Control Engineering Problems Research Articles

Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations

In this study, solutions of random complex partial differential equations were found using the two-dimensional Sumudu transformation method(STM). The initial conditions of a deterministic equation or the non-homogeneous part of the equation are transformed into random variables to obtain a random complex partial differential equation. With the help of the properties of two-dimensional Sumudu and inverse Sumudu transformation, an approximate analytical solution of a complex partial differential equation with random constant coefficients was obtained by selecting a random variable with an initial condition of Normal and Gamma distribution. The probability characteristics of the resulting solutions, such as expected value and variance, were obtained and graphically shown with the help of the Maple package program.

Water-Coal Ratio Control Strategy of Ultra Supercritical Unit Based on Neural Network Inverse Model

Since the boiler water-coal ratio control system is a complex system with the characteristics of non-linearity and strong coupling, water-coal ratio control is one of the most difficult problems in the coal-fired power generation process control engineering, whose control strategy is of great importance. While, in order to achieve the control of water-coal ratio effectively during the coal-fired power generation process, the neural network inverse system scheme is proposed for the control of the water-coal ratio of ultra-supercritical units. Firstly, the model for the water-coal ratio system of an ultra-supercritical unit is presented in allusion to the characteristics of the water-coal ratio control system. Then the concept of the neural network based inverse system, the principle and method of the design of the neural network inverse controller are discussed. Finally, the control scheme is verified by establishing neural network inverse system on MATLAB toolbox. The experimental results show that the neural network based inverse system models has better control effect in terms of anti-interference ability, stability time than that of PID control system.

Optimization of robot manipulator configuration calibration by using Zhang neural network for repetitive motion

High precision and low complexity control algorithm plays an important role in the developing of the end-effector instrumentation of different robot manipulators. In order to reduce the kinetic energy and the high-speed drift phenomenon of the repetitive motion tracking task, the robot manipulator needs to calibrate its configuration. In this paper, we formulate the configuration calibration of the robot manipulator for the repetitive motion task as a future quadratic programming optimization problem constrained with equality constraints, which is also regarded as a fundamental problem in artificial intelligence and modern control engineering. Zhang neural network, which is a canonical method, can be adopted to deal with the continuous form of the future optimization problem, named as temporally dependent quadratic programming problem with equality constraints. In order to overcome the issue of temporally dependent inverse computing, a novel Zhang neural network model and its uncertain disturbance tolerant model, which are termed as filtered reciprocal-kind Zhang neural network model and uncertain disturbance tolerant filtered reciprocal-kind Zhang neural network model, respectively, are proposed by integrating the energy-type cost function and Zhang neural network design formula for solving the temporally dependent quadratic programming problem with equality constraints in this paper. Based on the Euler discrete formula and the models, the discrete filtered reciprocal-kind Zhang neural network and the discrete uncertain disturbance tolerant filtered reciprocal-kind Zhang neural network algorithms are proposed for solving the future quadratic programming problem with equality constraints and the robot manipulator configuration calibration problem of repetitive motion. The convergence properties of the reciprocal-kind Zhang neural network model and its corresponding uncertain disturbance tolerant model are obtained by Lyapunov stability theory of nonlinear system and its corresponding perturbed system, while the convergence property of the filtered reciprocal-kind Zhang neural network model is analyzed by the limit thinking. For the repetitive motion task, three experiments for solving the configuration calibration problem of PUMA560, Kinova Jaco2, and Franka Emika Panda robot manipulators are performed to illustrate the effectiveness, robustness and superiority of our proposed discrete filtered reciprocal-kind Zhang neural network algorithms.

Toward state estimation by high gain differentiators with automatic differentiation

Most applications of automatic differentiation concern the field of optimization in the broadest sense. This means that many applications only need first and second order derivatives. An exception are control engineering problems, where higher order derivatives are required. This contribution addresses a control engineering problem, namely the estimation of variables that are not measured directly. This problem can be solved with high gain observers and high gain differentiators. They are typically calculated symbolically. We show how automatic differentiation can be used for the implementation of high gain differentiators.

