Nonlinear Feedback Control Scheme Research Articles

Data-driven model based adaptive feedback-feed forward control schemes for open cycle - OTEC process

Open Cycle - Ocean Thermal Energy Conversion (OC-OTEC) is one of the most important renewable energy sources that generate electricity and fresh water from seawater utilizing the temperature gradient between the warm surface seawater and the cold deep seawater. This paper aims to develop non-linear data-driven model-based adaptive Feedback Control (FBC) schemes for the OC-OTEC process to track the output power and a dynamic Feed-Forward Control (FFC) scheme to reject the effects of temperature disturbance on power caused by climate variations in OC-OTEC. The experiments are conducted on a laboratory-scale OC-OTEC experimental setup at the National Institute of Ocean Technology, Chennai. Firstly, linear data-driven models are developed using system identification techniques. Based on the developed models, gain scheduling-based adaptive control schemes are developed: Proportional Integral (PI) control and Model Predictive Control (MPC). Secondly, the closed-loop performances of the developed FBC schemes are analysed under servo and regulatory operations. Furthermore, it is observed from the sensitivity analysis results that the temperature disturbance highly influences output over the manipulated variable. Hence, a dynamic FFC scheme is implemented to reject known disturbance of 1 °C variation in temperature gradient from 18 °C to 19 °C due to Sea Surface Temperature (SST) changes in temperature gradient. The results show that the proposed MPC-based FBC-FF scheme effectively enhances the tracking and disturbance rejection performance compared to the PI-based FBC-FF control scheme with a minimum Integral Square Error (ISE) of 3.055 and Control Effort (CE) of 7.505. This experimental data-based, data-driven modelling and adaptive control research provides a new direction for automating OC-OTEC. Further, these studies will help to develop a rugged and automated upscaling OC-OTEC plant control system with proposed feasible control schemes.

Optimization of wind energy extraction for variable speed wind turbines using fuzzy backstepping sliding mode control based on multi objective PSO

This study addresses the problem of designing a nonlinear feedback control strategy for horizontal axis variable speed wind turbines in the below-rated wind speed operating region (whether the wind turbine is offshore or onshore). The objective is to operate the wind turbines to maximum wind energy extraction while reducing the mechanical load. To overcome both issues, a robust nonlinear control strategy based on sliding mode control (SMC) is proposed which tries to seek for an improved performance. The proposed controller has been developed to compensate for negative consequences of external disturbances, measurement noises and unmodeled dynamics. This control strategy exploits a tracking controller that keeps an optimal value for the ratio between the rotor angular speed and the wind speed. For maximum wind energy extraction, the control algorithm employs the sliding mode state output feedback torque controller to provide robustness, combined with backstepping scheme to ensure better performance in the presence of matched and mismatched uncertainties. Next, a fuzzy logic system (FLS) approach is introduced to the backstepping sliding mode controller (BSMC) to achieve better mechanical loads prevention suffered by the transmission shaft by adjusting the parameters of the controller. Finally, multi-objective particle swarm optimization (MOPSO) algorithm is used to find the optimal values for the adjustable parameters of the proposed fuzzy BSMC (FBSMC). To validate the proposed control structure, FAST aeroelastic simulator is used. The obtained results illustrate that the presented control scheme has satisfactory performance.

Nonlinear robust adaptive control for bidirectional stabilization system of all-electric tank with unknown actuator backlash compensation and disturbance estimation

Since backlash nonlinearity is inevitably existing in actuators for bidirectional stabilization system of all-electric tank, it behaves more drastically in high maneuvering environments. In this work, the accurate tracking control for bidirectional stabilization system of moving all-electric tank with actuator backlash and unmodeled disturbance is solved. By utilizing the smooth adaptive backlash inverse model, a nonlinear robust adaptive feedback control scheme is presented. The unknown parameters and unmodelled disturbance are addressed separately through the derived parametric adaptive function and the continuous nonlinear robust term. Because the unknown backlash parameters are updated via adaptive function and the backlash effect can be suppressed successfully by inverse operation, which ensures the system stability. Meanwhile, the system disturbance in the high maneuverable environment can be estimated with the constructed adaptive law online improving the engineering practicality. Finally, Lyapunov-based analysis proves that the developed controller can ensure the tracking error asymptotically converges to zero even with unmodeled disturbance and unknown actuator backlash. Contrast co-simulations and experiments illustrate the advantages of the proposed approach.

