hw2_ece238_F11

hw2_ece238_F11 - ECE 238 Advanced Control Design Laboratory...

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Unformatted text preview: ECE 238 Advanced Control Design Laboratory Fall 2011 Homework 2 (due 5pm Oct.14, in dropbox outside 3120A HFH) 2.1 Non-collocated Partial Feedback Linearization (PFL) control for the acrobot. In class, we looked at MATLAB simulation results for collocated PFL control of the acrobot (Figure 1), as outlined in Spong [2]. Download two m-files from the course homework website: ac- robot_collocated_linearization.m , which solves the equations of motion (EOMs) for the system with collocated PFL control , and acrobot_animate.m , which will allow you to ani- mate the motion. You can then run a simulation using the following MATLAB commands: X0 = [-pi/2+.1;0;0;0]; % set an initial condition [t,y] = ode45(@acrobot_collocated_linearization,[0 20],X0); % to simulate gure(1) acrobot_animate(t,y) % to animate a) Modify acrobot_collocated_linearization.m to implement non-collocated PFL control, as outlined in [2]. (It is probably best to begin by copying this m-file to a new file called ac- robot_noncollocated_linearization.m , so you have the old code to look at if you need to debug anything as you edit. In addition to [2], you may wish to reference the PFL class notes, handed out in class and also available for download from the class handouts website.) (i) Include a print-out of your code in your homework. (ii) Also include of a plot of the states over time, using X0 as given above. X Fig. 1. The Acrobot. Figure 1: The acrobot (image taken from [2, 1]; torque input at elbow not shown). (Last revised October 6, 2011) 1 Homework 2 ECE 238 Advanced Control Design Laboratory Fall 2011 2.2 Underpowered actuators. The torque required to achieve PFL control was not an issue ad- dressed in [2] nor in class so far. Separate from the issue of being underactuated (where we cannot independently control every degree of freedom), the system dynamics may be notice- ably underpowered. Motors, for example, generally provide much lower torque and higher velocity than desired (which is why they are often geared down). However, gearing down avelocity than desired (which is why they are often geared down)....
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hw2_ece238_F11 - ECE 238 Advanced Control Design Laboratory...

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