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Industrial robots have a key role in the concept of Industry 4.0. On the one hand, these systems improve quality and productivity, but on the other hand, they require a huge amount of energy. Energy saving solutions have to be developed and applied to provide sustainable production. The purpose of this research is to develop the optimal control strategy for industrial robots in order to minimize energy consumption. Therefore, a case study was conducted for the development of two control strategies to be applied to the RV-2AJ Mitsubishi robot arm with 5 DOF, where the system is a nonlinear one. The first examined controller is the classical linear proportional integral derivative (PID) controller, while the second one is the linear model predictive control (MPC) controller. In our study, the performances of both the classical PID model and the linear MPC controller were compared. As a result, it was found that the MPC controller in the execution of the three defined reference trajectories [(1) curve motion, (2) N-shaped motion, and (3) circle motion] was always faster and required less energy consumption, whereas in terms of precision the PID succeeded in executing the trajectory more precisely than the MPC but with higher energy consumption. The main contribution of the research is that the performances of the two control strategies with regard to a complex dynamic system were compared in the case of the execution of three different trajectories. The evaluations show that the MPC controller is, on the one hand, more energy efficient; on the other hand, it provides a shorter cycle time compared to the PID controller.

This article presents a comparison between a classical PID controller and a fractional-order PID (FOPID) controller for a gyroscope with Cardan suspension (3 DOF). A gyroscope dynamics model accounting for gyroscopic couplings and viscous damping is adopted, while the FOPID controller is implemented in discrete form using the Grünwald–Letnikov (GL) operator, which reduces smoothly to the classical PID when λ = μ = 1. The effectiveness of both strategies is assessed in a moving-target tracking task using the IAE (tracking accuracy) and ISC (control effort) indices. MATLAB/Simulink R2025a simulations (ode4, Δt = 2 × 10−4 s) show that, under cross-axis couplings of the gyroscope suspension, FOPID yields smaller tracking errors and smoother control signals than PID. The results indicate the usefulness of fractional-order controllers in gyroscope control systems and provide a basis for further experimental studies.

In this paper, the velocity and altitude control problem of hypersonic vehicles is studied. Aiming at the nonlinear parameter uncertainties, external disturbances and coupling of the hypersonic vehicle system, a control method combining backstepping control with linear active disturbance rejection control is proposed. The backstepping control solves the coupling of the system and transforms the longitudinal dynamic model of the hypersonic vehicle into the form of strict feedback, which is divided into the altitude subsystem and velocity subsystem. The linear extension state observer (LESO) can observe parameter uncertainty disturbance and external disturbance. At the same time, the stability of the system is proved by Lyapunov theory. Finally, the effectiveness of the designed controller is verified by numerical simulation and comparison with classical PID control.

This paper presents a hybrid fuzzy-PID controller for air flow supply on a Proton Exchange Membrane fuel cell (PEMFC) system. The control objective is to adjust the oxygen excess ratio at a given a set-point in order to prevent oxygen starvation and damage of the fuel-cell stack. The proposed control scheme combines a fuzzy logic controller (FLC) and classical PID controller with a view to benefit the advantages of both controllers. The results show that the proposed technique performs significantly better than the classical PID controller and the FLC in terms of several key performances indices such as the Integral Squared Error (ISE), the Integral Absolute Error (IAE) and the Integral Time-weighted Absolute Error (ITAE) for the closed-loop control system.

In this paper, we introduce a novel tuning procedure to ensure semi-global exponential stability for the classical PID control of rigid robots. This tuning procedure is expressed in terms of conditions which are more relaxed than those proposed previously in the literature. This allows us to perform, for the first time, experimental tests with a classical PID controller ensuring semi-global exponential stability. Finally, we show numerically that previous formal tuning procedures in the literature result in very large controller gains which prohibit the performance of any experimental test.

Based on the real operation requirements of experimental advanced superconducting tokamak (EAST) articulated inspection arm (AIA) CASK baking system, this paper focuses on how to achieve high accuracy of temperature control. Given the complexity of temperature control system, a hybrid of fuzzy and proportional-integral-derivative (PID) controller is designed. According to the conditions that exist, a testing experiment that simulates the CASK baking system is built. Through the analysis of the experimental results, a hybrid of fuzzy and PID control algorithm is designed as the core strategy of the temperature control system.

