Control Law Research Articles

Dynamic event-triggered synchronization for semi-Markovian switching inertial neural networks with generally uncertain transition rates in finite-time interval

This paper investigates the finite-time synchronization for inertial neural networks with stochastic switching parameters based on dynamic event-triggered protocol. Due to the complexity of network environment, semi-Markovian process is introduced into the modeling of inertial neural networks, in which the transition rates vary with the operating time. The dynamic event-triggered protocol is developed to determine whether the signal is transmitted, in which Zeno phenomenon is eliminated under limited bandwidth resources. The objective is to construct an appropriate dynamic event-triggered control law such that the drive-response system maintains finite-time synchronization under generally uncertain transition rates. Based on the Lyapunov functional theory, finite-time synchronization criterion is proposed for the related inertial neural networks. Furthermore, a dynamic event-triggered controller is constructed in a finite-time interval. A numerical example and an image encryption process are given to show the efficiency of the proposed method.

Nonlinear Robust Control of Vehicle Stabilization System with Uncertainty Based on Neural Network

To effectively suppress the effects of uncertainties including unmodeled dynamics and external disturbances in the vehicle stabilization system, a nonlinear robust control strategy based on a multilayer neural network is proposed in this paper. First, the mechanical and electrical coupling dynamics model of the vehicle stabilization system, considering model uncertainty and actuator dynamics, is refined. Second, the lumped uncertainty of the vehicle stabilization system is estimated by a multi-layer neural network and compensated by feedforward control. The high robustness of the system is ensured by constructing the sliding mode feedback control law. The proposed control method overcomes the limitations of sliding mode technology and the neural network and is naturally applied to the vehicle stabilization system, avoiding the adverse effects of high-gain feedback. Based on Lyapunov theory, it is demonstrated that the proposed controller is able to achieve the desired stability tracking performance. Finally, the effectiveness of the proposed control strategy is verified by co-simulation and comparative experiments.

An Advanced IBVS-Flatness Approach for Real-Time Quadrotor Navigation: A Full Control Scheme in the Image Plane

This article presents an innovative method for planning and tracking the trajectory in the image plane for the visual control of a quadrotor. The community of researchers working on 2D control widely recognizes this challenge as complex, because a trajectory defined in image space can lead to unpredictable movements of the robot in Cartesian space. While researchers have addressed this problem for mobile robots, quadrotors continue to face significant challenges. To tackle this issue, the adopted approach involves considering the separation of altitude control from the other variables, thus reducing the workspace. Furthermore, the movements of the quadrotor (pitch, roll, and yaw) are interdependent. Consequently, the connection between the inputs and outputs cannot be reversed. The task complexity becomes significant. To address this issue, we propose the following scenario: When the quadrotor is equipped with a downward-facing camera, flying at high altitude is sensible to spot a target. However, to minimize disturbances and conserve energy, the quadrotor needs to descend in altitude. This can result in the target being lost. The solution to this problem is a new methodology based on the principle of differential flatness, allowing the separation of altitude control from the other variables. The system first detects the target at high altitude, then plots a trajectory in the image coordinate system between the acquired image and the desired image. It is crucial to emphasize that this step is performed offline, ensuring that the image processing time does not affect the control frequency. Through the proposed trajectory planning, complying with the constraints of differential flatness, the quadrotor can follow the imposed dynamics. To ensure the tracking of the target while following the generated trajectory, the proposed control law takes the form of an Image Based Visual Servoing (IBVS) scheme. We validated this method using the RVCTOOLS environment in MATLAB. The DJI Phantom 1 quadrotor served as a testbed to evaluate, under real conditions, the effectiveness of the proposed control law. We specifically designed an electronic card to transfer calculated commands to the DJI Phantom 1 control joystick via Bluetooth. This card integrates a PIC18F2520 microcontroller, a DAC8564 digital-to-analogue converter, and an RN42 Bluetooth module. The experimental results demonstrate the effectiveness of this method, ensuring the precise tracking of the target as well as the accurate tracking of the path generated in the image coordinate system.

