Runge–Kutta model-based adaptive predictive control mechanism for non-linear processes

Abstract

This paper proposes a novel non-linear model predictive control mechanism for non-linear systems. The idea behind the mechanism is that the so-called Runge–Kutta model of a continuous-time non-linear system can be regarded as an approximate discrete model and employed in a generalized predictive control loop for prediction and derivative calculation purposes. Additionally, the Runge–Kutta model of the system is used for state estimation in the extended Kalman filter framework and online parameter adaptation. The proposed method has been tested on two different non-linear systems. Simulation results have revealed the effectiveness of the proposed method for different cases.

A novel auto-tuning PID control mechanism for nonlinear systems

“…In addition to the introduction of a novel method, we have conducted two real-time control experiments on a SISO (unstable nonlinear MagLev system) and a MIMO (nonlinear three-tank liquid-level system) system. Moreover, the experimental studies include noisy and disturbance cases, and comparisons to control methods namely, standard PID, standard NMPC, RK-MPC [29] and standard SMC from the literature, which reinforces the contribution of the paper to the control theory literature.…”

“…In this work, a novel RK model-based auto-tuning PID controller for nonlinear continuous-time system is presented. In this structure, a discretized model of the nonlinear system which is called the RK model [29] is obtained by the fourth-order RK algorithm and then utilized for the control of the systems. The RK model of the system is used for many purposes such as control, prediction, Jacobian calculation, parameter and state estimation [29,30].…”

“…In the fuzzy predictive model, fuzzy control is used for controlling the uncertainty of the linear/nonlinear systems whose dynamics are unknown. In [29], a RK model-based predictive control, state and parameter estimation approach has been proposed, which inspired us to develop a robust, adaptive and predictive PID auto-tuning mechanism.…”

Multimode laser cooling and ultra-high sensitivity force sensing with nanowires

“…We use two different estimation strategies based on the discrete extended Kalman filter (EKF) 33 and the virtual cooling method 18 to enhance the SNR (refer to Supplementary Note 5 for more details). To identify the statetransition matrix of the EKF, we need to know the natural frequency, damping rate, initial amplitude, initial velocity, time interval, process and measurement noise vectors and initial covariance estimates.…”

Observer Design for the Hodgkin-Huxley Neuronal Model

“…As a leading work on state observers have been first published for linear systems [6], and then extended for nonlinear systems [7]. With the requirements on the state estimation, there have introduced several nonlinear observers such as extended-Luenberger observer [8], extendedKalman filter [9], sliding-mode observer [10], [11], high-gain observer [12], Takagi-Sugeno fuzzy observers [13], Runge-Kutta observer [14]- [16] etc. The nonlinear observers mentioned above are based on the mathematical model of the nonlinear system.…”