Tree-structured neural networks: Spatiotemporal dynamics and optimal control

How the network topology drives the response dynamic is a basic question that has not yet been fully answered in neural networks. Elucidating the internal relation between topological structures and dynamics is instrumental in our understanding of brain function. Recent studies have revealed that the ring structure and star structure have a great influence on the dynamical behavior of neural networks. In order to further explore the role of topological structures in the response dynamic, we construct a new tree structure that differs from the ring structure and star structure of traditional neural networks. Considering the diffusion effect, we propose a diffusion neural network model with binary tree structure and multiple delays. How to design control strategies to optimize brain function has also been an open question. Thus, we put forward a novel full-dimensional nonlinear state feedback control strategy to optimize relevant neurodynamics. Some conditions about the local stability and Hopf bifurcation are obtained, and it is proved that the Turing instability does not occur. Moreover, for the formation of the spatially homogeneous periodic solution, some diffusion conditions are also fused together. Finally, several numerical examples are carried out to illustrate the results’ correctness. Meanwhile, some comparative experiments are rendered to reveal the effectiveness of the proposed control strategy.

Application of social spider optimization and improved active disturbance rejection controller in hierarchical control of cooperative multi-lift with four unmanned helicopters

To achieve the three-dimensional free movement of the slung load, a load-leading hierarchical control strategy has been adopted recently which divides the cooperative multi-lift system into a load layer, a cable layer, and an aircraft layer. But there exists a non-convex optimization problem in the cable layer when computing the force of each cable, and more control difficulties of the aircraft due to the additional disturbances resulting from the load movement. To solve these problems, an application of the social spider optimization (SSO) algorithm and the improved active disturbance rejection controller (IADRC) in hierarchical control of cooperative multi-lift with four unmanned helicopters is proposed in this study. First, the unmanned helicopters as well as the load are modeled. Then the three layers mentioned above are designed, respectively. Specifically, an optimization method combining SSO with the MATLAB/fmincon function is proposed to solve the non-convex problem in the cable layer. And within the unmanned helicopter layer, the fuzzy theory is introduced into the nonlinear error feedback control strategy of the traditional active disturbance rejection controller (ADRC) to realize the control of the unmanned helicopter. At last, some simulations are carried out, and the results indicate that the system has higher calculation efficiency, smaller steady-state error, and better adaptability to trajectory change or load release with the designed hierarchical control strategy.

A modification of nonlinear feedback controller

This paper derives new results for the modify of nonlinear feedback controller. The stability results are established using the Lyapunov's second method as a main tool. Since the finding characteristic equations are not required for the modify method, the nonlinear feedback control strategy with this modification is very effective and convenient to realise the chaos control for dynamical systems. Furthermore, modify method is used to overcome some problem in nonlinear feedback controller, which helps to achieve the convergence of dynamics system easily. This proposed method has certain significances for reducing the effort and complexity of controller implementation. Finally, numerical simulations are given to illustrate and verify the results.

A New Nonlinear Control Design Strategy for Fixed Wing Aircrafts Piloting

This paper proposes a novel nonlinear feedback control strategy for velocity and attitude control of fixed wing aircrafts. The key feature of the control design strategy is the introduction of a virtual control input in order to deal with the underactuation property of such vehicles and to indirectly control the orientation of the aircraft. As such, the proposed strategy consists of three control loops each realizing a specific task. Simulations are carried out by using the jetstream-3102 aircraft in a real-time virtual Simulation Platform for the development of Aircraft Control Systems (SP-ACS). The proposed approach of control is model-based for which we have introduces an identification part before test and validation. We use the Total Least Squares Estimation (TLSE) technique to identify the aerodynamic parameters, which are unknown, variable and classified. Each aerodynamic coefficient is defined as the mean of its numerical values. All other variations are considered as modeling uncertainties that will be compensated by the robustness of the piloting law. Simulation results on Jetstream-3102 aircraft show very good performance in terms of convergence towards the desired reference trajectories and in terms of robustness with respect to modeling uncertainties.