Boundary feedback control of Navier–Stokes equations around arbitrary bluff body with prescribed drag and lift coefficients

This paper presents a boundary feedback control method for the two- and three-dimensional Navier–Stokes equations around an arbitrary bluff body, with prescribed drag and lift coefficients. In order to determine the feedback control law, we consider an extended system coupling the equations governing the Navier–Stokes problem with an equation satisfied by the control on the bluff body, which is a part of the domain boundary. We utilize the artificial compressibility method, which approximates the Navier–Stokes equations in the limit, along with a priori estimation techniques, to establish a boundary control. Such a control law ensures that the prescriptions of the drag and lift coefficients are attained. Subsequently, a compactness result allows to let the compressibility parameter tend to zero. The application of the Faedo-Galerkin method is essential in reaching this result.

Nonlinear Attitude and Altitude Trajectory Tracking Control of a Bicopter UAV in Geometric Framework

In this paper, we deal with a Bicopter drone that has two thrusters and two tilting servos. Both the position and attitude dynamics of Bicopter are globally expressed on the Special Euclidean group SE3. A simple control allocation method is proposed to map between the control wrench and actuator inputs for the Bicopter. A geometric nonlinear attitude and altitude tracking controller is developed for the Bicopter and the asymptotic stability analysis is performed using the Lyapunov method for the closed-loop nonlinear system. The performance of the proposed altitude and attitude stabilization controller is validated through experimental hardware developed in-house. The attitude controller performance is validated through simulations and shown to be comparable against an linear matrix inequality-based control law.

Dual therapy of cancer using optimal control supported by swarm intelligence.

The scientific revolution in the treatment of many illnesses has been significantly aided by stem cells. This paper presents an optimal control on a mathematical model of chemotherapy and stem cell therapy for cancer treatment. To develop effective hybrid techniques that combine the optimal control theory (OCT) with the evolutionary algorithm and multi-objective swarm algorithm. The developed technique is aimed to reduce the number of cancerous cells while utilizing the minimum necessary chemotherapy medications and minimizing toxicity to protect patients' health. Two hybrid techniques are proposed in this paper. Both techniques combined OCT with the evolutionary algorithm and multi-objective swarm algorithm which included MOEA/D, MOPSO, SPEA II and PESA II. This study evaluates the performance of two hybrid techniques in terms of reducing cancer cells and drug concentrations, as well as computational time consumption. In both techniques, MOEA/D emerges as the most effective algorithm due to its superior capability in minimizing tumour size and cancer drug concentration. This study highlights the importance of integrating OCT and evolutionary algorithms as a robust approach for optimizing cancer chemotherapy treatment.

Non-singular control strategies for a class of strict-feedback nonlinear time-delay systems

This paper focuses on the non-singular control for strict-feedback nonlinear time-delay systems. The boundedness of all the signals of the closed-loop system is rigorously proved by introducing a class of Lyapunov-Krasovskii functionals, including exponential functions. Besides, novel auxiliary functions with continuous derivatives are proposed to construct the control law to avoid the discontinuity of the virtual controllers. Besides, the amount of computation is reduced by applying the new auxiliary functions when the other control methods require loads of calculations for handling singular problems. In the end, numerical examples are given to validate the effectiveness of the proposed control scheme.

Adaptive neural network‐based security asynchronous control for uncertain Markov jump power systems with dead zone under DoS attack

AbstractThe article deals with the security control stabilization problem of uncertain Markov jump power systems with input dead zone under stochastic denial‐of‐service (DoS) attack. DoS attack is modeled as a discrete‐time Markov process. Dual hidden Markov models are respectively used to detect the modes of the original power systems and the one under DoS attack. Based on the detected modes and neural networks (NNs), adaptive NN‐based security asynchronous control strategies are proposed, where both state feedback and output feedback are studied simultaneously. With the developed control laws, all trajectories of the closed‐loop systems are bounded stable in the stochastic setting. Simulation results demonstrate the correctness and usefulness of the proposed techniques.

