Nonlinear PID Research Articles

New tuning formulas for a nonlinear PID control scheme

New tuning formulas for a nonlinear PID control scheme

Parameter optimization of nonlinear PID controller using RBF neural network for continuous stirred tank reactor

The temperature system of the Continuous Stirred Tank Reactor (CSTR) has the characteristics of strong nonlinearity and uncertain parameters. The linear PID controller makes it difficult to meet CSTR’s control requirements. Nonlinear PID (NPID) can improve the control effect of nonlinear controlled objects, but due to the influence of nonlinear function selection and manual parameter setting, when parameters are uncertain or subject to external interference, the control performance of the system will decrease. To improve the adaptive capability of the NPID controller, the RBF-NPID control algorithm is proposed. The learning ability of RBF neural network is used to adjust NPID parameters online to improve the control performance of the system. In order to verify the effectiveness of the proposed algorithm, a CSTR model was established in MATLAB and algorithm comparison research was carried out. Simulation results show the effectiveness and superiority of the proposed algorithm.

A Comparative Study of Various Intelligent Algorithms Based Nonlinear PID Neural Trajectory Tracking Controller for the Differential Wheeled Mobile Robot Model

This paper presents a comparative study of two learning algorithms for the nonlinear PID neural trajectory tracking controller for mobile robot in order to follow a pre-defined path. As simple and fast tuning technique, genetic and particle swarm optimization algorithms are used to tune the nonlinear PID neural controller's parameters to find the best velocities control actions of the right wheel and left wheel for the real mobile robot. Polywog wavelet activation function is used in the structure of the nonlinear PID neural controller. Simulation results (Matlab) and experimental work (LabVIEW) show that the proposed nonlinear PID controller with PSOlearning algorithm is more effective and robust than genetic learning algorithm; this is demonstrated by the minimized tracking error and obtained smoothness of the velocity control signal, especially when external disturbances are applied.

Design of the roll and heel reduction controller on ship’s turning motion

When the ship turns, it will heel and exacerbate the roll triggered by the sea waves, ultimately impacting the safe navigation of the ship. A study was conducted on a design method for a roll and heel reduction controller based on nonlinear feedback to mitigate the ship’s roll and heel during turning motion. A mathematical model was established for a ship with four degrees of freedom. Subsequently, a systematic analysis was conducted on the hydrodynamic force, rudder force, fin force and wave disturbance force of the ship. The ship’s roll and heel motion are reduced by controlling the roll reduction force generated by the fin. The roll and heel reduction controller uses a nonlinear PID controller with parameters that vary with the feedback signal. This effectively enhances the dynamic response characteristics of the system. Simulations were performed to analyze the effect of different rudder angles and different fin angles on the performance of the ship’s turning motion. The nonlinear feedback technique is employed to decrease the output of the fin angle, minimize the mechanical wear of fin stabilizer and save energy without compromising the control performance. The study analyzed the effect of a nonlinear feedback based controller in reducing roll and heel during turning motions of a ship. Simulations were conducted and compared with the classical PID controller method. The results indicated that the nonlinear feedback controller had a better performance in reducing roll and heel, validating the effectiveness of the designed method.

Co-optimization energy management strategy for a novel dual-motor drive system of electric tractor considering efficiency and stability

The challenge in developing an electric tractor control strategy lies in operating efficiently and smoothly in most conditions. This paper put forward a co-optimization energy management strategy (EMS) for dual-motor electric tractors to achieve working efficiency and smoothness simultaneously in typical conditions including ploughing, rotary tillage and transportation. Firstly, the mathematical models for components of the drive system are established, such as the power transfer model and gear shifting model. Secondly, the novel EMS combining demand torque calculation method (DTCM) and driving torque distribution strategy (DTDS) is proposed, which is based on nonlinear PID control and modified snake optimizer (SO) algorithm respectively. Then, the hardware in the loop (HIL) platform is manufactured, and load data for the HIL test collecting by a tractor operating in the field. Finally, the performances of the electric tractor with the novel EMS in three typical conditions are validated. It shows that EMS can identify the demand torque accurately. Compared to the rule-based algorithm with reasonable parameters, the novel EMS improves efficiency and stability significantly, especially in ploughing increasing efficiency by 14.44% and decreasing jerk fluctuates by 73.33%. The research results can provide theoretical references for developing the EMS of the electric tractor.