Optimal metaheuristic-based sliding mode control of VSC-HVDC transmission systems

The design of classical controllers for Voltage Source Converter High Voltage Direct Current (VSC-HVDC) transmission systems, is load-dependent and has to be adjusted for each operating condition. Thus, the robustness of such controllers becomes necessary to cope with operating condition continuous variations. Therefore, the design of hybrid optimal Artificial Intelligence Based-Sliding Mode Controllers (AI-SMCs) for VSCHVDC transmission systems is crucial research interest. These AI based controllers are proved to improve the system’s dynamic stability over a wide range of operating conditions considering different parameter variations and disturbances. For this purpose, a comprehensive state of the art of the VSC-HVDC stabilization dilemma is discussed. The nonlinear VSC-HVDC model is developed. The problem of designing a nonlinear feedback control scheme via two control strategies is addressed seeking a better performance. For ensuring robustness and chattering free behavior, the conventional SMC (C-SMC) scheme is realized using a boundary layer hyperbolic tangent function for the sliding surface. Then, the Modified Genetic Algorithm (MGA) and Particle Swarm Optimization technique (PSO) are employed for determining the optimal gains for such SMC methodology forming a modified nonlinear MGA-SMC and PSO-SMC control in order to conveniently stabilize the system and enhance its performance. The simulation results verify the enhanced performance of the VSC-HVDC transmission system controlled by both MGA-SMC and PSO-SMC compared to the C-SMC. The comparative dynamic behavior analysis for both the conventional SMC and the two meta-heuristic optimization based SMC control schemes are presented. Through simulation results, the effectiveness of the proposed metaheuristic optimization approaches and their applicability to VSC-HVDC system global stabilization and dynamic behavior enhancement are validated.

A Nonlinear Control Design Strategy for Piloting Fixed Wing Aircrafts

Abstract This paper proposes a novel nonlinear feedback control strategy for velocity and attitude control of fixed wing aircrafts. The key feature of the control design strategy is the introduction of a virtual control input in order to deal with the underactuation property of such vehicles and to indirectly control the orientaion of the aircraft. As such, the proposed strategy consists of three control loops each realising a specific task. Simulation results on Jetstream-3102 aircraft show very good performance in terms of convergence towards the desired reference trajectories and in terms of robustness with respect to modeling uncertainties.

Nonlinear Optimal Feedback Control and Stability Analysis of Solar Photovoltaic Systems

The efficiency of solar photovoltaic (PV) systems is directly affected by the convergence and steady-state responses of the implemented control method. In this paper, considering the nonlinearity appearing in the model of the solar PV system, we employ a nonlinear optimal feedback control scheme to deal with the oscillations around the maximum power point (MPP) of the system, induced by the chattering phenomenon in the control. Taking into account the improved transient response and flexibility, brought by including the cross-weighting terms in the cost functional, we develop an optimal control framework with a nonquadratic cost for addressing the MPP tracking (MPPT) problem of the solar PV system. Exploiting the fact that a Lyapunov function candidate can be considered as the steady-state solution of the Hamilton-Jacobi-Bellman (HJB) equation, we obtained the optimal feedback controller via minimizing the resultant Hamiltonian. The stability analysis of the closed-loop system is done for the obtained control law with a guaranteed performance measure. Moreover, to enhance the practicality of the obtained control law, we present two procedures to implement the obtained control scheme under nonuniform insolation and as a model-free approach, separately. To demonstrate the merits of the proposed framework, the obtained optimal feedback control, together with the partial shading condition and model-free approach, is simulated under various weather conditions. The optimal approach illustrates an improved performance in terms of the convergence rate and the amplitude of oscillations around the MPP, compared to existing results in the literature.

The synchronisation of two floating memristor-based oscillators and the circuit design

The synchronisation between two floating memristor-based Colpitts oscillators is studied in this paper. Firstly, the mathematical and circuit models of Colpitts oscillator based on a floating memristor with a diode bridge structure are built. On this basis, numerical simulations on the features of both the independent memristor and the floating memristor are conducted and compared using MATLAB software. Secondly, circuit simulation is made on the synchronisation of two floating memristor-based systems by using MULTISIM software. Finally, the physical circuit on the synchronisation of the two coupling Colpitts systems based on the diode bridge memristors is implemented by using the linear error feedback scheme and improved by the capacitor coupling scheme and the adaptive nonlinear feedback control scheme, respectively. The experimental results by the oscilloscope and simulation results show that approximate synchronisation is achieved.