Backstepping Synchronization Control for Four-dimensional Chaotic System Based on DNA Strand Displacement

Abstract Backstepping control is an important nonlinear control design method, which realizes the control of complex systems by constructing control law step by step, and has significant advantages for dealing with complex nonlinear systems. This article proposes a synchronization technique for four-dimensional chaotic systems using a combination of backstepping control method and DNA strand displacement technology. By relying on theoretical knowledge of DNA molecules, five basic chemical reaction modules such as trigger reaction, reference reaction, catalytic reaction, annihilation reaction and degradation reaction are given to construct a four-dimensional DNA chaotic system. On the basis of the relevant theory of chaotic dynamics, the constructed system is analyzed by Lyapunov exponent diagram and spectral entropy complexity algorithm, and the results come to the conclusion that the system reveals extremely complex and varied dynamic behaviors. Combining DNA strand displacement technology with backstepping control method, four controllers are developed to ensure that the trajectories of two homogeneous chaotic systems are synchronized. The numerical simulation results validate the feasibility and applicability of the proposed method. The method proposed in this paper may provide some references in the field of DNA molecular chaos synchronization control.

Rotor Flux and EEMF Observer for Interior Permanent Magnet Synchronous Machine

In recent years, the use of the Interior Permanent Magnet Synchronous Machine (IPMSM) in various applications has grown significantly due to numerous benefits. Sensors are used to achieve high efficiency and good dynamic response in IPMSM drives but due to their high cost and reduce overall size of system,sensorless control techniques are preferred. Non-sinusoidal distribution of rotor flux and slot harmonics are present in the considered IPMSM. In this article, these problems are considered as control system disturbances. With the above-mentioned problems, the classical observer structure based on (d-q) fails to estimate at low-speed ranges. This article proposes an observer structure based on a rotor flux vector in (α-β) stationary reference frame, which works using the adaptive control law to estimate speed and position, and a non-adaptive EEMF-based observer to estimate speed and position. Moreover, a comparative analysis between both observer structures at the different speed ranges is also considered in this article. The effectiveness of the observer structure is validated by simulation tests and experimental tests using the sensorless control system with a field-oriented control scheme for 3.5 kW IPMSM drive system.

Optimal orbit transfer of single-tether E-sail with inertially fixed spin axis

AbstractThis study analyzes the optimal transfer trajectory of a spacecraft propelled by a spin-stabilized electric solar wind sail (E-sail) with a single conducting tether and a spin axis with a fixed direction in an inertial (heliocentric) reference frame. The approach proposed in this study is useful for rapidly analyzing the optimal transfer trajectories of the current generation of small spacecraft designed to obtain in-situ evidence of the E-sail propulsion concept. In this context, starting with the recently proposed thrust model for a single-tether E-sail, this study discusses the optimal control law and performance in a typical two-dimensional interplanetary transfer by considering the (binary) state of the onboard electron emitter as the single control parameter. The resulting spacecraft heliocentric trajectory is a succession of Keplerian arcs alternated with propelled arcs, that is, the phases in which the electron emitter is switched on. In particular, numerical simulations demonstrated that a single-tether E-sail with an inertially fixed spin axis can perform a classical mission scenario as a circle-to-circle two-dimensional transfer by suitably varying a single control parameter.

Optimal controller for S–CO2 compressor inlet conditioning

The small, simple, and effective characteristics of a Supercritical CO2 (S–CO2) power system make it an ideal candidate for distributed power generation. However, the distributed power generation will be required with constant changes in the operating conditions to meet the varying demand. Thus, it is necessary for the S–CO2 power system to demonstrate that it can operate safely and efficiently under all anticipated operating conditions. One of the key issues in the S–CO2 power system is controlling the compressor inlet conditions. This paper focused on the control of the compressor inlet temperature. In this paper, a system dynamic simulation code is used to model the precooler system for the compressor inlet control first. Based on the analysis results to obtain the transfer function and the state space, a linear quadratic controller was designed using optimal control theory. Since the controller was estimated to have steady-state error, a disturbance observer was also used. To validate the designed controller, experiments were conducted. The experimental results show that the proposed controller can be used to maintain the S–CO2 compressor inlet conditions under various transient scenarios without additional tuning.

