Inverse dynamics of non-minimum phase systems with non-zero initial conditions

A method is presented for computing the inverse dynamics of a linear non-minimum phase system with non-zero initial conditions. The method is also used to change or correct a trajectory after it is already in motion, and consequently, it will allow for real time control by continually updating the inverse dynamics computation. Frequency domain techniques are used to compute the input function needed to produce a desired output trajectory at a particular degree of freedom. An output profile based on the difference between the desired trajectory and either a homogeneous response or a forced response to a previous forcing function is used to compute the required input function. The resulting input function actively damps out initial conditions in the system and makes it track the desired trajectory. The method is applied to a non-collocated single-link flexible robot arm. The finite element method using Timoshenko beam theory is used to discretize the equations of motion. Torque profiles are computed to control the tip displacement for several problems. The first problem is to control the tip to a desired trajectory when starting with non-zero initial conditions. The second problem is to change the desired trajectory while the previous desired trajectory is already in motion. The third problem is to correct the trajectory after a disturbance is added to the system. The fourth problem is to analyze sensitivity to errors in the model and initial conditions. The last problem is to compare tip responses for rigid and flexible link assumptions in the inverse dynamics computation.