Control Law Research Articles

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.

RBS and ABS Coordinated Control Strategy Based on Explicit Model Predictive Control

During the braking process of electric vehicles, both the regenerative braking system (RBS) and anti-lock braking system (ABS) modulate the hydraulic braking force, leading to control conflict that impacts the effectiveness and real-time capability of coordinated control. Aiming to enhance the coordinated control effectiveness of RBS and ABS within the electro-hydraulic composite braking system, this paper proposes a coordinated control strategy based on explicit model predictive control (eMPC-CCS). Initially, a comprehensive braking control framework is established, combining offline adaptive control law generation, online optimized control law application, and state compensation to effectively coordinate braking force through the electro-hydraulic system. During offline processing, eMPC generates a real-time-oriented state feedback control law based on real-world micro trip segments, improving the adaptiveness of the braking strategy across different driving conditions. In the online implementation, the developed three-dimensional eMPC control laws, corresponding to current driving conditions, are invoked, thereby enhancing the potential for real-time braking strategy implementation. Moreover, the state error compensator is integrated into eMPC-CCS, yielding a state gain matrix that optimizes the vehicle braking status and ensures robustness across diverse braking conditions. Lastly, simulation evaluation and hardware-in-the-loop (HIL) testing manifest that the proposed eMPC-CCS effectively coordinates the regenerative and hydraulic braking systems, outperforming other CCSs in terms of braking energy recovery and real-time capability.

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.

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.

Real-time and hardware in the loop validation of electric vehicle performance: Robust nonlinear predictive speed and currents control based on space vector modulation for PMSM

The transport industry's environmental impact has prompted various stakeholders to focus more on electric vehicles as a potential solution. Extensive research on electric vehicle motor control reveals their complexity, highlighting the crucial role of the traction motor control mechanism being one of their essential subsystems. This study presents a novel approach to control the drive system of an electric vehicle's permanent magnet synchronous motor, using a robust non-linear model predictive control in a cascaded structure combined with a space vector modulation technique. The formulation of the robust non-linear model predictive control law involves optimizing a new cost function with the inclusion of an integral action in the controller to ensure zero steady-state error. An important aspect of this control approach is its ability to enhance robustness without needing information about external perturbations and parameter uncertainties. Moreover, the space vector modulation technique is designed to address the issue of current harmonic distortion by carefully selecting appropriate switching vectors. The appropriate selection for space voltage vectors for every sampling period maintains a consistent switching frequency. As a result, the SVM can enhance torque-rippled regulation and accomplish effective flux and torque control. The performance of the proposed control system is evaluated through a series of numerical simulations using MATLAB/Simulink. The simulation results are analyzed and compared to assess the effectiveness of the proposed control system in terms of tracking accuracy, disturbance rejection, robustness against parameter uncertainties, reduction of torque, and current ripples. To further validate the numerical simulation results, a hardware-in-the-loop (HIL) setup is established using the OPAL-RT platform. Furthermore, experimental validation on a PMSM utilizing the dSPACE DS1202 board is carried out, demonstrating the efficacy of the proposed control system. These findings validate the suggested control technique's robustness and efficiency.

Design and Experimental Study of an Embedded Controller for a Model-Based Controllable Pitch Propeller

The controllable pitch propeller hydraulic system has high constraints and nonlinearity. Due to these inherent deficiencies, the proportional–integral–derivative (PID) control algorithm cannot meet the control accuracy requirements of nonlinear systems. A control law based on a model predictive control (MPC) algorithm is designed in this paper. The gain parameters of the predictive control are optimized. The MPC and PID control systems are compared and simulated to verify the MPC controller’s effectiveness. Subsequently, the embedded controller of a controllable pitch propeller is developed. The support package for the embedded circuit board target containing an underlying driver for each interface is written by introducing the C-MEX S-Function and TLC programming language. A semi-physical simulation experiment is performed. The results show that the established controllable pitch propeller with an embedded controller displays reliable running performance, good anti-interference, and the capacity to fulfill the control function of the pitch propeller under various working conditions.

