Partial pole placement by feedback control with inaccessible degrees of freedom

• Active vibration control by partial pole placement with inaccessible degrees of freedom.
• Double input controller with position, velocity and acceleration feedback.
• Linear formulation using measured receptances – typically from a modal test.
• Lower bound on the maximum number of inaccessible degrees of freedom.

Classical pole-placement theory requires that every degree of freedom shall be accessible to sensing but in physical systems there are often obstructions that make sensing at certain degrees of freedom impractical. In the classical formulation of the pole placement problem the input vector which determines the actuator gains is given and the pole placement problem is linear. If the input vector is not known and it is desired to find the gains of actuators and the gains of the measured state subject to some constraints then the problem becomes nonlinear since the unknown parameters multiply each other. It is shown that this nonlinear active vibration control problem is rendered linear by the application of a new double input control methodology implemented in conjunction with a receptance-based scheme where full pole placement is achieved while some chosen degrees of freedom are free from both actuation and sensing. A lower bound on the maximum number of degrees of freedom inaccessible to both actuation and sensing is established. A numerical example is provided to demonstrate the working of the method using the new double-input approach.