Nonlinear PI“D”-Type Control of Flexible Joint Robots by Using Motor Position Measurements Is Globally Asymptotically Stable

An important subject that arises in the position control of robot manipulators is the local or global asymptotic stability of the closed–loop system equilibrium point, especially when an integral action is added to the control loop. For rigid joint robot manipulators, global nonlinear PID controllers have been introduced few years ago. However, for the case of flexible join robot manipulators, the design and analysis of such nonlinear PID laws is much more challenging. Only local asymptotic stability results have been reported. Thus, a novel global regulator for flexible joint robots is presented in this document. The proposed controller considers a nonlinear integral action and it requires only motor position measurements because an estimator subsystem is used to replace the motor velocity measurements. In other words, a nonlinear proportional-integral-“derivative” (PI“D”)-type controller is introduced. According to the closed–loop system analysis, conditions on the controller gains are established. Thus, the global asymptotic stability is concluded. Finally, experimental results on a two degrees-of-freedom serial flexible joint robot are shown and discussed.

An adaptive neural network with nonlinear FOPID design of underwater robotic vehicle in the presence of disturbances, uncertainty, and obstacles

An adaptive neural network with nonlinear fractional-order PID (ANNFOPID) controller design is proposed for underwater robotic vehicle (URV) to solve the path tracking problem. The path tracking problem is caused by disturbances and unknown uncertainties of the underwater vehicle dynamic model. The disturbances were presented with the URV model to evaluate the performance of the ANNFOPID controller to reject the disturbances. At the same time, an obstacle avoidance model has been presented with ANNFOPID controller to evaluate the controller ability to maneuver around different obstacle locations. A radial base function (RBF) has been used to estimate both of the disturbances and the unknown uncertainties of the dynamic model. An improved slime mould algorithm (ISMA) is presented to invent a new trajectories for the underwater vehicle and enhance the ability of the URV to overcome the obstacles problems. At the end, the results obtained show that the ANNFOPID controller present an outstanding performance in comparison with other existing works to overcome the disturbances, unknown uncertainties, and obstacles problems effectively.

A New Self-Tuning Nonlinear PID Motion Control for One-Axis Servomechanism with Uncertainty Consideration

This paper introduces a new study for one-axis servomechanism with consideration the parameter variation and system uncertainty. Also, a new approach for high-performance self-tuning nonlinear PID control was developed to track a preselected profile with high accuracy. Moreover, a comparison study between the proposed control technique and the well-known controllers (PID and Nonlinear PID). The optimal control parameters were determined based on the COVID-19 optimization technique. The parameters of the servomechanism system changed randomly at a preselected range through the online simulation. The change of these parameters acts as the nonlinearity resources (friction, backlash, environmental effects) and system uncertainty. A comparative study between the linear and nonlinear models had been accomplished and investigated. The results show that the proposed controller can track several operating points with high accuracy, low rise time, and small overshoot.

Design of Auto-Tuning Nonlinear PID Tracking Speed Control for Electric Vehicle with Uncertainty Consideration

This study presents a new auto-tuning nonlinear PID controller for a nonlinear electric vehicle (EV) model. The purpose of the proposed control was to achieve two aims. The first aim was to enhance the dynamic performance of the EV regarding internal and external disturbances. The second aim was to minimize the power consumption of the EV. To ensure that these aims were achieved, two famous controllers were implemented. The first was the PID controller based on the COVID-19 optimization. The second was the nonlinear PID (NPID) optimized controller, also using the COVID-19 optimization. Several driving cycles were executed to compare their dynamic performance and the power consumption. The results showed that the auto-tuning NPID had a smooth dynamic response, with a minimum rise and settling time compared to other control techniques (PID and NPID controllers). Moreover, it achieved low continuous power consumption throughout the driving cycles.

A hybrid sliding mode control based on a nonlinear PID surface for nonlinear chemical processes

This work formulated and synthesized a hybrid control framework based on sliding mode control and internal model concepts. The resulting design conducts a Dynamic Sliding Mode Control (DSMC) approach based on a Nonlinear PID (NPID) sliding surface. The design procedure first uses the reaction curve identification method to obtain a reduced-order model from the nonlinear system. A First-Order Plus Dead-Time (FOPDT) model represents the reduced order model. The resulting controller is derived from the reduced-order model and the nonlinear surface. Therefore, a hybrid control framework (DSMC-NPID) is obtained and then applied to a couple of nonlinear chemical processes, a Variable Height Mixing Tank (VHMT), and a Continuous Stirred Tank Reactor (CSTR) in both cases to track reference trajectories and reject disturbances. Then, the proposed control approach is assessed and compared to a PID controller and a DSMC with a linear PID surface. Such evaluation is carried out using control performance indices such as Integral Square Error (ISE), Maximum Overshoot (MO), control total variation (TVu), and Settling Time (ST), respectively. Finally, the results of experimental trials were quantitatively compared to each controller, demonstrating that the DSMC-NPID approach could reduce the ISE by around 6.3%, MO by 89.3%, and ST by 17.6% regarding DSMC-PID. In addition, the results obtained for the CSTR system were similar, demonstrating that the proposed control strategy is suitable for different industrial processes.

