Nonlinear Control Design Research Articles

An approach to exact nonlinear feedback control design employing recursive approximations and the null space

A strategy to design exact nonlinear feedback controllers based on a recursive application of approximate linearization methods is examined. The computations are algebraic and computationally simpler than solving the set of coupled nonlinear partial differential equations thereby facilitating practical symbolic computer computations enabling discernment of evolving patterns in the approximate solutions as the order of approximation increases. Utilizing the null space that appears at each step in the computations as part of the computations, a family of analytic solutions can be generated asymptotically. There are possibilities for optimizing the performance by judiciously choice of analytic solution that emerge from the selective use of the null space.

Improved Back-Stepping Control for Nonlinear Small UAV Systems With Transient Prescribed Performance Design

This paper proposes an improved back-stepping control approach and its application to small nonlinear UAV control systems with uncertainties such as external disturbance. Unlike traditional back-stepping control methods, the idea of prescribed performance function (PPF) is incorporated into the control design, such that both the transient and steady-state control performance can be strictly guaranteed. Moreover, we design a novel tracking differentiator to avoid the “differential expansion” problem well caused by the calculation of derivative. Significantly, the function approximators (e.g. neural networks) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. Finally, the numerical simulation verifies the convergence and robustness of the system, and the results show that the control strategy can obtain better transient and steady-state performance.

Nonlinear feedforward controller design for air-path system with transport dynamics of external EGR system

Abstract Advanced combustion, such as homogenous charge compression ignition (HCCI), requires precise control of the in-cylinder gas condition. Such advanced combustion does not always result in stoichiometric combustion; therefore, the changes in the oxygen concentration of the burned gas must be considered in the controller design. Furthermore, the changes in the oxygen concentration in the exhaust manifold are transferred to the intake manifold with delay. In this research, the transport dynamics of the exhaust gas recirculation (EGR) path were modeled by a pure time-varying delay and a second-order filter, and the model was used to estimate the oxygen concentration through the EGR valve. The feedforward controller was obtained based on the inverse model, which calculates the throttle and EGR valve positions based on the target values of the intake manifold pressure, EGR ratio, and estimated oxygen concentration at the EGR valve. The control performance of the proposed feedforward controller was evaluated by conducting simulations using both the mean value model and the precise model constructed using 1D simulation software.

Throttle Control using NMPC with Soft Intake Temperature Constraint for Knock Mitigation

Abstract Knocking is an unwanted behavior that is affected by the intake manifold temperature. This paper demonstrates through simulation how nonlinear Model Predictive Control design could be used as a reference governor for the control of the throttle position, with a soft constraint on intake manifold temperature. The implementation is able to suppress the peak temperature during an acceleration by slowing down the pressure build-up. Because of the usually slow dynamics of the temperature sensors, the paper proposes an Extended Kalman Filter implementation that uses a transient detection to decide whether to rely on the sensor feedback or the model.

Restricted Structure Polynomial Systems Approach to LPV Generalized Predictive Control

Abstract A new polynomial systems method is defined for the restricted structure nonlinear predictive controllers design. The control algorithm is established for a discrete-time nonlinear system, described in the polynomial matrix linear parameter varying form. The low-order restricted structure controller is parameterized in terms of discrete transfer operators set that the designer chooses multiplied by a set of optimized gains. The controller within the feedback loop can have a general linear parameter varying form or something as simple as a PI structure. The predictive control multi-step cost-index, which is minimized, comprises weighted error, control signal costing, and gain magnitude terms. A simulation of an automotive example is used to evaluate the nonlinear restricted structure controller performance.

Nonlinear Fault-Tolerant Control Design for Singular Stochastic Systems With Fractional Stochastic Noise and Time-Delay

Nonlinear Fault-Tolerant Control Design for Singular Stochastic Systems With Fractional Stochastic Noise and Time-Delay

Trajectory Tracking Control of Quadrotor via Minimum Projection Method

Abstract In this paper, we consider a nonlinear tracking controller design problem for a quadrotor. For the controller design, we design a tracking control Lyapunov function (TCLF) based on the minimum projection method. However, it is not clear whether we can design the TCLF for a quadrotor by the method. In particular, it is difficult to calculate the TCLF without reducing the amount of computation. We show that the use of the orthogonal property of the direction cosine matrix in the quadrotor dynamics has the effect of reducing the computation. Finally, we demonstrate the computer simulation for a given trajectory.

Nonlinear state feedback control design for port-Hamiltonian systems with unstructured component

Abstract This paper considers the problem of state feedback controller design to stabilize generalized Hamiltonian systems with an unstructured component. This class of models enable one to exploit the structure of port-Hamiltonian systems for feedback control design while relaxing the constraint of deriving an exact structured port-Hamiltonian representation. For a given stabilizable nonlinear system, and with some assumptions on the unstructured part of the dynamics, a stabilizing control law is designed and asymptotic stability of a desired equilibrium of the system is demonstrated. A numerical illustration of the proposed approach is presented to demonstrate the design method.

