Patent ID: 8855826

Claim:
A controller for reducing vibration and positioning a load in a mechanical system driven by a motor connected to the load, comprising: an optimal feedforward module designed according to a model of the system; a linear feedback module; and a nonlinear feedback module, wherein inputs to the linear feedback module and the nonlinear feedback module are an angular position and an angular velocity of the motor, and outputs of the optimal feedforward module, the linear feedback module, and the nonlinear feedback module are summed and fed back to control a torque of the motor, wherein the model is a 3-mass lumped parameters model, wherein the load is represented by a mass m L with a linear damping coefficient d M , the base is represented by a mass m B with linear damping and spring coefficients d B and k B respectively, a linear motion of the load with respect to the base is x L , a linear motion of the base with respect to an inertial base is x B , and external disturbances due to an environment and acting on the load are represented by the a time function d(i), and the model is given by a differential equation J M {umlaut over (x)} M +D ( {dot over (x)} M −{dot over (x)} L )+ K ( x M −x L )= u−J M {umlaut over (x)} B J L {dot over (x)} L +D ( {dot over (x)} L −{dot over (x)} M )+ K ( x L −x M )=− J L {umlaut over (x)} B J B {dot over (x)} B +D B {dot over (x)} B +K B x B =−u y=x M where {dot over (x)} and {umlaut over (x)} are the first and second derivative of x with respect to time t, and wherein the position of the motor is x M , the load is represented by an inertia J L , the motor is represented with an inertia J M , the base is represented with an inertia J B , and the motor is controlled by a torque u, and K B , and D B represent linear spring coefficient and the linear damping coefficient of the base, respectively.