Problem-1: Assume a single-DOF motion control system whose mathematical model is given as: a(q) +b(9,4) + g(9) + text =

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Problem 1 Assume A Single Dof Motion Control System Whose Mathematical Model Is Given As A Q B 9 4 G 9 Text 1 (45.09 KiB) Viewed 23 times

Problem-1: Assume a single-DOF motion control system whose mathematical model is given as: a(q) +b(9,4) + g(9) + text = Kirer For this system, the torque constant and the inertia can respectively be given as a(q) = an + Aa and K = Kn+AK a) Express this system using the nominal parameters and lumping all of the remaining terms as disturbance. Clearly show the content of the disturbance in the parametric form. b) Find out the necessary current to compensate the disturbance term formulated in part a). c) The system is supposed to trace a twice differentiable continuous reference qref (t). Formulate a generalized error for this system. (Hint: The generalized error is a linear combination of the position and the velocity errors). d) Write down a differential equation for the error whose solution results in exponential convergence to zero from any initial value. e) Write down the expression for the desired current which enforces the tracking of the given reference qref (t).