Unbiased identification of finite impulse response linear systems operating in closed-loop

The force and position data used to construct models of joint dynamics are often obtained from closed-loop experiments, where the joint position is perturbed using an actuator configured as a position servo. If the position servo is orders of magnitude suffer than the joint, as is often the case, it is possible to treat the data as if they were obtained in open loop. It may be more relevant to study joint dynamics in compliant environments. This can be accomplished by adding an admittance controller, programmed to simulate a compliant environment, into the servo. Under these conditions, the presence of feedback cannot be ignored. Unbiased estimates of a system can be directly obtained from closed-loop data using the prediction error method. However, this is not true, in general, when linear regression or correlation-based analysis are used to fit nonparametric time- or frequency domain models. We develop a prediction error minimization based identification method for a nonparametric time-domain model, augmented with a parametric noise model. Simulations suggest that the method produces unbiased estimates of the dynamics of a system operating inside a feedback loop, even though linear regression results in substantial biases.