Extremum Seeking-based Adaptive PID Control applied to Neuromuscular Electrical Stimulation

A multivariable deterministic extremum seeking (ES) is being evaluated to construct an adaptive Proportional-Integral-Derivative (PID) control law for the functional Neuromuscular Electrical Stimulation (NMES) of stroke patients. The developed scheme is applied to control the position of the patient's arm so that movements of flexion/extension for its elbow can be produced. The true limitations of a PID controller for these types of applications is that a PID controller is designed for linear systems, but the system which is being controlled is nonlinear. Moreover, it is worth mention that clinicians' knowledge of control systems is limited. Therefore, their expertise in tuning controllers is limited. Also, in NMES applications each patient is unique and requires a unique set of PID parameters. Since it can be time consuming and difficult to find proper parameters for each patient, a better procedure, or a more intelligent adaptive controller, is needed. The PID parameters are updated by means of ES in order to minimize a cost function which brings the desired performance attributes. Experiments are performed with healthy volunteers and stroke patients, including significant advances based on real data and validation. Quantitative results show a reduction of 64:1% in terms of RMSE (Root-Mean-Square Error) - from 8:94º to 3:21º - when comparing the tracking curves of the last cycle to the first cycle in the experiments with all stroke patients.