Nonlinear Control Method Research Articles

Nonlinear optimal control for the multi-variable tumor-growth dynamics

The multivariable tumor-growth dynamic model has been widely used to describe the inhibition of tumor-cells proliferation under the simultaneous infusion of multiple chemotherapeutic drugs. In this article, a nonlinear optimal (H-infinity) control method is developed for the multi-variable tumor-growth model. First, differential flatness properties are proven for the associated state-space description. Next, the state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instant around a time-varying operating point which is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the system a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach.

Nonlinear optimal and multi-loop flatness-based control of induction motor-driven desalination units

In this article, the control problem for the induction-motor driven reverse osmosis in desalination units is solved with the use of (i) a nonlinear optimal control method (ii) a flatness-based control approach which is implemented in successive loops. To apply method (i) that is nonlinear optimal control, the dynamic model of the induction-motor driven reverse-osmosis desalination units undergoes approximate linearization at each sampling instant with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization point is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. To compute the feedback gains of the optimal controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the nonlinear optimal control method are proven through Lyapunov analysis. To implement control method (ii), that is flatness-based control in successive loops, the state-space model of the induction-motor driven reverse-osmosis desalination unit is separated into three subsystems, which are connected in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input–output linearized flat systems. The state variables of the preceding (ith) subsystem become virtual control inputs for the subsequent (i+1th) subsystem. In turn, exogenous control inputs are applied to the first and third subsystem. The whole control method is implemented in three successive loops and its global stability properties are also proven through Lyapunov stability analysis. The proposed method achieves stabilization of the induction-motor-driven reverse osmosis desalination unit without the need of diffeomorphisms and complicated state-space model transformations.

Design of nonlinear control method for pressure of pintle solid rocket motor

A pressure control method that incorporates parameter adaptation has been devised for the pressure control system of pintle solid rocket motors, which exhibit notable nonlinearities and uncertainties in parameters. Firstly, the mathematical relationship between pressure and pintle displacement is derived using the zero-dimensional interior ballistic model., and the state space equation is deduced by incorporating the dynamics of motor inertia load. Secondly, by capitalizing on the robustness of robust control, the parameter identification capabilities of adaptive control, and the rigor of Lyapunov stability theory, the proposed approach enables precise control of the pintle position while effectively addressing uncertainties, thereby enhancing the overall performance and stability of the system. Finally, the aforementioned theoretical framework has been validated through rigorous numerical simulations. The findings demonstrate a notable enhancement in the pressure response speed of the adaptive robust controller, with improvements of 10.01 % and 13.16 %, 0.03 % and 1.54 %, 0.06 % and 22.39 % in different orders of magnitude of free volume as compared to the robust controller and PID controller, respectively. Moreover, it is evident that the adaptive robust controller relies on the accuracy of the model. The applied controller demonstrates notable advantages in terms of stability, robustness, and accuracy, thereby substantially enhancing the overall performance of the pressure control system.

Retracted: Nonlinear Control Method of Superconducting Energy Storage considering Voltage Imbalance in Distribution Network

Retracted: Nonlinear Control Method of Superconducting Energy Storage considering Voltage Imbalance in Distribution Network

Adaptive Fuzzy Fault-Tolerant Control of Uncertain Fractional-Order Nonlinear Systems with Sensor and Actuator Faults

In this work, an adaptive fuzzy backstepping fault-tolerant control (FTC) issue is tackled for uncertain fractional-order (FO) nonlinear systems with sensor and actuator faults. A fuzzy logic system is exploited to manage unknown nonlinearity. In addition, a novel FO nonlinear filter-based dynamic surface control (DSC) method is constructed, effectively avoiding the inherent complexity explosion problem in the backstepping recursive process, and in the light of the construction of auxiliary functions, compensating the coupling term introduced by faults. On account of certain assumptions, the stability criterion of the FO Lyapunov function is applied to guarantee the stability of the closed-loop system. Finally, the simulation example verifies the validity of the presented control strategy.

