic Control Society and Wiley Publishin
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Explanation & Answer

sorry for the late, attached is my answer

The MATLAB code for crane is shown below:
function [input]= Crane(n,count1,begin,the_final,
d_A,d_B,theta_epsilon_final,nominaleps)
syms epsilon;
R = zeros(2*count1+2,2*count1+2);
r = zeros(2*count1+2,1);
INI = simplify(d_A^(2*count1+2));
steps = (2*count1+2)^2;
step = 0;
h = waitbar(0,'input calculated');
for j = 1:2*count1+2
f = simplify(d_A^(j-1)*d_B);
s=0;
for i = 1:count1
for m = 1:n-s
R(s+2*(i-1)+m,j) = real(1/factorial(i1)*subs(f(m+s),epsilon,nominaleps));
step = step+1;
waitbar(step/steps)
end
f=simplify(diff(f, sym('epsilon'), 1));
s=2;
end
end
s = 0;
for i=1:count1
ini = -(1/factorial(i-1))*subs(diff(INI* begin ', sym('epsilon'), (i1)),epsilon,nominaleps);
for count = 1:n-s
r(s+2*(i-1)+ count) = ini(count +s);
end
s = 2;
end
close(h)
for count = 1:n
r(count) = r(count)+ the_final(count);
end
if count1>1
r(5) = r(5)+theta_epsilon_final;
end
input = flipud(R\r);
end

The math equations for crane is shown below:

According to the above analysis, it can be verified that the above solution is correct.


The MATLAB code for pendulum is shown below:
g = 9.8;
l = 5;
ini_angle1 = pi/3;
ini_angle2 = 0;
pend_x = 0;
pend_y = l;
fprintf('simulation')
choice = input('1 = phase portrait; 2 = time serie');
iterations = 1;
time_pause = 0.2;
run = 40;
tx = 0;
deq1=@(t,x) [x(2); -g/l * sin(x(1))];
[t,sol] = ode45(deq1,[0 run],[ini_angle1 ini_angle2]);
s1 = sol(:,1)';
s2 = sol(:,2)';
arraysize = size(t);
timestep = t(run) - t(run-1);
Cx = l*sin(s1);
Cy = l*cos(s2);
for i = 1 : max(arraysize)
subplot(2,1,1)
plotx = [pend_x Cx(iters)];
ploty = [pend_y Cy(iters)];
plot(Cx(iters),Cy(iters),'ko',plotx,ploty,'r-')
title(['pendulum \theta = ' num2str(s1(iters))],'fontsize',15)
xlabel('x [m]','fontsize',15)
ylabel('y [m]','fontsize',15)
axis([min(Cx) max(Cx) min(Cy) max(Cy)])
subplot(3,2,3)
if choice == 1
plot(s1(iters),s2(iters),'bo')
hold on
title(' phase portrait','fontsize',15)
xlabel('\alpha1','fontsize',12)
ylabel('\alpha2','fontsize',12)
axis([min(s1) max(s1) min(s2) max(s2)])
elseif choice == 2
plot(t(iters),s1(iters),'bo')
title([' time series \alpha1 t = ' num2str(t(iters))],'fontsize',15)
xlabel('t [seconds]','fontsize',15)
ylabel('\alpha1...


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