Issued: 14-September-2016 (Wk 8) Due: 02-Nov-2016 (Wk 14) AUTO1029 PROJECT-2016 Page 1 AUTO-1029 "AUTOMOTIVE SYSTEMS & CONTROL" STANDARD PROJECT "INTEGRAL APPLICATION OF SKILLS ON THE DYNAMIC MODELLING, SIMULATION, CONTROL AND ANALYSIS OF COMPLEX SYSTEMS" Consider the mobile mechanical system shown below. Fig.1. Illustration of the mobile system to be explored in the Project. It is modelled as a continuous system (in 2D plane) with THREE degrees of freedom: translation h of the trolley, the angle of the cable  and the variable length l of the cable.Issued: 14-September-2016 (Wk 8) Due: 02-Nov-2016 (Wk 14) AUTO1029 PROJECT-2016 Page 2 Complete the following tasks: (1) Derive the non-linear Equations of Motion for the System, using the Lagrange's Equations method. Employ the generic notations. (2) For m1=2kg; m2=5kg;  =1m, simulate the motion of the system excited with the external force, shown in the figure below and described with the following ttt-uuu matrices: ttt=[0, 5, 5.1, 6, 6.1, 6.3, 6.4, 10, 10.1, 11, 11.1, 20]; uuu=[0, 0, 1, 1, -2, -2, 0, 0, -.3, -.3, 0, 0 ]*50. Calculate the final position of the trolley 'qf' and the number 'Nb' of the "barrel rolls" performed by the pendulum during 0-20sec. Clearly show your answers in the framed boxes. Fig.2. Illustration to the Task (2). (3) Use these equations for a particular case of the constant length  = 10m of the cable, m1=20kg and m2=50kg and design the control scenario [i.e. propose the appropriate F(t) ] for the transfer of the payload m2 from the system's equilibrium (h=0 and =0) to the new horizontal position (h=20m and =0) with the htransfer=20m.Issued: 14-September-2016 (Wk 8) Due: 02-Nov-2016 (Wk 14) AUTO1029 PROJECT-2016 Page 3 Fig.3. Illustration to the Task (3). The diagram is not to scale. Aim to minimize the time of the transfer and achieve the horizontal swing of the payload no larger than 10cm. Use any of the control methods of your choice and present your detailed solution. Simulate your results (using MATLAB or SIMULINK or both) and show that after the transfer the transfer requirements are satisfied. If possible, animate your solution – this could be used for the demonstration to the other Groups as convincing evidence of the successful solution of the problem. (4) For the case of the variable length cable start from static equilibrium ( = 10m, h=0 and =0), manipulate with the applied control force F and, IF you wish, with the length of the cable  to gently deploy the payload to the point h=10m, w=-5m.Issued: 14-September-2016 (Wk 8) Due: 02-Nov-2016 (Wk 14) AUTO1029 PROJECT-2016 Page 4 Fig.4. Illustration to the Task (4). The diagram is not to scale. Performing this operation, you are not restricted with the horizontal range of the trolley and are allowed any manipulation with the length of the cable, providing that the length  is not reduced below its minimal critical length of 2m. Aim to achieve the minimum time of the operation. (5) For the case of the variable length cable start from static equilibrium ( = 10m, h=0 and =0), manipulate with the applied control force F and, IF you wish, with the length of the cable   to "throw" the payload and land it on the flat surface w=-30m. Performing this operation, you are allowed any manipulation with the length of the cable and/or cut it at the appropriate time. At the same time, the trolley's centre of the mass should always stay within the h limits of plus/minus 2m.Issued: 14-September-2016 (Wk 8) Due: 02-Nov-2016 (Wk 14) AUTO1029 PROJECT-2016 Page 5 Fig.5. Illustration to the Task (5). The diagram is not to scale. Aim to achieve the largest horizontal position hlanding of the "landing" of the payload. You may wish to use open OR closed control loop techniques. Explain your strategies and solution. Simulate your results with the proposed payload transfer scenarios and, if possible, animate your solutions. (6) Comprehensively discuss your results.