Gain scheduling control of functional electrical stimulation for assisted standing up and sitting down in paraplegia: a simulation study

Abstract

This paper reports on a simulation study that concerns the design of a non-linear controller for the standing up and the sitting down of a paraplegic patient by means of functional electrical stimulation. The simulations refer to a specific experimental device developed at the Fondazione Don Gnocchi (Italy). This is a seesaw, with the patient on one side and a weight on the other side. The patient is seated so that its posture can be fully known in real-time by continuously monitoring the knee joint angle. By delivering a suitable electrical stimulation to the quadriceps muscles groups, the patient can be raised and made to sit via smooth movements. Hitherto, the only feedback control law, which has been implemented in this area, is based on a PID controller and usually provides poor tracking performances. Hence, in this work, a nonlinear gain scheduling controller has been designed and tested in a series of simulation experiments. The controller is tuned following a gain scheduling strategy: a set of local linear quadratic controllers is designed using a set of linear tangent models. A global non-linear gain scheduled controller is then obtained via interpolation. The gain-scheduled controller is implemented following an advanced strategy that guarantees that the so-called linearization property holds.

Robust compensation of electromechanical delay during neuromuscular electrical stimulation of antagonistic muscles

“…Examples of linear control methods include proportional integral derivative (PD/PID), linear quadratic Gaussian control, pole placement method, gain scheduling control method [13][14][15]. Nonlinear control methods [4][5][6][7][8][9][16][17][18] have also been recently developed for NMES.…”

“…Linear control methods for NMES applications include proportional integral derivative (PD/PID), linear quadratic Gaussian control, pole placement method, gain scheduling control [13][14][15]. However, because the musculoskeletal system is uncertain and nonlinear, and various external disturbances such as loads on muscle, muscle fatigue, and electromechanical delay (EMD) could lead the system to instability.…”

Predictor-Based Compensation for Electromechanical Delay During Neuromuscular Electrical Stimulation

“…A tracking error, denoted by , is defined to quantify the objective as (8) To facilitate the subsequent design and stability analysis, an auxiliary error signal is defined as (9) where are known constants (control gains). The unknown force-length, force-velocity, and moment arm relationships, represented by auxiliary function in (6), and the EMD present challenges for the subsequent control design.…”

“…The open-loop tracking error system can be developed by multiplying the time derivative of (9) by and utilizing the expressions in (1), (8), and (10) to obtain (12) where nonlinear functions and are defined as Let be defined as where the notation represents , expressed in terms of desired limb position and velocity. Based on (12) and the subsequent stability analysis, the voltage input is designed as (13) where is a known control gain that can be expanded as (14) to facilitate the subsequent analysis, where , , and are known constants.…”

Modelling and control of a device for rehabilitation of paraplegic patients

“…This means that a stabilizing PI feedback controller is applied to the plant. It is worth noting that this controller is not designed to achieve any specific tracking performance: its aim is only to provide external stability when closed in loop with the plant, so that data acquisition for identification can be done [10,11]. The I/O data for the model identification has been generated as follows: the closed loop system has been fed with a set of 27 pure-tone reference signals, i.e.…”