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Keywords = frequency domain PID control

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20 pages, 3835 KiB  
Article
Fuzzy PD-Based Control for Excavator Boom Stabilization Using Work Port Pressure Feedback
by Joseph T. Jose, Gyan Wrat, Santosh Kr. Mishra, Prabhat Ranjan and Jayanta Das
Actuators 2025, 14(7), 336; https://doi.org/10.3390/act14070336 - 4 Jul 2025
Viewed by 258
Abstract
Hydraulic excavators operate in harsh environments where direct measurement of actuator chamber pressures and boom displacement is often unreliable or infeasible. This study presents a novel control strategy that estimates actuator chamber pressures from work port pressures using differential equations, eliminating the need [...] Read more.
Hydraulic excavators operate in harsh environments where direct measurement of actuator chamber pressures and boom displacement is often unreliable or infeasible. This study presents a novel control strategy that estimates actuator chamber pressures from work port pressures using differential equations, eliminating the need for direct pressure or position sensors. A fuzzy logic-based proportional–derivative (PD) controller is developed to mitigate boom oscillations, particularly under high-inertia load conditions and variable operator inputs. The controller dynamically adjusts gains through fuzzy logic-based gain scheduling, enhancing adaptability across a wide range of operating conditions. The proposed method addresses the limitations of classical PID controllers, which struggle with the nonlinearities, parameter uncertainties, and instability introduced by counterbalance valves and pressure-compensated proportional valves. Experimental data is used to design fuzzy rules and membership functions, ensuring robust performance. Simulation and full-scale experimental validation demonstrate that the fuzzy PD controller significantly reduces pressure overshoot (by 23% during extension and 32% during retraction) and decreases settling time (by 31.23% and 28%, respectively) compared to conventional systems. Frequency-domain stability analysis confirms exponential stability and improved damping characteristics. The proposed control scheme enhances system reliability and safety, making it ideal for excavators operating in remote or rugged terrains where conventional sensor-based systems may fail. This approach is generalizable and does not require modifications to the existing hydraulic circuit, offering a practical and scalable solution for modern hydraulic machinery. Full article
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27 pages, 17572 KiB  
Article
Optimal Design of a Fractional Order PIDD2 Controller for an AVR System Using Hybrid Black-Winged Kite Algorithm
by Fei Dai, Tianli Ma and Song Gao
Electronics 2025, 14(12), 2315; https://doi.org/10.3390/electronics14122315 - 6 Jun 2025
Viewed by 368
Abstract
This study addresses the optimization of control performance for automatic voltage regulator systems by proposing a fractional-order PIDD2 (FOPIDD2) controller design method based on the hybrid Black-winged Kite Algorithm (BWOA). To overcome the challenges of complex parameter tuning and adaptability [...] Read more.
This study addresses the optimization of control performance for automatic voltage regulator systems by proposing a fractional-order PIDD2 (FOPIDD2) controller design method based on the hybrid Black-winged Kite Algorithm (BWOA). To overcome the challenges of complex parameter tuning and adaptability to high-dimensional nonlinear optimization in PID controllers, the BWOA integrates the precise search mechanism of the Black-winged Kite Algorithm (BKA) with the spiral encircling strategy of the Whale Optimization Algorithm (WOA). By dividing high-fitness individuals into subgroups for parallel optimization, combined with an elitism preservation mechanism and Levy flight perturbation, the BWOA effectively balances global exploration and local exploitation capabilities, preventing premature convergence. Furthermore, a multi-factor objective function is adopted to optimize the six parameters of the FOPIDD2 controller. Numerical simulations in MATLAB evaluate the controller’s performance across multiple dimensions, including transient response, frequency-domain stability, trajectory tracking, parameter uncertainty, and disturbance rejection, with comparisons to other recent controllers. Simulation results demonstrate that the BWOA-FOPIDD2 controller achieves superior performance in most metrics. Therefore, the proposed method provides an efficient hybrid optimization framework for AVR system controller design. Full article
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19 pages, 2109 KiB  
Article
Robust Frequency Regulation Management System in a Renewable Hybrid Energy Network with Integrated Storage Solutions
by Subhranshu Sekhar Pati, Umamani Subudhi and Sivkumar Mishra
Electricity 2025, 6(2), 22; https://doi.org/10.3390/electricity6020022 - 1 May 2025
Viewed by 934
Abstract
The rapid proliferation of renewable energy sources (RESs) has significantly reduced system inertia, thereby intensifying stability challenges in modern power grids. To address these issues, this study proposes a comprehensive approach to improve the grid stability concerning RESs and load disturbances. The methodology [...] Read more.