Abstract This paper presents a genetically trained PID (proportional-integral-derivative)-like ANFIS (adaptive neuro-fuzzy inference system) acting as a feedback controller to control non-linear systems. Three important issues are addressed in this paper, which are, first, the evaluation of the ANFIS as a PID-like controller; second, the utilization of the GA (genetic algorithm) alone to train the ANFIS controller, instead of the hybrid learning methods that are widely used in the literature; and, third, the determination of the input and output scaling factors for this controller by the GA. The GA, with real-coding operators, is used to adjust all of the ANFIS parameters, which include the input and output scaling factors, the centres and widths of the input membership functions (MFs), and the consequent parameters. To show the effectiveness of this controller and its learning method, several non-linear plants, including the CSTR (continuous stirred tank reactor), have been selected to be controlled by this controller through simulation. Moreover, this controller's robustness to output disturbances has also been tested and the results clearly indicated the remarkable performance of this controller and its learning algorithm. In addition, the result of comparing the performance of this controller with a genetically tuned classical PID controller has shown the superiority of the PID-like ANFIS controller.

The comparison of the stability robustness between the classical PID controller and two piecewise linear PID-like fuzzy controllers to the variations of the parameters in the second order plant is provided in this paper. The definition of a stability robust controller (to the parameter variations of the plant model) is presented. Then Kharitonov’s theorem is applied to find the regions of robustness to the parameter variations for the control systems with different controllers. Based on the size of regions of robustness, the relative robustness factor is defined, and the robustness comparison is provided. For every classical PID controller with gain coefficients determined and fixed, it is shown that we can always design the piecewise linear PID-like fuzzy controllers to be more robust than the specific classical PID controller. The results of robustness comparison is further confirmed in the simulation included for the second order uncertain plant.

This paper addresses the design of a robust Lyapunov-based controller for flexible-joint electrically driven robots considering to voltage as control input. The proposed approach is related to the key role of electrical subsystem of the motors, thus is free from mechanical subsystem of the actuator dynamics, considered here as unmodeled dynamics. The main contribution of this paper is to prove that the closed-loop system composed by full nonlinear actuated robot dynamics and the proposed controller is BIBO stable, while actuator/link position errors are uniformly ultimately bounded stable in agreement with Lyapunov’s direct method in any finite region of the state space. It also forms a constructive and conservative algorithm for suitable choice of gains in PID controller. The analytical studies as well as experimental results produced using MATLAB/SIMULINK external mode control on a flexible-joint electrically driven robot demonstrate high performance of the proposed control schemes.

We investigate the closed-loop control of a circular cylinder showing lock-in phenomena due to vortex-induced vibrations (VIV). The control action was implemented by a sampled-data proportional-integral-derivative (PID) controller to suppress the large amplitudes due to lock-in. The controller was first applied to a linearized system to observe its stability characteristics based on the eigenvalues of the system. Another method was also proposed, which employs a novel, time-dependent Lyapunov function that is positive definite at sampling times but not necessarily between the sampling times. A new set of sufficient conditions in terms of linear matrix inequalities is derived to obtain the sampled-data PID control gains for the VIV system. The PID controller tuned with these gains for various delays was applied to control the nonlinear responses of the circular cylinder during the lock-in. The results showed that the PID controller significantly reduced the rise in lock-in amplitude compared to only proportional control and for certain delays was able to completely mitigate the effects of lock-in. It was also observed that for delays ranging from 0.1 to 0.14 s, the nonlinear system was destabilized with increasing proportional gains as indicated by the eigenvalue analysis of the linearized system. Even under such situations, properly tuned integral and derivative gains could significantly reduce the amplitude rise otherwise observed due to lock-in of the uncontrolled system. Finally, an on-off control scheme was also proposed, which, if optimized properly, can restrict the lock-in amplitude to some prescribed limit by only using the control for some fraction of the total operational time. Thus, it can potentially save control power.