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

Abstract

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 8.94 • to 3.21 •-when comparing the tracking curves of the last cycle to the first cycle in the experiments with all stroke patients.

Speed Control of DC Motors: Optimal Closed PID-Loop Model Predictive Control

“…6: if L > T then 7: λ i ← λ 1 i 8: else 9: λ i ← λ 2 i λ 2 i ≥ λ 1 i > 0. 10: end if 11: K d ← f d (K p , ω n , ζ) 12: if τ L > 1 then 13: K d ← 1 /ts (L + ts) 14: end if 15: if L > T then 16: We have developed a method for optimizing the step response of a closed-loop system consisting of a 2DOF PID controller (b = 1 and c = 0) and the unknown dynamics of a LTI SISO plant. Compared to the Z-N methods, instead of using a stepresponse experiment to obtain a first-order plus dead time plant model estimate, we use this experiment to estimate the delayed settling time of the plant as its characteristic linear dynamic behaviour.…”

“…The tuning problem of searching for optimal PID parameters for a control task is NP-hard (nondeterministic polynomial-time) [15]. Hence, PID tuning for good control performance can be burdensome [13,16,17] even for very common servomechanism applications.…”

Optimized PID Control of Quadrotor System Using Extremum Seeking Algorithm

“…The body frame is specified by the quadrotor orientation, with the rotor axes positioned in the positive direction and the arms positioned in the and directions. The quadrotor attitude is concluded by three angles, which are terms, roll-φ, pitch-θ, and yaw-ψ [14,20]. The equations of quadrotor linear motion are [21]:…”

“…One of the most well-suited approach for achieving automated PID tuning, which is the Extremum Seeking Control (ESC) [12], where it utilizes a cost function that is based upon the difference between the real response and the preferred response. The output of the cost function will then be fed back to the extremum seeking (ES) loop to be able to tune the three parameters , and of the PID controller [13,14]. The ESC is a paradigm that aims to find an extremum value of an unknown nonlinear mapping.…”

Sintonia Ótima de Controladores PID Utilizando Técnicas de Modelagem Caixa-Cinza: Aplicação em um Sistema Viga-Hélice

“…O método proposto neste trabalho se encaixa neste contexto, pois utiliza técnica de otimização através da minimização de uma função de custo. Diversos métodos de sintonia de controladores PID podem ser encontrados na literatura, como por exemplo, o projeto de controladores PI e PID com especificação de desempenho transitório (Basilio, 2002) e projeto de controladores PID adaptativo baseados em busca extremal (Oliveira, 2019). O problema da sintoniaótima dos parâmetros do controlador PID pode ser enunciado da seguinte forma: "Definindo umíndice de desempenho para o sistema a ser controlado, determinar o ganhos do controlador PID(K p , K i , K d ) de maneira que, dentro do intervalo de tempo especificado, a resposta do sistema de controle minimize oíndice…”