Nonlinear delayed feedback control of synchronization in an excitatory–inhibitory coupled neuronal network

We explore nonlinear time-delayed feedback as a technique for the control of synchronization in excitatory–inhibitory coupled neuronal networks. The feedback signal can be expressed in two forms: differential feedback control and direct feedback control, to suppress bursting synchronization. In the two-dimensional plane of feedback strength and time delay, domains of effective synchronization suppression are described. For these two different types of nonlinear feedback, numerical simulations yield completely different results: The differential feedback is noninvasive, but it has a fragile robust performance. However, the direct feedback is robust against stimulation parameter variations, but it is invasive. Furthermore, electromagnetic induction is introduced by calculating the magnetic flux on membrane, and how it affects nonlinear time-delayed feedback control to suppress bursting synchronization is explored. We show that desynchronization effect of the differential feedback can be enhanced by appropriate electromagnetic induction. And desynchronization effect of the direct feedback is maintained by a small electromagnetic induction intensity, and no longer works once it exceeds a critical value. These presented results are expected to facilitate us to control abnormal brain synchrony, and promote the applications of the nonlinear feedback control scheme in practical clinical treatment.

Incremental SMC-based CNF control strategy considering magnetic ball suspension and inverted pendulum systems through cuckoo search-genetic optimization algorithm

A kind of incremental sliding mode control (SMC) approach in connection with the well-known composite nonlinear feedback (CNF) control strategy is newly considered in this research to deal with the nonlinear magnetic ball suspension and inverted pendulum systems, as well. The incremental SMC approach is in fact proposed to handle the aforementioned underactuated systems under control, which have a lower number of actuators than degrees of freedom. Based on the outcomes of the investigation presented here, the small overshoot and short settling time of the system response are fulfilled. In fact, the proposed CNF control strategy comprises two parts: the first term assures the stability of the closed-loop nonlinear system and provides a fast convergence response. The second term reduces its overshoot. The genetic-cuckoo hybrid algorithm is designed to minimize tracking errors for the purpose of finding the most suitable sliding surface coefficients. Finally, the finite time stability for the closed-loop system is proved, theoretically.

Analysis of a mathematical model with nonlinear susceptibles-guided interventions.

In this paper, we considered a mathematical model describing the nonlinear susceptibles-guided vaccination and isolation strategies, incorporating the continuously saturated treatment. In this strategy, we find that the disease-free periodic solution can always exist, and consequently the control reproduction number can be defined through analyzing the stability of the disease-free periodic solution. Also, we discussed the existence and stability of the positive order-1 periodic solution from two points of view. Initially, we investigated the transcritical and pitchfork bifurcation of the Poincaré map with respect to key parameters, and proved the existence of a stable or an unstable positive order-1 periodic solution near the disease-free periodic solution. For another aspect, by studying the properties of the Poincaré map, we verified the existence of the positive order-1 periodic solution in a large range of the control parameters, especially, we verified the co-existence of finite or infinite countable different positive order-1 periodic solutions. Furthermore, numerical simulations show that the unstable order-1 periodic solution can co-exist with the stable order-1, or order-2, or order-3 periodic solution. The finding implies that the nonlinear susceptibles-triggered feedback control strategy can induce much rich dynamics, which suggests us to carefully choose key parameters to ensure the stability of the disease-free periodic solution, indicating that infectious diseases die out.

Disturbance observer based control for spacecraft proximity operations with path constraint

This paper investigates the application of a nonlinear feedback control strategy for driving a chaser spacecraft to rendezvous and dock with a target spacecraft in space. The nonlinear coupled models are established to describe the relative position and relative attitude dynamics, while a nonlinear disturbance observer is employed to estimate and compensate the external disturbances. Furthermore, a specific potential function is designed to prevent the chaser from entering into the forbidden zone or colliding with the target during the final phase of rendezvous and docking. Within the Lyapunov framework, the ultimate boundedness of the closed-loop system is guaranteed in the existence of external disturbances. Numerical simulations are performed to illustrate the feasibility and effectiveness of the proposed control strategy for motion synchronization as well as collision avoidance.