The rapid proliferation of renewable energy sources (RESs) has significantly reduced system inertia, thereby intensifying stability challenges in modern power grids. To address these issues, this study proposes a comprehensive approach to improve the grid stability concerning RESs and load disturbances. The methodology integrates controlled energy storage systems, including ultra-capacitors (UC), superconducting magnetic energy storage (SMES), and battery storage, alongside a robust frequency regulation management system (FRMS). Central to this strategy is the implementation of a novel controller which combines a constant with proportional–integral–derivative (PID) and modified fractional-order (MFO) control, forming 1+MFOPID controller. The controller parameters are optimized using a novel formulation of an improved objective function that incorporates both frequency and time domain characteristics to achieve superior performance. The efficacy of the proposed controller is validated by comparing its performance with conventional PID and fractional-order PID controllers. System stability is further analyzed using eigenvector analysis. Additionally, this study evaluates the performance of various energy storage systems and their individual contributions to frequency regulation, with a particular emphasis on the synergistic benefits of battery storage in conjunction with other storages. Finally, sensitivity analysis is conducted to assess the impact of parameter uncertainties in the system design, reinforcing the robustness of the proposed approach. Full article
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25 pages, 6006 KiB  
Article
High-Order Engineering Fastest Controller and Its Application in Thermal Power Units
by Shangyao Shi, Jun Li, Yijia Huo, Ruiqi Li and Pengyun Chen
Energies 2025, 18(2), 441; https://doi.org/10.3390/en18020441 - 20 Jan 2025
Viewed by 974
Abstract
In the domain of industrial process control, the ubiquitous proportional–integral–derivative (PID) control paradigm, while foundational, is deemed insufficient amidst evolving complexities. In alignment with China’s strategic “dual-carbon” targets, extant thermal power installations are mandated to facilitate profound peak load navigation and expedited frequency [...] Read more.
In the domain of industrial process control, the ubiquitous proportional–integral–derivative (PID) control paradigm, while foundational, is deemed insufficient amidst evolving complexities. In alignment with China’s strategic “dual-carbon” targets, extant thermal power installations are mandated to facilitate profound peak load navigation and expedited frequency modulation services. The incumbent PID control schema is found wanting in this regard, precipitating the imperative for an innovative process control technology to supplant the conventional PID regimen. Power system engineers have consequently devised the engineering fastest controller (EFC), which has adeptly succeeded PID control in nascent applications, thereby meeting the stringent control exigencies for deep peak regulation and agile frequency modulation. Employing rigorous theoretical analysis and sophisticated simulation experiments, this investigation meticulously compares the performance attributes of high-order controllers (HOCs) with the EFC. The empirical findings underscore the EFC’s pronounced superiority over PI, PID, and SOC in regulatory performance enhancements by 122.2%, 88.0%, and 77.3%, respectively, and in mitigating disturbances by 140.0%, 80.9%, and 54.5%, respectively. This study culminates in the assertion that the EFC represents a paradigmatic advancement in industrial control technology, not only manifesting pronounced performance benefits but also furnishing a robust theoretical scaffolding that transcends the performance zeniths of traditional PID and HOC technologies. Full article
(This article belongs to the Special Issue Energy, Electrical and Power Engineering: 3rd Edition)
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36 pages, 14447 KiB  
Article
A Comprehensive Approach to Load Frequency Control in Hybrid Power Systems Incorporating Renewable and Conventional Sources with Electric Vehicles and Superconducting Magnetic Energy Storage
by K. Nagendra, K. Varun, G. Som Pal, K. Santosh, Sunil Semwal, Manoj Badoni and Rajeev Kumar
Energies 2024, 17(23), 5939; https://doi.org/10.3390/en17235939 - 26 Nov 2024
Cited by 2 | Viewed by 1069
Abstract
This study addresses the load frequency control (LFC) within a multiarea power system characterized by diverse generation sources across three distinct power system areas. area 1 comprises thermal, geothermal, and electric vehicle (EV) generation with superconducting magnetic energy storage (SMES) support; area 2 [...] Read more.
