An unstable robot system is described by the vector differential equation [9] *1 _-r 2_

Chapter 0, Problem P11.3

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An unstable robot system is described by the vector differential equation [9] *1 _-r 2_ 1 [_- l o" 2 J *1 _*2 _ 4- r _ij "(') Both state variables are measurable, and so the control signal is set as u(t) = -k(xi + x2). Following the method of Section 11.7, design gain k so that the performance index is minimized. Evaluate the minimum value of the performance index. Determine the sensitivity of the performance to a change in k. Assume that the initial conditions are x(0) Is the system stable without the feedback signals due to u(0?

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