Performance of the optimal nonlinear pid controller for position control of antenna azimuth position system

This study presents the improvement in the performance of the Proportional-integral-derivative (PID) controller for position control of antenna azimuth position system subjected to external disturbance. The design of the PID controller is developed by adding the arc tan function of error instead of the direct error in an integral part of the PID controller, yielding a Nonlinear PID controller (NPID). A Particle Swarm Optimization (PSO) is used in this study to tune the parameters of the PID and NPID controllers using the Root Mean Square Error (RMSE) cost function. The simulations have been accomplished under the MATLAB/Simulink environment. The simulation results show that a PSO-based NPID controller provides superior steady and transient state performance compared to a PSO-based PID controller. In addition, the effectiveness of the proposed controller is verified via numerical simulation compared to the performance of other controllers with and without external disturbance.

Design of intelligent nonlinear robust controller for hydro-turbine governing system based on state-dynamic-measurement hybrid feedback linearization method

Due to the stochastic grid loads and intermittent renewable energy sources in today’s power grid, hydro-generator and grid system stability is increasingly dependent on the hydro-turbine governing system (HTGS). For the HTGS with external disturbances and system uncertainties, an intelligent nonlinear robust controller (INRC) based on state-dynamic-measurement feedback linearization (SDMFL) is proposed to enhance the HTGS’s control performance in this paper. This strategy establishes a dynamic output function including actuator displacement, generator rotor angle, and turbine parameters. The relationship between dynamic output and control input is derived based on this function to establish the corresponding linear state-space model. Then, the mixed H2/H∞ robust controller based on the linear model is designed to suppress the effects of external disturbances and system uncertainties on the system performance. In addition, the controller performance is optimized by levy flight and chaos theory-based gravitational search algorithm (LCGSA), resulting in the INRC. Simulations are performed in MATLAB, and the results are compared with the nonlinear robust controller (NRC) and PID controller. The results show that the proposed controller INRC improves the control performance of nonlinear HTGS with smaller overshoot and shorter adjustment time in all cases.

Application of Nonlinear PID Active Disturbance Rejection Control in the Temperature Control System of Fast Steering Mirror

Application of Nonlinear PID Active Disturbance Rejection Control in the Temperature Control System of Fast Steering Mirror

Design of Cross‐Coupled Nonlinear PID Controller Using Single‐Objective Evolutionary Algorithms

The effectiveness of evolutionary algorithms (EAs) such as differential search algorithm (DSA), Real‐Coded genetic algorithm with simulated binary crossover (RGA‐SBX), particle swarm optimization (PSO), and chaotic gravitational search algorithm (CGSA) on the optimal design of cross‐coupled nonlinear PID controllers is compared in this paper. A cross‐coupled multivariable PID controller structure for the binary distillation column was developed with two inputs and two outputs. EA simulations are run to lower IAE using two stopping criteria, namely, maximum number of functional evaluations (Fevalmax) and Fevalmax plus PID parameter and IAE tolerance. Over 20 separate trials were used to compare the performances of several EAs using statistical measures such as best, mean, standard deviation of outcomes, and average calculation time. This article presents the design of a cross‐coupled nonlinear PID controller using single‐objective evolutionary algorithms. Using evolutionary algorithms (EAs) with a multicrossover strategy, the results achieved by various EAs are compared to previously reported results. The results of a multivariable cross‐coupled system clearly show that a single‐objective nonlinear PID controller performs better. Simulations further show that all four techniques evaluated are suitable for PID controller tweaking off‐line. However, only the single‐objective evolutionary algorithms are acceptable for online PID tuning due to their higher consistency and shorter computation time.

A new nonlinear PID controller design for a quadrotor system using teaching learning based optimisation algorithm

A new nonlinear PID controller design for a quadrotor system using teaching learning based optimisation algorithm

Fall down and re-levitation dynamics of an electric rotor system with nonlinear AMB forces under base excitations: Modeling and experiment

The fall down and re-levitation dynamics of an eccentric electric rotor system under base excitations are investigated theoretically and experimentally. A universal unbalanced electromagnetic force model considering both the dynamic and static eccentricities is proposed. The coordinate system can remain unchanged and the direction of eccentricities can be characterized. The nonlinear suspension model for the AMB is derived and the scope of application is enlarged. Based on the unbalanced electromagnetic forces, nonlinear suspension forces and contact forces of touchdown, the dynamic models of electric rotor system and inner race are established, respectively. Furthermore, the re-levitation control is examined and a nonlinear PID re-levitation approach is adopted. Numerical simulations and experiments are conducted to investigate the regular, fall down and re-levitation dynamics for different eccentricities, rotating speeds and base excitations, etc. Results of experiments and numerical simulations are in perfect good agreement. Results and discussions indicate that the unbalanced electromagnetic model considering the amplitude and direction of various eccentricity cases is universal and can be smoothly applied in the analytical or numerical calculation. Moreover, the fall down state can be classified into bounce, friction and bounce as well as full rubbing, which is largely determined by the initial fall down speeds. The increasing rotating speeds exacerbate the fall down performances. The nonlinear PID re-levitation method behaves more effectively and reliably than traditional PID re-levitation approaches. The proposed method can withstand many common interferences such as sinusoidal acceleration, shock acceleration and random acceleration.

