Control of a fourth-order linear system with mixed constraints (Q2761359)

The paper deals with a linear controlled mechanical fourth-order system containing an oscillating link. The equations of motion are \(m_1\ddot y+ky = -u\), \(m_2\ddot z = u\), where \(m_1\) and \(m_2\) are masses of bodies, \(k>0\) is a positive parameter, and constraint has the form \(|u(t)|\leq a\), \(a>0\). The author solves the problem of bringing this system to a given state in a finite time. The solution employs an approach based on Kalman's general scheme for constructing controls as linear combinations of characteristic motions of uncontrolled system. Results of numerical simulation of the dynamics of a closed system are presented.