This study addresses the load frequency control (LFC) within a multiarea power system characterized by diverse generation sources across three distinct power system areas. area 1 comprises thermal, geothermal, and electric vehicle (EV) generation with superconducting magnetic energy storage (SMES) support; area 2 encompasses thermal and EV generation; and area 3 includes hydro, gas, and EV generation. The objective is to minimize the area control error (ACE) under various scenarios, including parameter variations and random load changes, using different control strategies: proportional-integral-derivative (PID), two-degree-of-freedom PID (PID-2DF), fractional-order PID (FOPID), fractional-order integral (FOPID-FOI), and fractional-order integral and derivative (FOPID-FOID) controllers. The result analysis under various conditions (normal, random, and parameter variations) evidences the superior performance of the FOPID-FOID control scheme over the others in terms of time-domain specifications like oscillations and settling time. The FOPID-FOID control scheme provides advantages like adaptability/flexibility to system parameter changes and better response time for the current power system. This research is novel because it shows that the FOPID-FOID is an excellent control scheme that can integrate these diverse/renewable sources with modern systems. Full article
(This article belongs to the Section E: Electric Vehicles)
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19 pages, 8889 KiB  
Article
A Frequency Domain PID Control Strategy for an In-House Friction and Wear Test Rig
by Di Li, Jing Wang, Hongguang Li, Guang Meng and Anlue Li
Aerospace 2024, 11(8), 623; https://doi.org/10.3390/aerospace11080623 - 30 Jul 2024
Viewed by 1595
Abstract
The contact behavior greatly influences the damping performance of frictional interfaces. Numerous experimental studies on friction and fretting wear have investigated the evolution of contact parameters. An in-house friction and wear test rig has been developed to obtain hysteresis loops at certain normal [...] Read more.
The contact behavior greatly influences the damping performance of frictional interfaces. Numerous experimental studies on friction and fretting wear have investigated the evolution of contact parameters. An in-house friction and wear test rig has been developed to obtain hysteresis loops at certain normal forces. However, the test rig lacks load control and is thus unable to ensure precise stabilization at a preset normal force, which affected the hysteresis behavior. In this paper, we developed a frequency-domain PID controller to ensure the stable application of a target normal force with constant (0–300 N) and harmonic (0–50 N) components. Compared to the commonly used time-domain strategy, the control signal error is reduced from 6.30% to 0.54% at 50 Hz. With a 3% error as the standard, the controller enables stabilized control of signals with frequencies up to 300 Hz. Friction experiments on various typical materials are conducted using this improved test rig. The results indicate a general tendency for contact stiffness to increase with a rising normal force, while the relationship between the friction coefficient and the normal force does not exhibit a clear pattern. The contact stiffness is not sensitive to the relative displacement or vibration frequency. Full article
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19 pages, 6293 KiB  
Article
Reaction Curve-Assisted Rule-Based PID Control Design for Islanded Microgrid
by T. K. Bashishtha, V. P. Singh, U. K. Yadav and T. Varshney
Energies 2024, 17(5), 1110; https://doi.org/10.3390/en17051110 - 26 Feb 2024
Cited by 14 | Viewed by 1781
Abstract
In a renewable energy-based islanded microgrid system, frequency control is one of the major challenges. In general, frequency oscillations occur in islanded microgrids due to the stochastic nature of load and variable output power of distributed generating units (DGUs). In the presented research [...] Read more.
In a renewable energy-based islanded microgrid system, frequency control is one of the major challenges. In general, frequency oscillations occur in islanded microgrids due to the stochastic nature of load and variable output power of distributed generating units (DGUs). In the presented research proposal, frequency oscillations are suppressed by implementing the proportional integral derivative (PID) controller-based control design strategy for an islanded microgrid. The modeling of the islanded microgrid is firstly presented in the form of a linearized transfer function. Further, the derived transfer function is approximated into its equivalent first-order plus dead time (FOPDT) form. The approximated FOPDT transfer function is obtained by employing the reaction curve method to calculate the parameters of the FOPDT transfer function. Furthermore, the desired frequency regulation is achieved for the manifested FOPDT transfer function by incorporating PID control design. For PID controller tuning, different rule-based methods are implemented. Additionally, comparative analysis is also performed to ensure the applicability of the comparatively better rule-based tuning method. The Wang–Chan–Juang (WCJ) method is found effective over other rule-based tuning methods. The efficacy of the WCJ method is proved in terms of transient response and frequency deviation. The tabulated data of tuning parameters, time domain specifications, and error indices along with responses are provided in support of the presented control strategy. Full article
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22 pages, 1024 KiB  
Article
Reinforcement Learning-Based Control of a Power Electronic Converter
by Dajr Alfred, Dariusz Czarkowski and Jiaxin Teng
Mathematics 2024, 12(5), 671; https://doi.org/10.3390/math12050671 - 25 Feb 2024
Cited by 10 | Viewed by 3096
Abstract
This article presents a modern, data-driven, reinforcement learning-based (RL-based), discrete-time control methodology for power electronic converters. Additionally, the key advantages and disadvantages of this novel control method in comparison to classical frequency-domain-derived PID control are examined. One key advantage of this technique is [...] Read more.
This article presents a modern, data-driven, reinforcement learning-based (RL-based), discrete-time control methodology for power electronic converters. Additionally, the key advantages and disadvantages of this novel control method in comparison to classical frequency-domain-derived PID control are examined. One key advantage of this technique is that it obviates the need to derive an accurate system/plant model by utilizing measured data to iteratively solve for an optimal control solution. This optimization algorithm stems from the linear quadratic regulator (LQR) and involves the iterative solution of an algebraic Riccati equation (ARE). Simulation results implemented on a buck converter are provided to verify the effectiveness and examine the limitations of the proposed control strategy. The implementation of a classical Type-III compensator was also simulated to serve as a performance comparison to the proposed controller. Full article
(This article belongs to the Special Issue Modeling, Simulation and Control of Dynamical Systems)
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13 pages, 3975 KiB  
Article
System Identification and Fractional-Order Proportional–Integral–Derivative Control of a Distributed Piping System
by Xiaomeng Zhang, Shuo Zhang, Furui Xiong, Lu Liu, Lichuan Zhang, Xuan Han, Heng Wang, Yanzhu Zhang and Ranzhen Ren
Fractal Fract. 2024, 8(2), 122; https://doi.org/10.3390/fractalfract8020122 - 19 Feb 2024
Cited by 4 | Viewed by 1780
Abstract
The vibration of piping systems is one of the most important causes of accelerated equipment wear and reduced work efficiency and safety. In this study, an active vibration control method based on a fractional-order proportional–integral–derivative (PID) controller was proposed to suppress pipeline vibration [...] Read more.
The vibration of piping systems is one of the most important causes of accelerated equipment wear and reduced work efficiency and safety. In this study, an active vibration control method based on a fractional-order proportional–integral–derivative (PID) controller was proposed to suppress pipeline vibration and reduce pipeline damage. First, a mathematical model of the distributed piping system was established using the finite element analysis method, and the characteristics of the distributed piping system were studied effectively. Further, the time-frequency domain parameter identification method was used to realise the system identification of the cross-point vibration transfer function between the brake and sensor, and the particle swarm optimisation algorithm was utilised to further optimise the transfer function parameters to improve the system identification accuracy. Therefore, a fractional-order PID controller was designed using the D-decomposition method, and the optimal controller parameters were obtained. The experimental and numerical simulation results show that the improved system identification algorithm can significantly improve modelling accuracy. In addition, the designed fractional-order PID controller can effectively reduce the system’s overshoot, oscillation time, and adjustment time, thereby reducing the vibration response of piping systems. Full article
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24 pages, 5280 KiB  
Article
Design of Multivariable PID Control Using Iterative Linear Programming and Decoupling
by Juan Garrido, Sergio Garrido-Jurado, Francisco Vázquez and Orlando Arrieta
Electronics 2024, 13(4), 698; https://doi.org/10.3390/electronics13040698 - 8 Feb 2024
Cited by 5 | Viewed by 1574
Abstract
The design of multivariable process control systems is specially complicated when there are strong interactions between the different control loops, and even more with multiple time delays. This paper proposes an iterative design method of centralized proportional-integral-derivative (PID) controllers for stable linear systems. [...] Read more.
The design of multivariable process control systems is specially complicated when there are strong interactions between the different control loops, and even more with multiple time delays. This paper proposes an iterative design method of centralized proportional-integral-derivative (PID) controllers for stable linear systems. The methodology is based on the linear parameterization of equivalent loop transfer functions (ELTFs) for centralized control. These functions capture the dynamics of the other loops and, from a prior design, allow solving the design problem at each iteration with linear programming that shapes the Nyquist plot of the ELTFs in the frequency domain, which also avoids the need for approximations. Two optimizations are proposed: (I) maximizing integral gains by fulfilling linear robustness margins in each ELTF and (II) maximizing linear robustness margins by fulfilling minimum bandwidths in each loop. In both optimizations, static decoupling and decoupling at a frequency close to the bandwidth of each loop are included as constraints, which improves the decoupling performance and the procedure convergence. The effectiveness of the method is verified in three simulation examples (square and non-square) and a lab experimental process. The proposed designs achieve a similar or better response when compared to that achieved by other authors. Full article
(This article belongs to the Section Systems & Control Engineering)
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31 pages, 13657 KiB  
Article
A Comprehensive Performance Analysis of a 48-Watt Transformerless DC-DC Boost Converter Using a Proportional–Integral–Derivative Controller with Special Attention to Inductor Design and Components Reliability
by Kuldeep Jayaswal, D. K. Palwalia and Josep M. Guerrero
Technologies 2024, 12(2), 18; https://doi.org/10.3390/technologies12020018 - 30 Jan 2024
Cited by 3 | Viewed by 2878
Abstract
In this research paper, a comprehensive performance analysis was carried out for a 48-watt transformerless DC-DC boost converter using a Proportional–Integral–Derivative (PID) controller through dynamic modeling. In a boost converter, the optimal design of the magnetic element plays an important role in efficient [...] Read more.
In this research paper, a comprehensive performance analysis was carried out for a 48-watt transformerless DC-DC boost converter using a Proportional–Integral–Derivative (PID) controller through dynamic modeling. In a boost converter, the optimal design of the magnetic element plays an important role in efficient energy transfer. This research paper emphasizes the design of an inductor using the Area Product Technique (APT) to analyze factors such as area product, window area, number of turns, and wire size. Observations were made by examining its response to changes in load current, supply voltage, and load resistance at frequency levels of 100 and 500 kHz. Moreover, this paper extended its investigation by analyzing the failure rates and reliability of active and passive components in a 48-watt boost converter, providing valuable insights about failure behavior and reliability. Frequency domain analysis was conducted to assess the controller’s stability and robustness. The results conclusively underscore the benefits of incorporating the designed PID controller in terms of achieving the desired regulation and rapid response to disturbances at 100 and 500 kHz. The findings emphasize the outstanding reliability of the inductor, evident from the significantly low failure rates in comparison to other circuit components. Conversely, the research also reveals the inherent vulnerability of the switching device (MOSFET), characterized by a higher failure rate and lower reliability. The MATLAB® Simulink platform was utilized to investigate the results. Full article
(This article belongs to the Collection Electrical Technologies)
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26 pages, 9753 KiB  
Article
Design and Research of Series Actuator Structure and Control System Based on Lower Limb Exoskeleton Rehabilitation Robot
by Chenglong Zhao, Zhen Liu, Liucun Zhu and Yuefei Wang
Actuators 2024, 13(1), 20; https://doi.org/10.3390/act13010020 - 5 Jan 2024
Cited by 9 | Viewed by 3105
Abstract
Lower limb exoskeleton rehabilitation robots have become an important direction for development in today’s society. These robots can provide support and power to assist patients in walking and movement. In order to achieve better interaction between humans and machines and achieve the goal [...] Read more.
Lower limb exoskeleton rehabilitation robots have become an important direction for development in today’s society. These robots can provide support and power to assist patients in walking and movement. In order to achieve better interaction between humans and machines and achieve the goal of flexible driving, this paper addresses the shortcomings of traditional elastic actuators and designs a series elastic–damping actuator (SEDA). The SEDA combines elastic and damping components in parallel, and the feasibility of the design and material selection is demonstrated through finite element static analysis. By modeling the dynamics of the SEDA, using the Bode plot and Nyquist plot, open-loop and closed-loop frequency domain comparisons and analyses were carried out, respectively, to verify the effect of damping coefficients on the stability of the system, and the stiffness coefficient ks = 25.48 N/mm was selected as the elastic element and the damping coefficient cs = 1 Ns/mm was selected as the damping element. A particle swarm optimization (PSO)-based algorithm was proposed to introduce the fuzzy controller into the PID control system, and five parameters, namely the the fuzzy controller’s fuzzy factor (ke, kec) and de-fuzzy factor (kp1, ki1, kd1), are taken as the object of the algorithm optimization to obtain the optimal fuzzy controller parameters of ke = 0.8, kec = 0.2, kp1 = 0.5, ki1 = 8, kd1 = −0.1. The joint torque output with and without external interference is simulated, and the simulation model is established in the MATLAB/Simulink environment The results show that when fuzzy PID control is used, the amount of overshooting in the system is 14.6%, and the regulation time is 0.66 s. This has the following advantages: small overshooting amount, short rise time, fast response speed, short regulation time, good stability performance, and strong anti-interference ability. The SEDA design structure and control method breaks through limitations of the traditional series elastic actuator (SEA) such as its lack of flexibility and stability, which is very helpful to improve the output effect of flexible joints. Full article
(This article belongs to the Special Issue Actuators and Robots for Biomedical Applications)
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30 pages, 8878 KiB  
Article
Development of Boom Posture Adjustment and Control System for Wide Spray Boom
by Jinyang Li, Zhenyu Nie, Yunfei Chen, Deqiang Ge and Meiqing Li
Agriculture 2023, 13(11), 2162; https://doi.org/10.3390/agriculture13112162 - 17 Nov 2023
Cited by 23 | Viewed by 3336
Abstract
To obtain a more consistent droplet distribution and reduce spray drift, it is necessary to keep the entire spray boom parallel to the crop canopy or ground and maintain a certain distance from the spray nozzles to the crop canopy or ground. A [...] Read more.
To obtain a more consistent droplet distribution and reduce spray drift, it is necessary to keep the entire spray boom parallel to the crop canopy or ground and maintain a certain distance from the spray nozzles to the crop canopy or ground. A high-performance boom active control system was developed for boom trapezoid suspension. The hydraulic system and hardware circuit of the boom control system were designed based on analyzing the configuration of active trapezoid suspension. The mathematical models of valve-controlled hydraulic cylinders and active boom suspensions were developed. Step response and frequency domain response analysis of passive suspension were conducted by Simulink simulations, and then key parameters of the boom suspension and hydraulic system were determined. A feedforward proportion integration differentiation (FPID) control algorithm was proposed to improve the tracking performance. The designed control system was assembled on a 24 m boom with trapezoid suspension. The response characteristic of the active boom control system was tested by the step signal and the sinusoidal signal from a six-degree-of-freedom hydraulic motion platform. Firstly, the tracking performance of the active balance control system for the PID (proportion integration differentiation) and FPID control algorithms was compared for a given 0.2 Hz sine signal. Then, for the ground-following control system, the response characteristics in challenging terrain and tracking performance in less challenging terrain were tested. Field experiment results indicate that the maximum rolling angle of the chassis was 3.896° while the maximum inclination angle of the boom was 0.453°. The results show that the designed boom adjustment and control system can effectively adjust the boom motion in real time and meet the requirements of field operation. Full article
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32 pages, 2379 KiB  
Article
Parametrization and Optimal Tuning of Constrained Series PIDA Controller for IPDT Models
by Mikulas Huba, Pavol Bistak and Damir Vrancic
Mathematics 2023, 11(20), 4229; https://doi.org/10.3390/math11204229 - 10 Oct 2023
Cited by 14 | Viewed by 1937
Abstract
The new modular approach to constrained control of higher-order processes with dominant first-order dynamics using generalized controllers with automatic resets (ARCs) is addressed. The controller design is based on the multiple real dominant pole (MRDP) method for the integrator plus dead time (IPDT) [...] Read more.
The new modular approach to constrained control of higher-order processes with dominant first-order dynamics using generalized controllers with automatic resets (ARCs) is addressed. The controller design is based on the multiple real dominant pole (MRDP) method for the integrator plus dead time (IPDT) process models. The controller output constraints are taken into account by inserting the smallest numerator time constant of the controller transfer function into the positive feedback loop representing the automatic reset (integral) term. In the series realization of the proportional–integral–derivative–acceleration (PIDA) controller (and other controllers with even derivative degree), the time constant mentioned is complex, so only the real part of the time constant has been used so far. Other possible conversions of a complex number to a real number, such as the absolute value (modulus), can be covered by introducing a tuning parameter that modifies the calculated real time constant and generalizes the mentioned conversion when designing controllers with constraints. In this article, the impact of the tuning parameter on the overall dynamics of the control loop is studied by simulation. In addition, an evaluation of the stability of the closed-loop control system is performed using the circle criterion in the frequency domain. The analysis has shown that the approximation of the complex zero by its real part and modulus leads to a near optimal response to the set point tracking. The disturbance rejection can be significantly improved by increasing the tuning parameter by nearly 50%. In general, the tuning parameter can be used to find a compromise between servo and regulatory control. The robustness and applicability of the proposed controller is evaluated using a time-delayed process with first-order dominant dynamics when the actual transfer function is much more complicated than the IPDT model. A comparison of the proposed MRDP-PIDA controller with series PI, PID and PIDA controllers based on a modified SIMC method has shown that the MRDP-PIDA controller performs better than the SIMC method, although the SIMC uses a more complex process model. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamical Systems and Control Systems)
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18 pages, 843 KiB  
Article
On a Data-Driven Optimization Approach to the PID-Based Algorithmic Trading
by Vadim Azhmyakov, Ilya Shirokov, Yuri Dernov and Luz Adriana Guzman Trujillo
J. Risk Financial Manag. 2023, 16(9), 387; https://doi.org/10.3390/jrfm16090387 - 30 Aug 2023
Cited by 2 | Viewed by 2671
Abstract
This paper proposes an optimal trading algorithm based on a novel application of conventional control engineering (CE). We consider a fundamental CE concept, namely, the feedback control, and apply it to algorithmic trading (AT). The concrete feedback control strategy is designed in a [...] Read more.
This paper proposes an optimal trading algorithm based on a novel application of conventional control engineering (CE). We consider a fundamental CE concept, namely, the feedback control, and apply it to algorithmic trading (AT). The concrete feedback control strategy is designed in a form of the celebrated proportional–integral–derivative (PID) model. The highly fluctuating nature of the modern financial markets has led to the adoption of a model-free realization of the generic PID framework. The control theoretical methodology we propose is combined with the advanced statistics for the historical market data. We obtain a specific log-normal probability distribution function (pdf) associated with the specific quantities associated with the available stock data. The empirical log-normal pdf mentioned above enables the necessary PID gains optimization. For this aim, we apply the data-driven optimization approaches and consider the corresponding Monte Carlo solution procedure. The optimized PID trading algorithm we propose is also studied in the Fourier analysis framework. This equivalent frequency domain representation involves a new concept in financial engineering, namely, the “stock market energy” concept. For the evaluation, we implement the proposed PID optimal trading algorithm and develop a Python-based prototype software. We finally apply the corresponding prototype software to a data set from the Binance BTC/USDT (Bitcoin/Tether) stock market. The experimental result illustrates the implementability of the proposed optimal PID trading scheme and also shows the effectiveness of the proposed CE methods in the modern AT. Full article
(This article belongs to the Section Mathematics and Finance)
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