Data-Driven Adaptive Steady-State-Integral-Derivative Controller Using Recursive Least Squares With Performance Conditions

This paper presents a data-driven adaptive steady state-integral-derivative (SS-ID) control algorithm that uses gradient descent and recursive least squares (RLS) with a forgetting factor. A simplified first-order differential equation of the control system was designed and its parameters were estimated in real-time using the RLS algorithm. The steady-state control input for target-state tracking was derived based on the estimated parameters and steady-state performance conditions. The gradient of the integrated control error to the gain was estimated based on the least-squares method, using the saved past error and gain data in a finite sliding window to determine the control input. The integral gain was adapted based on the gradient descent method, using the estimated gradient, integrated error, and adaptation rate. Simplified control error dynamics were designed, and their parameter was estimated using the RLS algorithm. The derivative control gain can be adapted in real time using the estimated parameters from the simplified control error dynamics and time constant-based performance conditions. The proposed controller was designed in the MATLAB/Simulink environment. A performance evaluation was conducted under various scenarios using a DC motor simulation model and an actual test platform equipped with an optical encoder.

[1]  S. Redkar,et al.  Data-driven Koopman fractional order PID control of a MEMS gyroscope using bat algorithm , 2023, Neural Computing and Applications.

[2]  V. Agarwal,et al.  Design of Robust PID Controller Using PSO-Based Automated QFT for Nonminimum Phase Boost Converter , 2022, IEEE Transactions on Circuits and Systems - II - Express Briefs.

[3]  Mohd Ariffanan Mohd Basri,et al.  Position and Attitude Tracking of MAV Quadrotor Using SMC-Based Adaptive PID Controller , 2022, Drones.

[4]  K. Srinivasan,et al.  Reinforcement learning based adaptive PID controller design for control of linear/nonlinear unstable processes , 2022, Appl. Soft Comput..

[5]  Lu Liu,et al.  Robust yaw control of autonomous underwater vehicle based on fractional-order PID controller , 2022, Ocean Engineering.

[6]  S. Patil,et al.  Observer-based anti-windup robust PID controller for performance enhancement of damped outrigger structure , 2022, Innovative Infrastructure Solutions.

[7]  Ning Zhu,et al.  A data-driven approach for on-line auto-tuning of minimum variance PID controller. , 2022, ISA transactions.

[8]  Dario Giuseppe Lui,et al.  Leader tracking control for heterogeneous uncertain nonlinear multi-agent systems via a distributed robust adaptive PID strategy , 2022, Nonlinear Dynamics.

[9]  Edward Rajan Samuel Nadar,et al.  Real‐time data‐driven PID controller for multivariable process employing deep neural network , 2022, Asian journal of control.

[10]  Zili Wang,et al.  An Improved Fuzzy PID Control Method Considering Hydrogen Fuel Cell Voltage-Output Characteristics for a Hydrogen Vehicle Power System , 2021, Energies.

[11]  Tao Yu,et al.  A novel data-driven controller for solid oxide fuel cell via deep reinforcement learning , 2021, Journal of Cleaner Production.

[12]  Burhanettin Koc,et al.  Data-Driven Tuning of PID Controlled Piezoelectric Ultrasonic Motor , 2021, Actuators.

[13]  Hao Yu,et al.  Design of data-driven PID controllers with adaptive updating rules , 2020, Autom..

[14]  Aminurrashid Noordin,et al.  Adaptive PID Controller Using Sliding Mode Control Approaches for Quadrotor UAV Attitude and Position Stabilization , 2020, Arabian Journal for Science and Engineering.

[15]  N. Nejadkourki,et al.  Optimal fuzzy adaptive robust PID control for an active suspension system , 2020, Australian Journal of Mechanical Engineering.

[16]  Mingjun Zhang,et al.  Adaptive Sliding Mode PID Control for Underwater Manipulator Based on Legendre Polynomial Function Approximation and Its Experimental Evaluation , 2020, Applied Sciences.

[17]  Choi,et al.  A New Adaptive Fuzzy PID Controller Based on Riccati-Like Equation with Application to Vibration Control of Vehicle Seat Suspension , 2019, Applied Sciences.

[18]  Vincent Creuze,et al.  Saturation based nonlinear PID control for underwater vehicles: Design, stability analysis and experiments , 2019, Mechatronics.

[19]  Ravi Kumar Mandava,et al.  An adaptive PID control algorithm for the two-legged robot walking on a slope , 2019, Neural Computing and Applications.

[20]  Jamaluddin Hishamuddin,et al.  Implementation of PID controller tuning using differential evolution and genetic algorithms , 2012 .

[21]  Bore-Kuen Lee,et al.  FPGA-based adaptive PID control of a DC motor driver via sliding-mode approach , 2011, Expert Syst. Appl..

[22]  Nasser Sadati,et al.  Design of a fractional order PID controller for an AVR using particle swarm optimization , 2009 .

[23]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[24]  T. Chai,et al.  Signal-Compensation-Based Adaptive PID Control for Fused Magnesia Smelting Processes , 2023, IEEE transactions on industrial electronics (1982. Print).

[25]  Chun-Liang Zhang,et al.  Particle Swarm Sliding Mode-Fuzzy PID Control Based on Maglev System , 2021, IEEE Access.

[26]  Guoliang Zhong,et al.  Fuzzy adaptive PID fast terminal sliding mode controller for a redundant manipulator , 2021 .

[27]  W. Marsden.  I and J , 2012 .