Impact of warranty and green level of the product with nonlinear demand via optimal control theory and Artificial Hummingbird Algorithm

Due to the current environmental situation and human health, a green manufacturing system is very essential in the manufacturing world. Several researchers have developed various types of green manufacturing models by considering green products, green investments, carbon emission taxes, etc. Motivated by this topic, a green production model is formulated by considering selling price, time, warranty period and green level dependent demand with a carbon emission tax policy. Also, the production rate of the system is an unknown function of time. Per unit production cost of the products is taken as increasing function of production rate and green level of the products. In our proposed model, carbon emission rate is taken as linear function of time. Then, an optimization problem of the production model is constructed. To validate of our proposed model, a numerical example is considered and solved it by AHA. Further, other five metaheuristics algorithms (AEFA, FA, GWOA, WOA and EOA) are taken to compare the results obtained from AHA. Also, concavity of the average profit function and convergence graph of different metaheuristics algorithms are presented. Finally, a sensitivity analysis is carried out to investigate the impact of different system parameters on our optimal policy and reach a fruitful conclusion from this study.

Coordinated management of oxygen excess ratio and cathode pressure for PEMFC based on synthesis variable-gain robust predictive control

In this research endeavor, a novel synthesis variable-gain robust model predictive control (SVGRPC) method using the min-max technique with parameter dependent Lyapunov functions is introduced to achieve the desired trajectory tracking of oxygen excess ratio (OER) and cathode pressure in the polymer electrolyte membrane fuel cells (PEMFCs) system. Initially, a simplified control-oriented model of the air supply system is developed and then transformed into a polytopic form to accommodate the inherent uncertainties in the PEMFC. Subsequently, the polytopic model is integrated with the reference trajectory to construct an augmented state-space model for deriving an error state representation. In the framework of robust model predictive control (RPC) utilizing a parameter-dependent Lyapunov function, a series of variable feedback gains are employed to mitigate conservatism. Additionally, the online solution process imposes a significant computational burden, presenting challenges for the real-time implementation of RPC-based control strategy. Therefore, the offline computing is introduced to significantly reduce the computational burden, resulting in the development of the SVGRPC strategy proposed in this paper. Subsequently, the SVGRPC strategy computes explicit linear state-feedback control laws by solving linear matrix inequalities (LMIs) using an offline control algorithm. The effectiveness of the proposed controller is then validated through assessments conducted under three distinct operating conditions of the PEMFC system. The outcomes of this study affirm that the proposed controller improves the requirements of control performance when compared to the online RPC with a quadratic Lyapunov function while significantly alleviating the computational workload.

Shoulder viscoelasticity in a raptor-inspired model alleviates instability and enhances passive gust rejection

Recent experiments with gliding raptors reveal a perplexing dichotomy: remarkably resilient gust rejection, but, at the same time, an exceptionally high degree of longitudinal instability. To resolve this incompatibility, a multiple degree of freedom model is developed with minimal requisite complexity to examine the hypothesis that the bird shoulder joint may embed essential stabilizing and preflexive mechanisms for rejecting rapid perturbations while simplifying and reducing control effort. Thus, the formulation herein is centrally premised upon distinct wing pitch and body pitch angles coupled via a Kelvin–Voigt viscoelastic shoulder joint. The model accurately exhibits empirical gust response of an unstable gliding raptor, generates biologically plausible equilibrium configurations, and the viscoelastic shoulder coupling is shown to drastically alleviate the high degree of instability predicted by conventional linear flight dynamics models. In fact, stability analysis of the model predicts a critical system timescale (the time to double amplitude of a pitch divergence mode) that is commensurate with in vivo measured latency of barn owls (Tyto alba). Active gust mitigation is studied by presupposing the owl behaves as an optimal controller. The system is under-actuated and the feedback control law is resolved in the controllable subspace using a Kalman decomposition. Importantly, control-theoretic analysis precisely identifies what discrete gust frequencies may be rapidly and passively rejected versus disturbances requiring feedback control intervention.

Finite-time asynchronous control for semi-Markov jump systems with random uncertainties and actuator faults

This article is aimed at studying the finite-time reliable asynchronous control issue for continuous semi-Markov jump systems (S-MJSs) with actuator failures and randomly occurring uncertainties (ROUs). To characterize the asynchronous phenomenon between the system mode and the controller mode, the mode detector approach via a hidden semi-Markov model (HSM) is adopted. The transition probability (TP) matrix of the HSM is nonhomogeneous, which can be provided by a polytopic structure. By resorting the mode-dependent Lyapunov function, sufficient conditions are attained to guarantee the stochastic finite-time boundedness (SFTB) and H∞ performance of the closed-loop system. Then, according to a skillful matrix inequality transforming method, the reliable asynchronous control law is constructed. Finally, a tunnel diode circuit system and a mass-spring-damper mechanical system are proposed to demonstrate the superiority, effectiveness and practicality of the developed design method.