A deep reinforcement learning framework to modify LQR for an active vibration control applied to 2D building models

Abstract Deep reinforcement learning (DRL) has emerged as a promising approach for optimizing control policies in various fields. In this article, we explore the use of DRL for controlling vibrations in building structures. Specifically, we focus on the problem of reducing vibrations induced by external sources such as wind or earthquakes. We propose a DRL-based control framework that learns to adjust the control signal of a classical adaptive linear quadratic regulator (LQR)-based model to mitigate the vibration of building structures in real-time. The framework combines the proximal policy optimization method and a deep neural network that is trained using a simulation environment. The network takes input sensor readings from the building and outputs signals that work as a corrector to the signals from the LQR model. It demonstrates the approach’s effectiveness by simulating a 3-story building structure. The results show that our DRL-based control approach outperforms the classical LQR model in reducing building vibrations. Moreover, we show that the approach is robust for learning the system’s dynamics. Overall, the work highlights the potential of DRL for improving the performance of building structures in the face of external disturbances. The framework can be easily integrated into existing building control systems and extended to other control problems in structural engineering.

Fostering Female Futures: Outcomes and Insights from applying The Girls-in-Control Workshop in Spain

The underrepresentation of women in Science, Technology, Engineering, and Mathematics (STEM) fields remains a significant concern despite ongoing efforts towards gender equality. This gender gap not only underscores disparities in educational opportunities but also raises critical questions about diversity in thinking and innovation within STEM disciplines. Initiatives such as The Girls-in-Control workshop aim to address this gap by providing access to essential knowledge and skills in a supportive environment that encourages confidence and motivation among female students. This article presents a detailed analysis of The Girls-in-Control workshop held in Spain, focusing on specific control engineering problems and fundamental concepts. Developed in collaboration with several universities and research centers nationwide, the workshop was held on the Day of Women and Girls in Science (11F). Results from questionnaires filled out by both instructors and students highlight the success of the workshop, with students learning key control theory concepts in an engaging way using Scratch programming. Considerations for future editions are also explored.

Design and analysis of root locus based controllers

The root locus method is the classical method for analyzing the variation of the position of the poles of a closed-loop control system transfer function in the complex plane. It is also the basis for guiding the design of various controllers. Starting from the nature of the root locus, this paper takes a standard form of closed-loop feedback control system as an example, and analyzes in detail the internal logic of designing a controller and compensator by the root locus method. At the same time, software such as MATLAB/Simulink, and Octave are used. The working principles and properties of the PD controller; the lead and lag compensator, their interconnections, advantages, and characteristics, as well as the adjustment of parameters to better suit practical needs, are sorted out. The PD controller improves the system response, the lead compensator eliminates the PD controller’s defects, and the lag compensator reduces the steady-state error of the system. It provides help for understanding the essence of controller design and provides design ideas for control problems in actual engineering.

Robust Tracking and Disturbance Rejection for Decentralized Neutral Distributed-time-delay Systems

An important problem in control engineering is to design a controller to achieve robust asymptotic tracking of certain reference signals despite certain disturbance inputs. In the present work, this problem, which is known as the robust servomechanism problem, is considered for decentralized linear time-invariant (LTI) neutral systems with distributed time-delay. However, the system is also allowed to have discrete time-delays besides distributed time-delays. The reference signals and the disturbance input are assumed to satisfy a LTI neutral delay-differential equation with distributed and/or discrete time-delays. The necessary and sufficient conditions for the existence of a controller which solves this problem are derived. The structure of this controller (when it exists) is also presented.

Novel Kinds of Fractional λ–Kinetic Equations Involving the Generalized Degenerate Hypergeometric Functions and Their Solutions Using the Pathway-Type Integral

In recent years, fractional kinetic equations (FKEs) involving various special functions have been widely used to describe and solve significant problems in control theory, biology, physics, image processing, engineering, astrophysics, and many others. This current work proposes a new solution to fractional λ−kinetic equations based on generalized degenerate hypergeometric functions (GDHFs), which has the potential to be applied to calculate changes in the chemical composition of stars such as the sun. Furthermore, this expanded form can also help to solve various problems with phenomena in physics, such as fractional statistical mechanics, anomalous diffusion, and fractional quantum mechanics. Moreover, some of the well-known outcomes are just special cases of this class of pathway-type solutions involving GDHFs, with greater accuracy, while providing an easily calculable solution. Additionally, numerical graphs of these analytical solutions, using MATLAB Software (latest version 2023b), are also considered.