Course keeping Control Based on Integrated Nonlinear Feedback for a USV with Pod-like Propulsion

In this paper, a response model of an Unmanned Surface Vehicle (USV) with a pod-like propulsion device is established. To improve the robustness of motion control in heavy sea states, an integrated nonlinear feedback course-keeping controller is proposed. First, to establish a response model of a USV with pod-like propulsion, model parameters are obtained by the method of system identification, then an integrated nonlinear feedback control strategy is proposed. The essence of this method is to make the original error signal pass through a nonlinear function, and then the output of this function is used to replace the original error signal. Simulation results show that under ordinary sea states, nonlinear feedback can save up to 34.5% of energy used compared with standard feedback methods; under heavy sea states, this can rise to 40.8%. A set of field experiments were carried out with a USV with pod-like propulsion. Results show that under heavy sea states, the test USV can maintain the target course well, which proves the correctness of the model and the robustness of the proposed method.

Hopf bifurcation control of hydro-turbine governing system with sloping ceiling tailrace tunnel using nonlinear state feedback

Aiming at improving the regulation quality of a hydro-turbine governing system with sloping ceiling tailrace tunnel, Hopf bifurcation control using nonlinear state feedback is studied. Firstly, the nonlinear mathematical model of a hydro-turbine governing system with sloping ceiling tailrace tunnel is presented. Then, a novel control strategy using nonlinear state feedback with polynomial functions is proposed, and Hopf bifurcation control of a hydro-turbine governing system using the proposed control strategy is described. Finally, the application and functional mechanism of the proposed control strategy are analyzed by comparison with the PID strategy. The results indicate that: The proposed nonlinear state feedback control strategy is able to make the frequency of a hydro-turbine unit return to the initial value (i.e. rated frequency), and the regulation quality and the response speed are obviously better than those under the PID strategy. The effect of the linear term of nonlinear state feedback control strategy is to modify the system's linear stability, in order to eliminate or delay an existing bifurcation. Altering the nonlinear term can change the stability of bifurcation solutions, for example, converting a Hopf bifurcation from subcritical to supercritical.

Nonlinear state-dependent feedback control strategy in the SIR epidemic model with resource limitation

In present work, in order to avoid the spread of disease, the impulse control strategy is implemented to keep the density of infections at a low level. The SIR epidemic model with resource limitation including a nonlinear impulsive function and a state-dependent feedback control scheme is proposed and analyzed. Based on the qualitative properties of the corresponding continuous system, the existence and stability of positive order-k (kinmathbf{Z}^{+}) periodic solution are investigated. By using the Poincaré map and the geometric method, some sufficient conditions for the existence and stability of positive order-1 or order-2 periodic solution are obtained. Moreover, the sufficient conditions which guarantee the nonexistence of order-k (kgeq3) periodic solution are given. Some numerical simulations are carried out to illustrate the feasibility of our main results.

Stabilization of rigid body attitude motion with time-delayed feedback

A continuous nonlinear full-state time-delayed feedback control scheme is designed within the framework of geometric mechanics to stabilize the rigid body attitude motion, which is subject to an unknown constant time delay in feedback measurement. The attitude kinematics is globally described on the matrix Lie group SO(3) of rigid body rotations. A Morse–Lyapunov–Krasovskii functional is utilized to guarantee the asymptotic stability of the system, which yields the control gain matrices via linear matrix inequality stability conditions. In light of this result, a delayed feedback control scheme is also designed for the planar rotational motion to examine the almost global asymptotic stability of the system in the presence of an unknown time delay in feedback measurement. Simulations are performed for the proposed control schemes based on the discretized models of the controlled systems and the performance of the proposed controllers are evaluated by employing large maneuvers.

Nonclassical state generation for linear quantum systems via nonlinear feedback control

In this paper, we propose a measurement nonlinear feedback control scheme to generate Wigner-function negativity in an optical cavity having dynamics described as a linear quantum system. In general, linear optical quantum systems can be easily constructed with reliable devices; therefore, the idea of constructing the entire system with such an optical system and nonlinear feedback is reasonable for generating Wigner-function negativity. However, existing studies have insufficiently examined the realizability or actual implementation of feedback control, which essentially requires fast responses from the sensors and actuators. In order to solve this problem, we consider the realizable feedback control of the optical phase of a pumping beam supplied to a cavity by using electro-optical modulation, which can be utilized as a fast control actuator. Then, we introduce mathematical models of the feedback-controlled system and evaluate its effect on the generation of the Wigner-function negativity by using numerical simulation. Through various numerical simulations, we show that the proposed feedback control can effectively generate the negativity of the Wigner function.