Time-Optimal Motions of a Mechanical System with Viscous Friction

Optimal control is a critical tool for mechanical robotic systems, facilitating the precise manipulation of dynamic processes. These processes are described through differential equations governed by a control function, addressing a time-optimal problem with bilinear characteristics. Our study utilizes the classical approach complemented by Pontryagin’s Maximum Principle (PMP) to explore this inverse optimal problem. The objective is to develop an exact piecewise control function that effectively manages trajectory control while considering the effects of viscous friction. Our simulations demonstrate that the proposed control law markedly diminishes oscillations induced by boundary conditions. This research not only aims to delineate the reachability set but also strives to determine the minimal time required for the process. The findings include an exact analytical solution for the stated control problem.

Vision-based adaptive LT sliding mode admittance control for collaborative robots with actuator saturation

Abstract In this paper, we propose a novel vision-based adaptive leakage-type (LT) sliding mode admittance control for actuator-constrained collaborative robots to realize the synchronous control of the precise path following and compliant interaction force. Firstly, we develop a vision-admittance-based model to couple the visual feedback and force sensing in the image feature space so that a reference image feature trajectory can be obtained concerning the contact force command and predefined trajectory. Secondly, considering the system uncertainty, external disturbance, and torque constraints of collaborative robots in reality, we propose an adaptive sliding mode controller in the image feature space to perform precise trajectory tracking. This controller employs a leakage-type (LT) adaptive control law to reduce the side effects of system uncertainties without knowing the upper bound of system uncertainties. Moreover, an auxiliary dynamic is considered in this controller to overcome the joint torque constraints. Finally, we prove the convergence of the tracking error with the Lyapunov stability analysis and operate various semi-physical simulations compared to the conventional adaptive sliding mode and parallel vision/force controller to demonstrate the efficacy of the proposed controller. The simulation results show that compared with the controller mentioned above, the path following accuracy and interaction force control precision of the proposed controller increased by 50% and achieved faster convergence.

Analysis, Simulation, and Experiments of Dynamics and Control of a Hydrostatic Wind Turbine Under Partial Load

Abstract Kω2 control, also called torque control, is a popular method for maximizing wind turbine power. For hydrostatic wind turbines, torque control becomes pressure control with pc=K'ω2 because pressure is proportional to torque. Inverse Kω2 control is an alternative approach using rotor speed control with pc=(p/K')1/2. This work analyzes the dynamics of hydrostatic wind turbines using forward and inverse Kω2 control with P-, PD-, PI-, and PID-control for feedback. Dimensionless, linearized models are used. Analysis shows that the mechanical rotor dynamics are much slower than the hydrostatic transmission dynamics and that frictional and leakage losses are negligible. Linear perturbation of the nonlinear model reveals that the closed-loop control is not in Evan's form, so that closed-loop poles and zeros both vary with the loop gain. Pole and zero root locus analysis shows how systems responses change with controller gains. Both control approaches require derivative controller action to sufficiently dampen their responses; both are also fundamentally limited in speed of response by a slow stable pole regardless of controller loop gains. Nonlinear system simulation shows that both control approaches track the maximum power point with nearly identical transient behavior and have nearly identical power losses when using suboptimal values of the control law gain, K. Pressure control has a gain margin of infinity and a phase margin of 99.3 degrees, while speed control has a gain margin of 22.4 dB and a phase margin of 73.8 degrees showing that pressure control is more robust than speed control. Experiments using the power regenerative hydrostatic test stand at the University of Minnesota show that the control approaches have different transient responses but capture comparable power under steady and turbulent conditions.

Study on SEAI Model of COVID-19 Based on Asymptomatic Infection

In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number R0 and calculate the equilibrium point. Secondly, when R0<1, the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When R0>1, the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of R0 is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease.