Nonlinear feedback control of Lorenz system

A robust non-linear feedback control strategy combined with neural network (NN) estimator is presented, for the non-linear model of bank-to-turn (BTT) missile with modeling uncertainties. The non-linearities in the missile dynamics are taken into account, including coupling items between three channels. Standard feedback linearisation is implemented to linearise and decouple the nominal system. In the presence of unknown bounded uncertainties, the performance will deteriorate because the precise model cannot be obtained. Then, linear matrix inequality (LMI) based guaranteed cost control (GCC) is adopted to solve the robust control problem for the linearised uncertain models. Further, adaptive neural network estimators, which use Lyapunov based tuning rules, are integrated in the control strategy to eliminate the effect of high-order uncertain terms. Simulation results on a specified BTT missile model are provided to demonstrate the feasibility and effectiveness of the proposed approach, which achieves more improved tracking performance comparing with conventional method.

SummaryIn this work, a new robust nonlinear feedback control method with dynamic active compensation is proposed; the active control method has been applied to an integral series of finite‐time single‐input single‐output nonlinear system with uncertainty. In further tracking the closed‐loop stability and nonlinear uncertainty, an extended state observer has been employed to solve the immeasurability and nonlinear uncertainty within a nonlinear system. A singular perturbation theory has been used to solve for the finite‐time stability of the closed‐loop system; furthermore, numerical simulations showed that the robust nonlinear feedback controller tracked the uncertainty in a nonlinear Duffing‐type oscillator and has proven the effectiveness of the approximate finite‐time control strategy proposed. By using an approximate finite‐time control approach with active compensation, the uncertainty in a nonlinear system could be accurately estimated and controlled. Copyright © 2017 John Wiley & Sons, Ltd.

The paper presents a robust nonlinear output feedback control system for the attitude control of satellites, with unstructured (unmodelled) dynamics in elliptic orbits, using solar radiation pressure. The nonaffine-in-control spacecraft model includes the gravity gradient torque, the control torque produced by two solar flaps, and external time-varying disturbance torque. The objective is to control the pitch angle of the spacecraft using the solar flaps. A robust feedback linearizing control law is derived for the trajectory control of the pitch angle. The controller includes a high-gain observer, which estimates the derivatives of the pitch angle as well as a lumped unstructured nonlinearity including the external disturbance moment in the pitch dynamics for synthesis. In the closed-loop system, the designed output feedback law accomplishes large angle rotational maneuvers. Simulation results are presented which show that in the closed-loop system, precise pitch angle control is accomplished, despite unmodelled nonlinearities and external disturbance torque in the model.KeywordsPitch AngleElliptic OrbitSolar Radiation PressureAttitude Control SystemSolar SailThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A robust nonlinear output feedback control method is presented, which achieves three degree of freedom (3-DOF) attitude control of a hover system test bed. The proposed control method formally incorporates the practical limitations in the voltage control inputs to the control actuators (i.e., the quadrotor propellers). In addition, the control law is designed to compensate for uncertainty in the hover system dynamic model, including input-multiplicative parametric uncertainty resulting from uncertain drag and friction coefficients in the propellers' dynamic model. To reduce the computational requirement in the closed-loop system, constant feedforward estimates of the input-multiplicative uncertainty are utilized in lieu of adaptive parameter estimates. Eschewing the high-gain feedback requirement that is characteristic of standard sliding mode observer methods, the proposed control method utilizes a bank of dynamic filters, which operates as a velocity estimator in the closed-loop system. A rigorous error system development and Lyapunov-based stability analysis are presented to prove that the proposed output feedback control law achieves asymptotic 3-DOF attitude control in the presence of parametric input uncertainty and unmodeled dynamics. Experimental results are provided to demonstrate the performance of the attitude control method using the Quanser 3-DOF hover system test bed.

A nonlinear robust controller design method is proposed for the lateral control of heavy vehicles for automated highway systems. In the controller design, the actuator dynamics is explicitly taken into account. A first order pre-filter is introduced to reduce chattering which is inherent in the nonlinear robust controller and to prevent the saturation in the front wheel steering angle and steering system slew rate. A constructive backstepping design technique is utilized in the design of a robust controller for the augmented system. Simulation results are shown.

The design of a robust nonlinear feedback controller is analyzed for temperature control of continuous stirred tank reactors (CSTRs)which have strong nonlinearities and steady-state multiplicities. The present method treats the original nonlinear system as it is without transforming into an equivalent linear system. The controller is robust to modelling errors and random disturbances occurring in the system. The controller design is also analyzed for situation when the kinetics, activation energy and heat of reaction are unknown and also only limited state-variables measurements are available.