Extremum Seeking For Economic Driving as An OnLine Mobile Application

Economic driving or energy-efficient driving plays a crucial role at reducing pollution caused by mass-production cars and fuel consumption. Operating a technical system at its most efficient set point is well known. But economic driving in traffic scenarios are more difficult to traffic flow, road grades and engine characteristics. In this study, the scalar energy-efficient variable is defined in order to seek energy efficient set point of the engine dynamics producing driving torque as a response to the travelling tasks in the road infrastructure and traffic. As an alternative solution to the well presented nonlinear controllers, a rough modelling is used to enable mobile computing on a smart-phone as an on-board unit in the car measuring the vehicle controller area network, global positioning coordinate system information and acceleration information. Overall, from the nonlinear controller design including its stability proof to the human-machine interface design to be used in road tests is elaborated. A 11% energy saving is obtained during road tests by using the presented on-line mobile and portable solution.

Simple adaptive control strategy for a class of systems subjected to real parametric uncertainty with application to unified chaotic system

In this paper, a relatively simplified adaptive control strategy for set of chaotic systems is presented. The results utilise the basic linear state feedback control strategy blended with algebraic matrix Riccati equation (AMRE) to derive the control mechanism for chaotic systems operating in uncertain environment. The proposed approach utilises lesser number of control inputs in comparison to methods available in literature. Moreover, the controller structure turns out to be simple linear combination of states of system for the chaotic systems belonging to the proposed class, which are otherwise handled with nonlinear controller design strategies. The Lyapunov stability approach is exploited to analytically derive the control function and the parametric updation laws for uncertain parameters. Extensive simulation results are elaborated for set of chaotic systems to demonstrate effectiveness and validity of the presented approach.

Parameters determination of time-delayed embedding with application to Koopman operator-based model predictive frequency control

Power systems around the world have been registering a degenerating inertial response in view of the growth of inverter-based resources along with the withdrawal of conventional coal units. Therefore, there is a need for swift frequency support and its control, preferably by means of power electronic-interfaced storage devices, owing to their beneficial capabilities. Despite being particularly efficient, pragmatically, the traditional model-based non-linear control techniques are not highly popular in power system control design, primarily due to the complications faced in obtaining accurately suitable models for certain power system components. Lately, the modelfree Koopman operator-based model predictive control (KMPC) has proven to be highly conducive for data-driven non-linear control design. The principle behind KMPC is to change the coordinates in a manner to get an approximately linear model, which can then be controlled using a linear model predictive control. In this study, we employed time-delayed embedding of measurements to reconstruct a new set of preferable coordinates, thereby suggesting an approach for finding the optimal number of time lags and the embedding dimensions which are the key parameters of this algorithm. The efficacy of this KMPC framework is established by adopting a decentralized frequency control problem through a decoupled synchronous machine system, which we proposed for both the Kundur two-area system as well as the IEEE 39-bus test system.

Nonlinear Control of Non-Combined Integrated Governor for Kaplan Turbine Generator Set

In this paper, a nonlinear model is established for the Kaplan turbine generator set (KTGS) with dual input governor and generator excitation to solve unsatisfactory regulation performance caused by the deviation from the combination curve during the transient process. According to the model characteristics, the constraint effect of the objective function in multi-objective feedback nonlinear control design is utilized to replace the associative relationship between the wicket gate and the blade. Then, a three-variable integrated nonlinear control strategy (TVINCS) is applied to the wicket gate, blade governor, and generator excitation. Simulation results demonstrate the precise tracking performance of hydraulic and electrical parameters controlled by TVINCS. The controller is designed to guarantee the turbine's output efficiency, and effectively coordinate the wicket gate and blade actions in the dynamic regulation process, providing a superior dynamic adjustment performance for the system under various disturbances.

Fuzzy descriptor tracking control with guaranteed L∞ error-bound for robot manipulators

This paper is concerned with the nonlinear tracking control design for robot manipulators. In spite of the rich literature in the field, the problem has not yet been addressed adequately due to the lack of an effective control design. Using a descriptor fuzzy model-based framework, we propose a new approach to design a feedback-feedforward control scheme for robot manipulators in a general form. The goal is to guarantee a small level of an [Formula: see text] gain specification to improve the tracking performance while significantly reducing the numerical complexity for real-time implementation. Based on Lyapunov stability arguments, the control design is formulated as a convex optimization problem involving linear matrix inequalities. Numerical experiments performed with a high-fidelity manipulator benchmark model, embedded in the Simscape MultibodyTM environment, demonstrate the effectiveness of the proposed control solution over existing standard approaches.

Tensor product model transformation‐based control for fractional‐order biological pest control systems

AbstractAs environmental pollution and safety of human and creatures have been an issue of concern, pest management based on nonchemical use is preferable. Biological pest control can satisfy the regulation of pest population without causing environmental problems. Moreover, representation of dynamical systems in the form of fractional‐order dynamic models can explain several phenomena better than the integer‐order dynamic models can. The aim of this study is to determine the biological pest control policy for the fractional‐order pest control systems, which is a complex nonlinear multiple input and multiple output control problem. Here, the system is represented in the form of a fractional‐order Lotka–Volterra model. In order to avoid complexity in the nonlinear feedback controller design process, the tensor product (TP) model transformation was applied to automatically transform the biological pest control system to the TP polytopic model which allows the designer to synthesize the controller under linear framework. Moreover, the design process can be easily carried out by solving an linear matrix inequality (LMI) problem, which is very well applicable to high‐dimensional multiple input and multiple output control problems. Simulation studies were conducted to demonstrate the ease of the TP‐based design process. The simulation results showed that the designed control policy effectively manipulates the pest populations of the fractional‐order Lotka–Volterra model to the desired level which is economically viable.

Double integral action based sliding mode controller design for the back-to-back converters in grid-connected hybrid wind-PV system

In this paper, a double integral sliding mode based nonlinear controller (DISMC) is developed for the grid-connected hybrid wind-PV system. The proposed control approach provides better steady state response and robustness as compared to the existing control methods. The topology considered in this study for the wind and PV based hybrid distributed generator system is efficient. Wind and PV generator are connected to the utility grid via boost converter at the machine side followed by inverter at the grid side. Thus, the realized scheme has reduced number of DC-DC conversion stages as compared to the previous schemes. So far, no study investigates the design of nonlinear controller for this scheme. Proposed DISMC offers the maximum power point tracking (MPPT) for both wind and PV generator, DC bus voltage regulation, and smooth transfer of active power to the utility grid. Firstly, the detailed small-signal mathematical models for the proposed hybrid system and DC bus dynamics are developed. After that, three control laws based on DISMC are designed to ensure the stable operation under varying weather conditions and system uncertainties. Then, the stability of the hybrid system is proved using Lyapunov theory. Finally, the performance of the proposed framework has been verified using model-based MATLAB time-domain simulations, and controller hardware-in-the-loop (C-HIL) experiments. The superiority of the proposed control technique was approved by comparing the result with other control methods.

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.

A novel condition for fixed-time stability and its application in controller design for robust fixed-time chaos stabilization against Hölder continuous uncertainties

This paper presents a new nonlinear state-feedback controller design for robust fixed-time chaos stabilization of chaotic systems in the presence of a relatively large class of uncertainties known as Holder continuous uncertainties. Based on Lyapunov's second method, a novel sufficient condition for fixed-time stability is derived. The spectacular property of the proposed controller is that the upper bound of the convergence time exists as an explicit parameter in the control's law, thus the true fixed stabilization time can be set in advance. To show the effectiveness of the proposed controller, two scenarios are provided, and the simulation results are reported.

Nonlinear control for modular multilevel converters with enhanced stability region and arbitrary closed loop dynamics

This paper presents the nonlinear control design with formal stability proof for a Modular Multilevel Converter (MMC), which is critical for the interaction between AC and DC grids. Lyapunov theory is used to develop the proposed controller, which is based on Backstepping and Feedback Linearization techniques and to perform the stability analysis. The proposed controller allows to asymptotically stabilize all converter’s states, i.e., AC currents, circulating currents, and internal energy. The proposed algorithm allows to manage the converter in a wide range of operation points, by means of arbitrary tuning assignment. Robustness and performances of proposed control are verified by means of Matlab Simscape Electrical simulations, including active and reactive power reference variations and grid imbalance conditions. A detailed MMC switching model, of 450MVA is considered on Matlab validation. A phase-shift PWM is considered, with a sorting algorithm. Also, a comparison with a standard PI controller is performed. In addition, MMC’s internal energy is also controlled, which can contribute to the high-speed frequency control by using this energy for synthetic inertia.

An improved two‐loop model predictive control design for nonlinear robust reference tracking with practical advantages

SummaryIn this paper, the nonlinear robust reference tracking problem is considered and an Improved Two‐Loop Nonlinear Model Predictive Control (ITL‐NMPC) design is proposed for a pre‐controlled system with bounded uncertainties subject to input and state constraints. In the industry, this scheme leads the lower design cost and fewer implementation risks since (i) it allows the existing controller to remain unchanged without any manipulation, (ii) it does not need the open‐loop model of the pre‐controlled system, and (iii) it does not require the terminal cost and constraint definition. For the proposed ITL‐NMPC, a practical parameter tuning algorithm is introduced and its robust exponential stability, as well as recursive feasibility, are guaranteed. Simulation results are used to better illustrate the effectiveness of the proposed approach and show that the proposed method not only improves the control performance of the pre‐controlled system but also reduces the design cost while satisfying the constraints.

Design of gain scheduled fuzzy PID controller for multi-link robot manipulators

Gain Scheduling (GS) controller is one of the most popular approaches to nonlinear control design. Commonly, Gain Scheduling (GS) controllers have better performance than robust ones. In this paper, the structure of a proposed gain scheduled PID fuzzy controller (GS-PIDF) designed and analyzed. The Fuzzy PID controller gains weighted through gain scheduling designed system to grantee both the stability and the best performance of a multi links robot manipulator system. The overall designed controller system is applied to two links robot manipulator system, which is subject to modelling using Lagrangian dynamics method and simulation vie MatLab and Simulink package to minimize the vibration and acquire best performance.