Control Design For Nonlinear Systems Research Articles

Comparison of methods of nonlinear control systems design

The issue of designing nonlinear control systems is a complex problem. A lot of methods are known that allow us to find a suitable control for a given nonlinear object that provides asymptotic stability of the nonlinear system equilibrium and an acceptable quality of the transient process. Many of these methods are difficult to apply in practice. Thus, comparing some of the methods in terms of simplicity of use is of great interest. Two analytical methods for the synthesis of nonlinear control systems are considered. They are the algebraic polynomial-matrix method that uses a quasilinear model, and the feedback linearization method that uses the Brunovsky model in combination with special feedbacks. A comparative analysis of the algebraic polynomial-matrix method and the feedback linearization method is carried out. It is found out that the algebraic polynomial-matrix method (APM) is much simpler than the feedback linearization method (FLM). A numerical example of designing a system that is synthesized by these methods is considered. It is found out that the system synthesized by the APM method has a region of attraction of the equilibrium position twice as large as the region of attraction of the system synthesized by the FLM method. It is reasonable to use the algebraic polynomial-matrix method with the quasilinear models in case of synthesis of control systems of objects with differentiable nonlinearities.

Multi-objective Lyapunov-based controller design for nonlinear systems via genetic programming

Multi-objective Lyapunov-based controller design for nonlinear systems via genetic programming

A Multi-Spectral Approach to Fuzzy Quantum Modelling of Nonlinear Systems

In this work, we explore multi-input multi-output (MIMO) nonlinear control systems design by generalizing concepts from radio link analysis. We demonstrate practical applications of multidimensional sampling and reconstruction to reducing computational overhead in nonlinear systems analysis. Using multi-spectral analysis, we show that (de)fuzzification in control systems and (de)modulation in communication systems are analogous. Finally, we explore the values of fuzzy submodels as quantum mechanics objects for stability analysis and feedback controller synthesis of nonlinear mechanical systems. The effectiveness of the proposed approach is confirmed by simulating the attitude model a telecommunications satellite.

Global EPD regulation of uncertain nonlinear systems without global normal forms

AbstractThis article considers the global regulation problem for a class of non‐affine nonlinear uncertain systems. We will investigate the extended proportional‐derivative (EPD) controller together with its parameters design. The EPD controller is the natural extension of the classical PD control, which adjusts the input signal by using the regulation error together with its derivatives only. We will show that under some suitable conditions on nonlinearity and uncertainty of the systems, the regulation error of the closed‐loop system will converge to 0 exponentially, provided that the EPD controller parameters are chosen from an n‐dimensional unbounded set constructed in the article. In contrast to most of the existing literature on controller design of nonlinear systems, we do not require such special system structures as normal or triangular forms. We will also give an example where the regulation problem is solvable globally by the classical PD control, while the controlled system cannot be transformed into the nonlinear normal form globally.

Optimal adaptive guaranteed-cost H-infinity model reference controller design for nonlinear systems

Optimal adaptive guaranteed-cost H-infinity model reference controller design for nonlinear systems

Control of Nonlinear Uncertain Systems by Extended PID

Since the classical proportional-integral-derivative (PID) controller is the most widely and successfully used ones in industrial processes, it is of vital importance to investigate theoretically the rationale of this ubiquitous controller in dealing with nonlinearity and uncertainty. Recently, we have investigated the capability of the classical PID control for second-order nonlinear uncertain systems, and provided some analytic design methods for the choices of PID parameters, where the system is assumed to be in the form of cascade integrators. In this article, we will consider the natural extension of the classical PID control for high-order affine-nonlinear uncertain systems. In contrast to most of the literature on controller design of nonlinear systems, we do not require such special system structures as normal or triangular forms, thanks to the strong robustness of the extend PID controller. To be specific, we will show that under some suitable conditions on nonlinearity, and uncertainty of the systems, the extended PID controller can semiglobally stabilize the nonlinear uncertain systems, and at the same time the regulation error converges to zero exponentially fast, as long as the control parameters are chosen from an open unbounded parameter manifold constructed in this article.