The Synchronization of a Class of Time-Delayed Chaotic Systems Using Sliding Mode Control Based on a Fractional-Order Nonlinear PID Sliding Surface and Its Application in Secure Communication

A novel approach for the synchronization of a class of chaotic systems with uncertainty, unknown time delays, and external disturbances is presented. The control method given here is expressed by combining sliding mode control approaches with adaptive rules. A sliding surface of fractional order has been developed to construct the control strategy of the abovementioned sliding mode by employing the structure of nonlinear fractional PID (NLPID) controllers. The suggested control mechanism using Lyapunov’s theorem developed robust adaptive rules in such a way that the estimation error of the system’s unknown parameters and time delays tends to be zero. Furthermore, the proposed robust control approach’s stability has been demonstrated using Lyapunov stability criteria and Lipschitz conditions. Then, in order to assess the performance of the proposed mechanism, the presented control approach was used to simulate the synchronization of two chaotic jerk systems with uncertainty, unknown time delays, and external distortion. The results of the simulation confirm the robust and desirable synchronization performance. Finally, a secure communications mechanism based on the proposed technique is shown as a practical implementation of the introduced control strategy, in which the message signal is disguised in the transmitter with high security and well recovered in the receiver with high quality, according to the mean squared error (MES) criteria.

Performance Comparison of Se formance Comparison of Several Contr al Control Algorithms for ol Algorithms for Tracking Contr acking Control of P ol of Pantograph Mechanism aph Mechanism

A sort of parallel manipulator known as a pantograph robot mechanism was created primarily for industrial requests that required high precision and satisfied speed. While tracking a chosen trajectory profile requires a powerful controller. Because it has four active robot links and one robot passive link in place of just two links like the open chain does, it can carry more loads than the open chain robot mechanism while maintaining accuracy and stability. The calculated model for a closed chain pantograph robot mechanism presented in this paper takes into account the boundary conditions. For the purpose of simulating the dynamics of the pantograph robot mechanism, an entire MATLAB Simulink has been created. The related Simscape model had been created to verify the pantograph mathematical model that had been provided. Five alternative tracking controllers were also created and improved using the Flower Pollination (FP) algorithm. The PID controller, which is used in many engineering applications, is the first control. An enriched Fractional Order PID (FOPID) controller is the second control. The third control considers an improved Nonlinear conventional PID (NLPID) controller, and the parameters for this controller were likewise determined using (FP) optimization using the useful objective function. Model Reference Adaptive Control (MRAC) with PID Compensator is the fourth control. The Fuzzy PD+I Control is the last and final controller. A comparison of the different control methods was completed. A rectangular trajectory was chosen as the end effector of the pantograph robot's position reference because it displays performance during sharp edges and provides a more accurate study. The proposed controllers were used for this task to analyse the performance. The outcomes demonstrate that the Fuzzy PD+I control outperforms the PID, FOPID, NLPID, and MRAC with PID Compensator controllers in terms of performance. In the case of the Fuzzy PD+I control, the angles end effector has a lower rise time, a satisfied settling time, and low overshoot with good precision.

Genetic algorithm-based design of a nonlinear PID controller for the temperature control of load-following coolant systems

Genetic algorithm-based design of a nonlinear PID controller for the temperature control of load-following coolant systems

Globally Attractive Hyperbolic Control for the Robust Flight of an Actively Tilting Quadrotor

This paper addresses the problem of robustly controlling an actively tilting quadrotor UAV. The proposed technique is model-free and it is based on hyperbolic functions of the six-dimensional pose error of the UAV with respect to the world reference frame; this hyperbolic controller globally attracts the error signals to an ultimate bound about the origin despite external disturbances, which is proved by way of a strict Lyapunov function based analysis. The effectiveness of the controller is evaluated by means of tracking and regulation experiments on adverse conditions, which were implemented on a virtual model of the UAV through a physics-engine-based simulation environment that provides an almost identical behaviour than a real UAV. The norm of the six-dimensional error signal converged to zero for the regulation experiments, whereas for tracking it did not exceed 0.05 meters, which indicated a successful operation of the control system. In addition, the performance of the hyperbolic controller was contrasted against a nonlinear PID, which resulted in a better performance in favour of the first one, who settled the errors to zero up to eight seconds before and demanded up to 2000 less revolutions per minute from the rotors while performing the same regulation tasks. All the aforesaid successful results place the proposed technique as a competitive alternative for controlling actively tilting multirotors due to its simplicity, robustness and demonstrated effectiveness.