Perturbation estimation based robust state feedback control for grid connected DFIG wind energy conversion system

The design of a robust nonlinear feedback controller is addressed for an N-degree-of-freedom robot with bounded uncertainty in the dynamic model's parameters. It is demonstrated that the proposed controller makes the robot system practically stable when both unknown payload variation and joint frictional force are taken into consideration. It is also shown that this controller can guarantee the practical stability of the robot system when a collision between the robot and its environmental occurs. Sufficient conditions for global practical stability are derived using Lyapunov's second method. A numerical simulation of a two-link robot manipulator with bounded parameter to illustrate the proposed control system. >

SummaryThis article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.

A vector decomposition approach to F–M model realization and its application to robust observed-state feedback control

In this brief, a novel robust nonlinear motion controller with disturbance observer (DOB) for positioning control of a nonlinear single-input-single-output (SISO) mechanical system is proposed. The controller is designed in a backstepping manner. First, a proportional-integral (PI) controller is designed to stabilize the position error. Consequently, a novel robust nonlinear velocity controller with DOB is designed to stabilize the velocity error. With the help of nonlinear damping terms, the input-to-state stability (ISS) property of the overall nonlinear control system is proven, which leads to a major contribution of construction of a theoretically guaranteed robust nonlinear controller with DOB. The performance of the proposed controller is verified through application to a magnetic levitation system. Comparative studies with an adaptive robust nonlinear controller are also carried out. It is shown that the proposed novel controller while being simple is superior over the adaptive robust nonlinear controller for the experimental setup under study.

We focus on the design of robust reduced-order dynamic feedback control for a class of nonlinear systems with uncertainties. A robust nonlinear reduced-order dynamic controller (RNRDC) is proposed. The resulting closed-loop system can be robustly stabilized for all admissible uncertainties via the proposed controller. The application of the proposed RNRDC to a permanent magnet brush DC motor driving a single-link manipulator is also considered. The parameters uncertainties can be up to /spl plusmn/80%. The load can vary ranging from 50% to +100% of the nominal value. Our simulation results show that for the example system the proposed RNRDC can achieve good performance.

This paper proposes a variable structure (VS) control algorithm, with which a system can be stabilized by switching the system control input among a set of simple feedback control laws. Each feedback control law is easy to be designed because it uses only one element of the state variable with a fixed positive or negative feedback gain. For an n-order system, 2n feedback control laws are needed to realize the proposed VS control. The concept of the sliding sector is used in the paper to show that there exists an area for each feedback control law, inside which a Lyapunov function decreases with the control law although the system may not be stabilized by it alone. It is shown that a common Lyapunov function for all control laws exists for a controllable system, i.e., for any state in the state space, there exists at least one control law among those laws mentioned above such that the system state is inside the sliding sector of the system with the corresponding control law. Thus a hybrid-type control rule of the variable structure control system is designed to switch the control input to the control law, which ensures the decrease of the common Lyapunov function. The proposed VS control system is quadratically stable. Simulation results are given to show the convergence of the proposed VS control system.

The robust integral control problem is studied for a class of nonlinear systems with input-to-state stable (ISS) unmodeled dynamics in this paper. It does not require a priori knowledge of the control coefficients. Combining the Nussbaum-type gain technique and the backstepping design, we propose a state feedback controller, which could achieve the global asymptotic tracking for any constant reference signal, irrespective of the unmeasured dynamic disturbance. It is shown that the proposed methodology further extends the existing robust nonlinear integral control results. Simulation results verify the correctness of the theoretical analysis.

This paper presents a control scheme for grid-connected PWM voltage source inverters (VSIs) featuring fast load voltage regulation and effective mitigation of fast voltage disturbances. To ensure perfect regulation of the voltage at the point of common coupling, and provide means for rejecting voltage disturbances, the voltage control loop should offer a high disturbance rejection performance. Toward this, a hybrid voltage controller combining a linear with variable-structure control (VSC) element is proposed to generate the reactive current reference in a grid-connected VSI. The proposed voltage controller can embed a wide band of frequency modes through an equivalent internal model. Subsequently, wide range of voltage perturbations, including capacitor-switching transients, can be rejected. To optimally tune the proposed nonlinear voltage controller, the tuning problem is formulated as a constrained optimization problem, and solved via an evolutionary search algorithm based on the particle-swarm-optimization (PSO) technique. Therefore, a simple and structured tuning methodology can be obtained. Theoretical analysis and comparative evaluation tests are presented to demonstrate the effectiveness of the proposed control scheme.