Robust Control of the Knee Joint Angle of Paraplegic Patients considering Norm-Bounded Uncertainties

Abstract

A proposal for the knee position control design of paraplegic patients with functional electrical stimulation (FES) using control systems and considering norm-bounded uncertainties is presented. A state-space representation of the knee joint model of the paraplegic patient with its nonlinearity is also demonstrated. The use of linear matrix inequalities (LMIs) in control systems with norm-bounded uncertainties for asymptotic stability is analyzed. The model was simulated in the Matlab environment. The matrix of state space feedback was obtained through LMIs.

Discrete Takagi-Sugeno Fuzzy Models Applied to Control the Knee Joint Movement of Paraplegic Patients

“…hold, where To guarantee the input constraint, LMIs (35) and (36) need to be added to the LMIs that guarantee stability, given in (31) and (32), or decay rate, given in (33) and (34).…”

“…Other articles on the human muscles command issue have been recently published, such as [16], [26]- [32], and [33]. The model of [16] uses a linear and a nonlinear block of the state space model to apply variable structure control.…”

Robust T-S Fuzzy Control of Electrostimulation for Paraplegic Patients considering Norm-Bounded Uncertainties

“…So, the mathematical model of the functional electrical stimulation of the knee angle of the paraplegic patient is represented as a T-S fuzzy combination of two local models, considering the minimum and the maximum values of the nonlinear term 􏽥 f 21 (x 1 ). In [9], the nonlinear term 􏽥 f 21 (x 1 ) is considered as the uncertain parameter, and the parameters B, J, τ, and G of the shank-foot complex model have definite values. However, these parameters assume different values each day, depending on the health conditions of the patient at each moment.…”

“…In order to obtain the muscle contraction, the amplitude (or intensity) and duration of the electrical stimulus must be inside specific bounds. en, the AP is generated and propagates in both directions of the nerve fiber [9]. Complex mechanisms of electrochemical stimuli occur in the neuromuscular structure causing the process of excitation-contraction coupling responsible for the movement of the leg [11].…”

“…Mathematical Problems in Engineering of the amplitude or pulse duration [9,11]. As can be seen in Figure 1, the degree of muscle activation (α) is a nonlinear function that depends on the duration of the stimulus d.…”