Numerical Design Method of Quasilinear Models for Nonlinear Objects

Design modern methods of nonlinear control systems of nonlinear objects in the majority assume transformation of initial object model to some special forms. In these cases, it is reasonable to use quasilinear models as they can be designed on condition only of differentiability of the nonlinearities of the initial objects models. These models allow to find control analytically, i.e. as a result of the solution of some equations system, if the object, naturally, meets the controllability condition. The quasilinear models are synthesized traditionally analytically, bytransformation of initial nonlinear models using operation of the taking of partial derivatives from the nonlinearities of the initial objects models and the subsequent integration of these derivatives on the auxiliary variable with application of the known formulas of differentiation and integration. However, in many cases, the objects nonlinearities have so complicated character, that the operations of the differentiation and, in particular, the integration are executed very difficult by shown way. This complexity can be overcome by application of the new numerical design method of the quasilinear models, which excludesneed of the analytical differentiation and integration, but demands considerable number of the arithmetic operations. But now it is not the big problem since the modern multiprocessor controllers can carry out all the necessary operations for a short time. The developed method allows to receive rather exact, approximate piecewise-constant quasilinear models for the objects with the complicated nonlinearities. It is convenient to apply such models at numerical control of the nonlinear objects. The efficiency of a numerical method is shown by comparison of phase portraits of piecewise constant quasilinear and nonlinear models of a simple object and also by comparison of the state variables values of these models. The offered method can be applied to nonlinear control systems design for the nonlinear, characterized by complicated characteristics objects ship, aviation, chemical, agricultural and other industries.

Modeling and Nonlinear Adaptive Control for Omnidirectional Mobile Robot

This study presents a complete model for RobotinoMD an omnidirectional mobile robot. This model includes the kinematics and dynamics. It is used for the simulation and design of an adaptive nonlinear control system. The hierarchical control system that is proposed has three levels. The level-one which is the inner loop is used to control the DC motors that drive the robot wheels. A control design method combining an adaptive feedback linearization technique and the Backstepping approach is used to find the controller equation. The adaptation module that is included in the control system maintains the performance of the system in the presence of uncertainties on the inertia, weight and other parameters in the robot dynamics. The level-one controller receives its reference signal from the level-two controller which converts the linear and rotational speeds into desired speeds. This level-two controller receives its reference signal from the level-three controller which is the outer loop controller. The level-three controller equation is found so that the robot can follow a desired path described in a Cartesian space. The proposed control system is evaluated in simulation in the MATLAB-SIMULINK environment. It is compared to a PID controller. Simulation results show that the nonlinear adaptive controller has better performances.

Finite-Time Adaptive Fuzzy Prescribed Performance Control for High-Order Stochastic Nonlinear Systems

In this article, the high-order nonlinear system is commonly studied in an underactuated weakly coupled mechanical system, the control design is difficult from the tractional control design for nonlinear systems. Thus, we study the finite-time fuzzy adaptive error constraint control problem for stochastic high-order nonlinear nonstrict feedback systems. Fuzzy logic systems are utilized to identify the unknown nonlinear dynamics, a new error transfer variable is used to achieve the prescribed performance. Based on adding a power integrator technique and adaptive backstepping recursive control, a novel adaptive fuzzy finite-time prescribed performance control scheme is developed. By utilizing stochastically finite-time stable theory, the proposed control method can guarantee that the high-order system is semi-global finite-time stable in probability. Finally, both numerical and practical simulations are provided to verify the feasibility and effectiveness of the developed control method.