Improved Inverted Pendulum Control through PID and EPID Controllers

This presentation is on studies of application of combined constant rate reaching law and proportional-integral-derivative (PID) control law (EPID) for the control of inverted pendulum system. The inverted pendulum system is similar to a typical attitude control of booster rocket undergoing the takeoff process. Recent studies indicated records of higher rates of accidents in aircrafts. The records show that about half results due to malfunctions of aircraft systems and close to one-third from propulsion system malfunctions. Others are higher complexities of modern aircraft systems and in trying to reduce cost of maintenance. Therefore, the need enhanced automation, fault detection, faults isolation, faults tolerance, faults diagnosis and faults correction. Linear control techniques may not yield the desired performances in aircraft systems due to high levels of system nonlinearities. Applications of the intelligent control counterparts may not guarantee the generation of mathematical model for in-depth analysis. The major demerit of nonlinear control methods is higher requirement of computational burden making practical implementation difficult. The model of the inverted pendulum system is a linearized analytical model. The system performance of the system was observed with the EPID and PID controllers. Furthermore the effect of sudden changes such as wind, gust or other related variations on the system was also studied using step disturbance. It was a simulation studies using MATLAB/SIMULINK software. Results showed that with the EPID a near zero deviation was achieved. Whereas with PID controller was able to only maintain a deviation of about 40. Results also indicated a near zero disturbance rejection ability with the EPID, while the PID was able to only suppress the disturbance to some extent. It implies a more robust control with the EPID was achieved for aircraft/inverted pendulum control. Hence, it implies enhanced performance and with further improvement it can be used for application in this class of systems as well as similar systems. The work would help to for basic researches in aircraft/inverted pendulum control for beginners as well as experienced researchers in the field.

Trajectory Tracking Control of Transformer Inspection Robot Using Distributed Model Predictive Control.

To overcome the difficulty in tracking the trajectory of an inspection robot inside a transformer, this paper proposes a distributed model predictive control method. First, the kinematics and dynamics models of a robot in transformer oil are established based on the Lagrange equation. Then, by using the nonlinear model predictive control method and following the distributed control theory, the motion of a robot in transformer oil is decoupled into five independent subsystems. Based on this, a distributed model predictive control (DMPC) method is then developed. Finally, the simulation results indicate that a robot motion control system based on DMPC achieves high tracking accuracy and robustness with reduced computing complexity, and it provides an effective solution for the motion control of robots in narrow environments.

Event-triggered multi-time scale control and low carbon operation for electric-hydrogen DC microgrid

This paper addresses the escalating need for low-carbon solutions and discusses the integrated control system for the electric-hydrogen DC microgrids. A multi-time scale control mechanism for the DC microgrid is proposed, which aims to enhance its adaptability and scalability. The proposed multi-time control scheme comprises two control layers. The system-level control layer utilizes optimization to address economic issues and carbon trading, aiming to minimize operational costs and carbon emissions in the microgrid. The local-level control layer incorporates an advanced nonlinear control method based on the exponential reaching law-powered terminal sliding mode control (ERL-TSMC) for accurate tracking capabilities at the local-level and to handle dynamic control challenges in real-time. Furthermore, an event-triggered control mechanism is introduced to reduce considerable control efforts while guaranteeing system robustness under various disturbances. Both simulations and hardware experiments demonstrate that the proposed control method guarantees efficient low-carbon operation, achieving a significantly lower average carbon intensity of 0.19 kg CO2/kWh. Additionally, it exhibits robust performance at the local-level, with a steady-state error of only 0.03%.

Nonlinear active noise control with tap-decomposed robust volterra filter

The Volterra filter is proven to be a structurally simple method for nonlinear active noise control (NLANC). However, its wide application is deeply constrained by computational complexity. This paper proposes a tap-decomposed Volterra filter, in which a long-tap Volterra filter is approximated as multiple short-tap filters by the nearest Kronecker decomposition. Since the number of taps of decomposed filters is much less than that of the original counterpart, the proposed method greatly reduces the implementation cost of the Volterra filter. Moreover, for impulsive noise sources in NLANC, decomposed filters are updated using the maximum correntropy criterion derived from information theory. Simulation experiments with different noise source types highlight the noise control performance of the proposed approach.

Nonlinear dynamic modeling and model-based AI-driven control of a magnetoactive soft continuum robot in a fluidic environment

In recent years, magnetoactive soft continuum robots (MSCRs) with multimodal locomotion capabilities have emerged for various biomedical applications. Developments in nonlinear dynamic models and effective control methods for MSCRs are deemed vital not only to gain a better understanding of their coupled magneto-mechanical behavior but also to accurately steer the MSCRs inside the human body. This study presents a novel dynamic model and model-based AI-driven control method to guide an MSCR in a fluidic environment. The MSCR is fully exposed to fluid flows at different rates to simulate the biofluidic environment within the body. A novel nonlinear dynamic model considering the effect of damping and drag force attributed to fluidic flows is first developed to accurately and efficiently predict the response of the MSCR under varying magnetic and mechanical loading. Fairly accurate correlations were observed between the theoretical responses based on the developed magneto-viscoelastic model and the experimental data for various scenarios. A novel model-based control algorithm based on a fractional-order sliding surface and deep reinforcement learning algorithm (DRL-FOSMC) is subsequently developed to accurately steer the magnetoactive soft robot on predefined trajectories considering varying fluid flow rates. A fractional-order sliding surface and a compensator, trained using the deep deterministic policy gradient algorithm, are designed to mitigate the amount of chattering and enhance the tracking performance of the closed-loop system. The stability proof of the developed control algorithm is also presented. A hardware-in-the-loop experimental framework has been designed to assess the effectiveness of the proposed control algorithm through various case studies. The performance of the proposed DRL-FOSMC algorithm is rigorously assessed and found to be superior when compared with other control methods.

Automatic scenario generation for efficient solution of robust optimal control problems

AbstractExisting methods for nonlinear robust control often use scenario‐based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time‐varying uncertainty. This paper draws from local reduction methods used in semi‐infinite optimization to solve robust optimal control problems with parametric and time‐varying uncertainty. By iteratively adding interim worst‐case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst‐case constraint violations. In particular, we present examples where local reduction methods find worst‐case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time‐varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time‐varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive.

Global Prescribed Performance Control of Unknown Strict-Feedback Systems With Quantized References

This article is concerned with the global prescribed performance tracking control problem for strict-feedback systems with quantized references, unknown nonlinearities, and unmatched disturbances. Discontinuity appears frequently in such references, for which most nonlinear control or filtering methods are not applicable straightforward. Besides, the existing approaches of predefining tracking performance work under local initial conditions, available nonlinearity knowledge, disturbance-free cases, or have complexity issues. In this article, a novel smoothing function is first designed for the online automatic generation of smooth trajectories in place of the quantized reference. Then, the tangent barrier functions are combined with a new form of performance functions (inverse proportional functions) to form a control. The strong robustness of the resulting controller against model uncertainties and disturbances evades the need for approximation, observation, etc., yielding simplicity of the control. The new performance functions relax the specific initial condition. Their combination ensures for any initial condition, the tracking error converges to a given bound. Simulation results on vehicular platoons illustrate the theoretical findings.

Ship-Mounted Cranes Hoisting Underwater Payloads: Transportation Control With Guaranteed Constraints on Overshoots and Swing

In recent years, with the rapid development of marine engineering, ship-mounted crane control for transporting payloads in the water has attracted more attention. Compared with the case of transporting payloads above water, ship-mounted cranes with underwater payloads are more difficult to control. On the one hand, the underwater payload is directly affected by the hydrodynamic force, and the dynamics of ship-mounted cranes is much more complex, nonlinear, and coupled; on the other hand, the unactuated underwater payload swing is quite sensitive to external disturbances; thus, the harsh marine environment will bring great challenges to the anti-swing control of underwater payloads. To address the above issues, this article puts forward a coupling characteristic indicator(CCI)-based nonlinear control method to realize accurate positioning and swing suppression for ship-mounted cranes hoisting payloads in the water, which not only simultaneously suppresses actuated boom overshoots and constrains <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unactuated</i> payload swing, but also indicates whether the coupling terms are beneficial or harmful to make full use of them to improve transient control performance. Rigorous theoretical derivation proves the closed-loop stability. To the best of our knowledge, this is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> solution to handle state constraints and utilizing the coupling characteristics of ship-mounted cranes for transferring payloads in the water. Finally, the proposed controller is applied to a self-made hardware platform, and the experimental results show that the designed method achieves satisfactory control performance.

Adaptive humidity and temperature nonlinear control for uncertain air-handling units

An adaptive temperature and humidity nonlinear control method is introduced to deal with unknown humidity source intensity and heat load for an air-handling unit (AHU). The serial-parallel estimation model is used to prevent the offset of the equilibrium point. By comparing with the linearization technique and fuzzy logics, an adaptive nonlinear controller is designed directly, which avoids the linearization of the system model and collapse of the calculation. With the stability analysis and simulation results comparison, it is verified that the control precision of the designed controller is higher and the tracking performance is better.

Nonlinear optimal control for permanent magnet synchronous spherical motors

Nonlinear optimal control for permanent magnet synchronous spherical motors

On the Synchronization of a novel fractional order chaotic system using nonlinear control method

On the Synchronization of a novel fractional order chaotic system using nonlinear control method

Finite-Time Synergetic Controller Design for DC Microgrids With Constant Power Loads

The negative impedance characteristic of constant power loads (CPLs) can cause DC bus voltage fluctuations or even DC microgrid instability. In this paper, a nonlinear synergetic control method is used to guarantee the DC bus voltage stability of DC microgrids with CPLs. First, to regulate the capacitor voltage to its desired value, a macro-variable is defined using the synergetic control theory. Then, due to the sensitivity of the system to the parameters of the input voltage, the CPL, and the resistive load, and also to enhance the overall system performance, an improved macro-variable is introduced by adding an integral action. Finally, the finite-time synergetic controller is proposed to provide the finite-time convergence for the DC microgrid voltage and also to avoid the chattering phenomenon. The simulation and experimental results demonstrate the acceptable performance of the proposed controller.

Nonlinear Quadratic Regulator Design With a Hybrid Switching Scheme for Wind Turbine Generators

This article proposes a new control scheme with a nonlinear quadratic regulator (NQR) associated with a hybrid switching stage for permanent magnet synchronous generator-based wind turbines (WTs). The proposed method shows a new approach combining a nonlinear optimal control method with a hybrid switching stage for WT generations (WTGs). As the WTG is a nonlinear system, NQR control design is directly employed to deal with the nonlinearity while a hybrid switching scheme can deal with constrained control inputs as discrete nonlinear characteristics of switch-mode power converters. A polynomial-based dynamic model is derived for the new NQR design. Unlike the previous state-dependent Riccatti equation (SDRE) technique where the solution of the nonlinear optimal controller is approximated, this technique finds the exact online solution of SDRE with nonlinear feedback gains flexibly depending on the tracking error. Then, the optimal control laws are implemented via a hybrid switching stage ensuring a smooth current regulation under a reduced switching frequency while avoiding any complicated modulator or finite state search. The proposed control design is investigated via comparative studies with linear quadratic regulator (LQR), direct switching, and space-vector pulse-width-modulation stages (SV-PWMs) implemented in both platforms of MATLAB/Simulink and real-time OPAL-RT. Comparative results exhibit flexible optimal performances via online hyper-parameter tuning to reduce the speed tracking error and low current ripples under a reduced switching frequency.

Dynamic obstacle avoidance of unmanned ship based on event-triggered adaptive nonlinear model predictive control

This article studies trajectory tracking and dynamic obstacle avoidance problems of unmanned ships, and an event-triggered adaptive nonlinear model predictive control (EANMPC) method is constructed to solve the above problems. Firstly, a novel adaptive nonlinear model predictive control is used to track the trajectory of the unmanned ship. And then, an obstacle avoidance mechanism is formulated to deal with the condition of dynamic obstacles that appear during the unmanned ship trajectory tracking process. Secondly, an event-triggered mechanism is established to reduce the computational burden of the controller. Finally, several simulation results are provided for demonstrating the effectiveness and advantage of EANMPC.

Projective Synchronization of Delayed Uncertain Coupled Memristive Neural Networks and Their Application.

In this article, the authors analyzed the nonlinear effects of projective synchronization between coupled memristive neural networks (MNNs) and their applications. Since the complete signal transmission is difficult under parameter mismatch and different projective factors, the delays, which are time-varying, and uncertainties have been taken to realize the projective synchronization of MNNs with multi-links under the nonlinear control method. Through the extended comparison principle and a new approach to dealing with the mismatched parameters, sufficient criteria have been determined under different types of projective factors and the framework of the Lyapunov-Krasovskii functional (LKF) for projective convergence of the coupled MNNs. Instead of the classical treatment for secure communication, the concept of error of synchronization between the drive and response systems has been applied to solve the signal encryption/decryption problem. Finally, the simulations in numerical form have been demonstrated graphically to confirm the adaptability of the theoretical results.