Simplified Strategy for Trajectory Tracking Application of a Passive Suspension Rover-Type Mobile Robot

In the present work, based on an approximate modelling of a rover-type robot and a proportional control law, a simplified trajectory tracking strategy for a passive suspension rover-type mobile robot was developed. This strategy achieves trajectory tracking and the autonomous displacement of a rover, of which its configuration involves complex kinematics and dynamics. All these lineaments reduce the complexity of the analysis, the number of electronic components to implement, the computational requirements and the energy consumption. The robotic system used is based on the Shrimp rover, which is a robot with a passive suspension that is capable of carrying out displacements over rough terrain. The tests were performed using numerical simulations with different desired trajectories, and also using experimental tests using a passive suspension rover-type mobile robot.

Space and time joint optimization for vertical takeoff and landing aircraft in dense obstacles and interference environments

ABSTRACT The Vertical Takeoff and Landing Aircraft (VTOL) is capable of both low-speed hovering and high-speed flight. This paper proposes an autonomous motion planning and anti-wind disturbance control algorithm for the VTOL, implemented spatial and temporal joint motion planning for VTOL, under the limitation of maximum flight speed of the aircraft, VTOL can achieve fully autonomous flight in complex environments, which can realize the autonomous flight of a single aircraft in a complex and dense environment, achieve real-time perception and avoidance of static and dynamic obstacles. The information generated by motion planning includes the position, velocity, and acceleration information of the aircraft, and proposes a wind disturbance estimation and active control strategy in a wind disturbance environment, accurate estimation of wind disturbance is achieved through a state observer, and the wind disturbance was suppressed through nonlinear error feedback control law, implemented wind disturbance estimation and suppression for aircraft in wind disturbance environments, and achieved complete autonomous motion planning and trajectory tracking of VTOL in a complex and wind disturbance environment. Our work can provide a basis for the collaborative control of multiple UAVs.

Fixed-time event-triggered sliding mode time-varying formation control for multiple surface vessels with fast convergence

ABSTRACT This paper proposes a new fixed-time sliding mode time-varying formation control strategy for multiple surface vessels (MSVs) to improve control performance and ensure navigation safety. First, a fixed-time extended state observer (FxESO) is designed to provide estimations of velocities and lumped disturbances. Then, the event-triggered fixed-time distributed time-varying formation control law is designed based on prescribed performance function (PPF) and fixed-time nonsingular terminal sliding mode (FxNTSM) manifold. Finally, system stability is analyzed based on Lyapunov theory. The salient features of the proposed scheme are as follows. First, a novel hyperbolic cosecant PPF is incorporated into the control scheme to enhance control performance. Then, the proposed scheme is combined with relative threshold event-triggered strategy to reduce unnecessary updates of actuators. Finally, a uniform exact differentiator is introduced to avoid the formation control law including the acceleration of adjacent vessel. Comparative results are given to demonstrate the superiority of the proposed scheme.

A review of dynamic optimization in aquaculture production economics

AbstractDynamic optimization (DO) has been applied to aquaculture industry to determine optimal management strategies of aquaculture production systems. Optimal control of feeding, optimal stocking successions, and harvesting time among other factors has been studied. This work shows a review of the application of optimal control theory (OCT) and dynamic programming in economics and management of aquaculture. The Pontriagyn's maximum principle and the Bellman's optimality are the most commonly used mechanisms to solve control problems that optimize the producer's benefit or cost. Recently, model‐based predictive control has also been applied. Such tools have been used in aspects involving the design, planning, and monitoring of variables relevant to the optimal management of the culture system. It was found that in aquaculture there is low scientific productivity in the application of DO in bioeconomic models. In this review, an example of OCT applied to the control of feeding of farmed tilapia using a bioeconomic model is shown. DO represents a useful tool for optimal decision‐making and this review discusses the implications of the use of DO in aquaculture and recommendations for its use in the future.