An Investigation into Accuracy, Computation, and Robustness of Stochastic Linearization of Systems with Saturation Nonlinearities

Quasilinear Control (QLC) is a theory with a set of tools that can be used for the analysis and design of stochastic feedback control systems with nonlinear actuators and sensors. It is based on Stochastic Linearization (SL), a method of linearization that approximates a nonlinearity with an equivalent gain and a bias using statistical properties of its input. While the QLC literature has studied many problems in controls (e.g., performance analysis and controller design), important issues such as accuracy, robustness, and computation of SL have not been fully investigated. This paper fills this gap, with a special focus on feedback systems with saturating actuators, which are commonly encountered in feedback control systems and the QLC literature. Specifically, the accuracy of SL in approximating the saturated response is investigated. A mathematical relationship is established between the saturation authority and the worst-case open-loop accuracy, and the implications on closed-loop accuracy are described. To study the robustness of SL in practical situations, the sensitivities of the equivalent SL gain and bias to system parameters are investigated. Finally, several root-finding algorithms are compared in terms of their computational speed in solving the SL equations, and a novel change of coordinates is presented to improve the performance. The results provide valuable insights into and methods for addressing the computational aspects of SL that are critical for proper design and analysis of nonlinear stochastic feedback control systems.

Discrete fractional order PID controller design for nonlinear systems

ABSTRACT In this study, a discrete fractional order PID controller for nonlinear systems is proposed. U-model is firstly employed to transform nonlinear systems into a linear-like model and model complexity is then degraded and easier for controller design. Then, a new discrete fractional order PID control law in difference equation is presented which takes advantage of two more adjustable parameters. Finally, robust stability of the control law is analysed. Both deterministic and stochastic examples are provided to illustrate the effectiveness and superiority of the proposed controller.

Global inverse optimal exponential path-tracking control of mobile robots driven by Lévy processes

AbstractThis paper formulates and solves a new problem of global practical inverse optimal exponential path-tracking control of mobile robots driven by Lévy processes with unknown characteristics. The control design is based on a new inverse optimal control design for nonlinear systems driven by Lévy processes and ensures global practical exponential stability almost surely and in the pth moment for the path-tracking errors. Moreover, it minimizes cost function that penalizes tracking errors and control torques without having to solve a Hamilton–Jacobi–Bellman or Hamilton–Jaccobi–Isaacs equation.

Reinforcement learning-based nonlinear tracking control system design via LDI approach with application to trolley system

In this paper, a novel scheme for the tracking problem of nonlinear systems is proposed. First, as a new technology of neural network in control field, linear differential inclusion is used to approximate the nonlinear term for the entire system. Based on the equivalent linear system, tracking reference signal is given and a new augmented system is built. According to the mentioned value function, two reinforcement learning algorithms are proposed to design the optimal control law. Notice that the online algorithm does not involve the system dynamics and tracking dynamics. In the simulation section, the model of trolley system is given to prove the effectiveness and accuracy of the scheme proposed in this paper.

Nonlinear Control System Design of an Underactuated Robot Based on Operator Theory and Isomorphism Scheme

The number of actuators of an underactuated robot is less than its degree of freedom. In other words, underactuated robots can be designed with fewer actuators than fully actuated ones. Although an underactuated robot is more complex than a fully actuated robot, it has many advantages, such as energy, material, and space saving. Therefore, it has high research value in both control theory and practical applications. Swing-up is a mechanism with two links, which mimics a gymnast performing a horizontal bar movement. Over the past few decades, many sufficiently robust control techniques have been developed for a fully actuated robot but almost none of them can be directly applicable to an underactuated robot system. The reason is that such control techniques require certain assumptions that are valid only for fully actuated robot systems but not for underactuated ones. In this paper, a control system design method for underactuated robots based on operator theory and an isomorphism scheme is first proposed. Bezout identity is designed using isomorphism. The effectiveness of the design method is confirmed by simulation. The simulation results show that the performances, such as robust stability and response time, of an underactuated robot control system are improved.

Time-varying IBLFs-based adaptive control of uncertain nonlinear systems with full state constraints

This paper presents an adaptive control design for nonlinear systems with time-varying full state constraints. It is the first time to introduce the novel time-varying Integral Barrier Lyapunov functions (TVIBLFs) into the adaptive control design, which not only overcomes the limitation of conservatism existing in the traditional BLFs, but also guarantees that the full state time-varying constraint bounds are not violated. The TVIBLFs are combined with the backstepping design procedure to construct the controllers and adaptation laws, and the integral mean value theorem is used to differentiate TVIBLFs. It can be proven that all the states are forced in the time-varying regions and the stability of the closed-loop system is achieved. The effectiveness of the proposed adaptive control strategy can be illustrated through a simulation example.

Finite frequency H∞control design for nonlinear systems

The work deals finite frequency H<sub>∞</sub> control design for continuous time nonlinear systems, we provide sufficient conditions, ensuring that the closed-loop model is stable. Simulations will be gifted to show level of attenuation that a H<sub>∞</sub> lower can be by our method obtained developed where further comparison.

Approximate optimal synthesis of operational control systems for dynamic objects based on quasilinearization and sufficient optimality conditions

A new approach to the analytical design of linear and nonlinear integrated automatic control systems (ACS) of a real (accelerated) time scale, based on the joint use of dynamic programming technologies and the quasilinearization method, is presented. For continuous dynamic systems, the foundations of the theory of nonlinear synthesis in a degenerate (synergetic) formulation are given.

Robust Output Feedback Sliding Mode State and Disturbance Observer-based Controller Design for Nonlinear Systems

This study uses an output feedback disturbance observer-based proportional derivative (PD) controller with variable damping ratios for a class of single-input, single-output nonlinear systems in the presence of unknown disturbances. The proposed sliding mode state and disturbance observer, in which the switching term of the output estimation error is employed to counteract the effect of external disturbance, ensures that the estimation error is finally bounded in a neighborhood and reconstructs simultaneously the system state and unknown disturbance. Herein, the characteristics of the proposed observer are presented in the frequency domain, followed by the corresponding analysis in the time domain. A nonlinear PD controller with a variable damping ratio designed using the estimation state and disturbances should achieve low overshoot and short settling time. Finally, the simulation results demonstrate the validity of the proposed method.

Event-Triggered H-Infinity Controller Design of Nonlinear Networked Cascade Control System

Nonlinearity is ubiquitous in practical industrial production, so this paper investigates the problems of modeling, $H_{\infty }$ control and stabilization for a class of nonlinear networked cascade control systems (NCCSs) under an event-triggered scheme, which makes the system have more practical application value. Firstly, aiming at a kind of typical nonlinear system in industrial production, a new mathematical model is established by adding networked cascade control system and event-triggered scheme. The collaborative design method of primary and secondary controller parameters and event-triggered parameters is completed utilizing linear matrix inequality (LMI). Secondly, based on ensuring its stability, combined with $H_{\infty }$ control, the system’s disturbance is suppressed, making the system more universal. Finally, the feasibility and effectiveness of the proposed method in the nonlinear networked cascade control system has verified by a marine boiler liquid level cascade control system.

A Reduced-order Model for Real-time NMPC of Ethanol Steam Reformers

One of the approaches to green energy of interest in recent years is through the use of hydrogen technologies in which the waste product of combustion is water rather than carbon dioxide, nitrous oxides, and other pollutants generated by the burning of hydrocarbon fuels. Ethanol steam reformers is one of the primary technologies with the potential to generate hydrogen efficiently and reliably. This article investigates the design of nonlinear optimal feedback control systems for ethanol steam reformers based on mechanistic models described by a system of nonlinear partial differential-algebraic equations, aka singular/descriptor systems. The mechanistic models are too complicated to simulate in real-time using the standard numerical discretization methods, much less to directly incorporate such models as nonlinear constraints into mechanistic model-based nonlinear model predictive control formulations. This article employs a rather sophisticated multivariate form of the method of characteristics to reformulate the nonlinear constraints into a much simpler form amenable to real-time control implementations.