Design Method for Automatic Assembly Production Line of Electric Valves in Space Propulsion Systems

This article proposes a design method for a valve automatic assembly production line in response to the automation assembly requirements of electric valve products in space propulsion systems and the engineering problems of inaccurate loading force control and low valve measurement accuracy in existing process methods. This method can achieve five assembly processes during the assembly process of electric valves, including pre-tightening force control, valve-core stroke measurement, performance testing, and shell structure welding. The article introduces the design of platform components such as process execution, positioning, and transportation, as well as the design and operation process of workstations. By combining the design of a three-axis motion mechanism, a small turntable, and a robotic arm, the product can achieve professional, positioning, full process automation, and equipment miniaturization design across multiple workstations. Through the design of precise control of loading force and non-contact optical measurement method of moving structure, compared with the original method, the parameters affecting product performance are precisely controlled and the precision is improved. And the multivariable decoupling of valve product performance is realized by this method. Through application verification, this automatic assembly production line can significantly improve the assembly efficiency of electric valve products and solve difficult problems in product engineering.

A novel mesh discretization strategy for numerical solution of optimal control problems in aerospace engineering

An effective approach is proposed for optimal control problems in aerospace engineering. First, several interval lengths are treated as optimization variables directly to localize the switching points accurately. Second, the variable intervals are usually refined into more subintervals homogeneously to obtain the trajectories with high accuracy. To reduce the number of optimization variables and improve the efficiency, the control and the state vectors are parameterized using different meshes in this paper such that the control can be approximated asynchronously by fewer parameters where the trajectories change slowly. Then, the variables are departed as independent variables and dependent variables, the gradient formulae, based on the partial derivatives of dependent parameters with respect to independent parameters, are computed to solve nonlinear programming problems. Finally, the proposed approach is applied to the classic moon lander and hang glider problems. For the moon lander problem, the proposed approach is compared with CVP, Fast-CVP and GPM methods, respectively. For the hang glider problem, the proposed approach is compared with trapezoidal discretization and stopping criteria methods, respectively. The numerical results validate the effectiveness of the proposed approach.

Normal forms of double Hopf oscillators with radial nonlinearities

We are concerned with the simplest normal forms of non-resonant double Hopf oscillators with radial nonlinearities. Due to the required Lie algebraic structure for preserving the radial structure in the normal form process, we appeal to the Lie algebra of radial and rotational transformation generators. The structure constants of the Lie algebra are presented, where we notice a Lie ideal structure for the rotational vector fields. This gives rise to an effective reduction technique through the use of its corresponding quotient Lie algebra. Yet, computations of kernel spaces of the generalized homological maps seem a formidable project and thus, we employ the multiple Lie brackets method to skip explicit kernel space derivations. The simplest normal forms and orbital normal forms of the nonlinear family are presented. We also address their parametric normal forms as multiple parametric perturbations of the corresponding vector fields. Transformation symmetry groups associated with truncated normal forms are also derived. An efficient algorithm is provided for the normal form computations using computer algebra systems. Finally, we derive state-feedback controllers for a two-arm vibrator using normal forms of radial double Hopf singularity. This is to illustrate how our normal forms can be applied on classical control engineering problems as a new alternative nonlinear controller technique to the existing methods in nonlinear control theory.

A new MOPSO algorithm for solving mathematical test functions and control engineering problems

In this article, a new multiobjective particle swarm optimization (MOPSO) algorithm is introduced to improve the performance of a sliding mode based robust fuzzy proportional–integral–derivative (PID) controller. In this regard, the non-dominated solution having minimum number of neighbors is considered as the global best position, while the sigma values of the members are employed to determine the personal best position. A modified multiple-crossover operator is combined with the operators of the particle swarm optimization to significantly increase the convergence speed of the algorithm. To limit the size of the archive, a dynamical elimination scheme defined in the Euclidean space is introduced. Besides, iteration-based linear relations are implemented to adaptively compute the inertia weight and learning coefficients. To evaluate the effectiveness of the introduced MOPSO algorithm, the requirements are conducted by means of three benchmark functions with regard to generational distance, spacing, and maximum spread metrics. This analysis demonstrates that the proposed algorithm operates better through comparison with well-known elitist multiobjective evolutionary algorithms. Moreover, the MOPSO algorithm is applied for optimal design of a hybrid robust fuzzy PID controller for a pneumatic system with two bellows. Conflicting objective functions are considered as the normalized values of overshoot and settling time of the displacement between the bellows that should be simultaneously minimized. The feasibility and efficiency of the strategy are assessed in comparison with the conventional controllers.

Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton–Jacobi PDEs

Solving high-dimensional optimal control problems and corresponding Hamilton–Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose two abstract neural network architectures which are, respectively, used to compute the value function and the optimal control for certain class of high-dimensional optimal control problems. We provide the mathematical analysis for the two abstract architectures. We also show several numerical results computed using the deep neural network implementations of these abstract architectures. A preliminary implementation of our proposed neural network architecture on FPGAs shows promising speedup compared to CPUs. This work paves the way to leverage efficient dedicated hardware designed for neural networks to solve high-dimensional optimal control problems and Hamilton–Jacobi PDEs.

A Review in Applications of Control Engineering Based on Genetic Algorithm

The most popular evolutionary search techniques are genetic algorithms (GAs). Even though they are frequently used to solve control engineering problems, they are currently not a common tool in the control engineer's toolbox. This may be due in part to the fact that there are currently few general overviews of the employment of GAs for control engineering problems, and that they are often reported on at computer science conferences rather than conferences for control engineers. This review study is intended to assist researchers and practitioners in identifying prospective research issues, potential solutions, as well as advantages and disadvantages of each technique. This study gives a brief overview of contemporary a Genetic Algorithm (GA) in control systems. Additionally, offers a number of control techniques used with the GA that have undergone extensive research. The conclusion of this study listed in a table to show the effectiveness of GA in various control technique and which field didn’t used till the time of preparing this review.

Shadowed Type-2 Fuzzy Sets in Dynamic Parameter Adaption in Cuckoo Search and Flower Pollination Algorithms for Optimal Design of Fuzzy Fault-Tolerant Controllers

In recent, various metaheuristic algorithms have shown significant results in control engineering problems; moreover, fuzzy sets (FSs) and theories were frequently used for dynamic parameter adaption in metaheuristic algorithms. The primary reason for this is that fuzzy inference system (FISs) can be designed using human knowledge, allowing for intelligent dynamic adaptations of metaheuristic parameters. To accomplish these tasks, we proposed shadowed type-2 fuzzy inference systems (ST2FISs) for two metaheuristic algorithms, namely cuckoo search (CS) and flower pollination (FP). Furthermore, with the advent of shadowed type-2 fuzzy logic, the abilities of uncertainty handling offer an appealing improved performance for dynamic parameter adaptation in metaheuristic methods; moreover, the use of ST2FISs has been shown in recent works to provide better results than type-1 fuzzy inference systems (T1FISs). As a result, ST2FISs are proposed for adjusting the Lèvy flight (P) and switching probability (P′) parameters in the original cuckoo search (CS) and flower pollination (FP) algorithms, respectively. Our approach investigated trapezoidal types of membership functions (MFs), such as ST2FSs. The proposed method was used to optimize the precursors and implications of a two-tank non-interacting conical frustum tank level (TTNCFTL) process using an interval type-2 fuzzy controller (IT2FLC). To ensure that the implementation is efficient compared with the original CS and FP algorithms, simulation results were obtained without and then with uncertainty in the main actuator (CV1) and system component (leak) at the bottom of frustum tank two of the TTNCFLT process. In addition, the statistical z-test and non-parametric Friedman test are performed to analyze and deliver the findings for the best metaheuristic algorithm. The reported findings highlight the benefits of employing this approach over traditional general type-2 fuzzy inference systems since we get superior performance in the majority of cases while using minimal computational resources.

Mechatronic design of dynamically decoupled manipulators based on the control performance improvement

AbstractThe control of industrial robot manipulators presents a difficult problem for control engineers due to the complexity of their nonlinear dynamics models. Nonlinear controls based on feedback linearization are developed to meet control requirements. Model-based nonlinear control is highly sensitive to parameter errors and leads to problems of robustness for tracking trajectories at high speeds, and there is the additional problem of a heavy computational burden to consider in the design of nonlinear controllers. In this paper, a mechatronic design approach is proposed, which aims to facilitate controller design by redesigning the mechanical structure. The problem is approached in two steps: first, the dynamic decoupling conditions of manipulators are described and discussed, involving redistribution of the moving mass, which leads to the decoupling of motion equations. A classical linear control law is then used to track the desired efficient bang-bang profile trajectory. Then, in the presence of parameter uncertainty and external disturbances, the nonlinear controls with simple structures are adopted to stabilize the decoupled system asymptotically. An analysis of the results from a simulation of this approach demonstrates its effectiveness in controller design. The proposed improvement in control performance is illustrated via two spatial manipulators.

Study of PID controller gain for active vibration control using FEM based particle swarm optimization in COMSOL multiphysics

Proportional integral derivative (PID) controllers are widely used to solve different control engineering problems. To know the dynamic behaviour of a working plant by mathematical modelling is quite challenging. Finite element method (FEM) is a well-known technique and broadly used for the modelling of engineering systems. This article presents the FEM-based heuristic approach to design and optimize the PID controllers. The ‘allowed area method’ has been used for the formulation of the objective function followed by the tuning of the PID controller. First, the proposed approach is tested on 2-degree of freedom (DOF) mass-spring-damper (MSD) system. FEM modelling of 2-DOF MSD system with PID controller has been carried out in COMSOL Multiphysics and coupling of particle swarm optimization (PSO) has been carried out with the FEM model of the MSD system, for the optimization of PID controller gain. The FEM results are in good agreement with the analytical one. Next, the established method is applied to design and optimize the PID controller gain to control the vibration of a cantilever beam using piezoelectric actuator. Similar to the MSD system, FEM modelling of PID controller for the smart beam has been carried out in COMSOL Multiphysics, and the coupling of PSO is carried out with the FEM model of the smart beam for the optimization of PID controller gain. Simulation of the uncontrolled and controlled responses of the smart beam is carried out at the optimum controller gain for free vibration and step excitation. The piezoelectric actuator of smart beam has successfully damped the vibration within approximately 2.5 s.

Multiobjective Optimal Control of Wind Turbines: A Survey on Methods and Recommendations for the Implementation

Advanced control system design for large wind turbines is becoming increasingly complex, and high-level optimization techniques are receiving particular attention as an instrument to fulfil this significant degree of design requirements. Multiobjective optimal (MOO) control, in particular, is today a popular methodology for achieving a control system that conciliates multiple design objectives that may typically be incompatible. Multiobjective optimization was a matter of theoretical study for a long time, particularly in the areas of game theory and operations research. Nevertheless, the discipline experienced remarkable progress and multiple advances over the last two decades. Thus, many high-complexity optimization algorithms are currently accessible to address current control problems in systems engineering. On the other hand, utilizing such methods is not straightforward and requires a long period of trying and searching for, among other aspects, start parameters, adequate objective functions, and the best optimization algorithm for the problem. Hence, the primary intention of this work is to investigate old and new MOO methods from the application perspective for the purpose of control system design, offering practical experience, some open topics, and design hints. A very challenging problem in the system engineering application of power systems is to dominate the dynamic behavior of very large wind turbines. For this reason, it is used as a numeric case study to complete the presentation of the paper.

Controlling forever love.

A stable and rewarding love relationship is considered a key ingredient for happiness in Western culture. Building a successful long-term relationship can be viewed as a control engineering problem, where the control variable is the effort to be made to keep the relationship alive and well. We introduce a new mathematical model for the effort control problem of a couple in love who wants to stay together forever. The problem can be naturally formulated as a dynamic game in continuous time with nonlinearities. Adopting a dynamic programming approach, a tractable computational formulation of the problem is proposed together with an accompanying algorithm to find numerical solutions of the couple’s effort problem. The computational analysis of the model is used to explore feeling trajectories, effort control paths, happiness, and stabilization mechanisms for different types of successful couples. In particular, the simulation analysis provides insight into the pattern of change of both marital quality and effort making in intact marriages and how they are affected by certain level of heterogamy in the couple.