Nonlinear State Feedback Control Law Research Articles

A High Performance Nonlinear Longitudinal Controller for Fixed-Wing UAVs Based on Fuzzy-Guaranteed Cost Control

Unmanned aerial vehicles (UAVs) have garnered more attention across various industries in recent years, leading to significant development in their design and application globally. Due to the high coupling between UAV states, model uncertainties, and various disturbances, precise longitudinal control of UAVs remains a significant research challenge. Oriented for the speed and altitude control of an electrical-powered fixed-wing UAV, this paper introduces a new control strategy based on the fuzzy guaranteed cost control (F-GCC) technique, which results in a nonlinear longitudinal state feedback control law with strict stability criterion, effectively addressing the issue of state coupling. Moreover, the strategy also includes a thrust estimation model of the electrical propulsion system to significantly reduce the nonlinearity, simplifying the controller design while effectively preserving tracking control performance. Through numerical validation, the UAV longitudinal nonlinear controller designed using the F-GCC technique offers better transient response and stronger robustness than the traditional linear and ADRC controllers.

ADRC‐based control strategy for DC‐link voltage of flywheel energy storage system

AbstractThe direct current (DC)‐link voltage control of the flywheel energy storage system plays an important role in realizing high‐quality grid connection. With the traditional proportional‐integral control, the DC‐link voltage cannot track its reference value quickly and smoothly when the flywheel energy storage system switches from the charging stage to other working stages. Therefore, a DC‐link voltage control strategy for the flywheel energy storage system based on active disturbance rejection control is proposed in this paper to deal with this issue. The DC‐link voltage and its differential value are considered as the state variables in this strategy. The internal and external disturbances, such as load power, switching loss, and parameter uncertainty, are regarded as an expanded state. By inputting the voltage error and the observed disturbance into the nonlinear state feedback control law, the rapidity and anti‐interference of the DC‐link voltage control are ensured under different States of Charge of the flywheel energy storage system. Then, the coefficient freezing method is used to analyze the effects of the disturbance observation bandwidth by nonlinear gain and pole position changes. The DC‐link voltage can track the reference value over a wider frequency range of disturbances. By configuring the appropriate observer structure parameters, the disturbance observation bandwidth under the nonlinear function gain variation is always higher than the expected bandwidth. The effectiveness of the proposed control strategy is verified by simulation results at last.

Cooperative Adaptive Containment Control With Parameter Convergence via Cooperative Finite-Time Excitation

This article addresses the problem of cooperative adaptive containment control for multiagent systems, which specifies the objective of jointly achieving containment control and accurate adaptive learning/identification of unknown system parameters. We consider a class of linear uncertain multiagent systems with multiple leaders subject to bounded unmeasurable inputs and multiple followers subject to unknown system dynamics. A novel cooperative adaptive containment control architecture is proposed, which consists of a discontinuous nonlinear state-feedback control law and a filter-based cooperative adaptation law. This new control architecture is compelling in the sense that exponential convergence of both containment tracking errors to zero and adaptation parameters to their true values can be achieved simultaneously under a mild cooperative finite-time excitation condition. This condition significantly relaxes existing ones (e.g., persistent excitation and finite-time excitation) for parameter identification in adaptive control systems. Effectiveness of the proposed approach has been demonstrated through both rigorous analysis and a case study.

Regional stabilization of nonlinear sampled-data control systems: A quasi-LPV approach

This paper addresses the asymptotic stabilization of a class of continuous-time nonlinear systems under a sampled-data control. The proposed approach is based on a quasi linear parameter varying (quasi-LPV) model for the nonlinear system and the use of a parameter dependent looped-functional to deal with the aperiodic sampling effects. Explicitly taking into account that the model parameters are functions of the state and therefore are bounded only in a given region of the state space, quasi-LMI conditions are proposed to compute a regional stabilizing nonlinear state feedback control law under aperiodic sampling. These conditions are then incorporated in convex optimization problems to compute the control law aiming at the maximization of an estimate of the region of attraction of the origin or the maximization of an upper bound on the intersampling time, with a guaranteed region of stability.

Distributed drive electric autonomous vehicle steering angle control based on active disturbance rejection control

Based on active disturbance rejection control technique and characteristics of electric power steering, a steering angle tracking controller is designed, which consists of an aligning moment estimator to deal with modeling error and nonlinearity of electric power steering. The aligning moment estimator is based on an extended state observer and takes steering system friction and differential drive steering torque, which is a unique phenomenon in a distributed drive electric vehicle, into consideration. According to the estimated aligning moment and tracking differentiator, the steering angle tracking controller is designed based on a nonlinear state feedback control and feedforward compensation control laws. Results of various simulations and experiments, including pivot steering, step input steering, and sinusoidal input steering, show that the proposed controller has good performance in tracking reference steering angle and is convenient to implement. With the aligning moment estimator, the proposed controller shows better results in comparative experiments than a conditional integral-based steering angle tracking controller.

A Robust LMI Approach on Nonlinear Feedback Stabilization of Continuous State-Delay Systems with Lipschitzian Nonlinearities: Experimental Validation

This paper suggests a novel nonlinear state-feedback stabilization control law using linear matrix inequalities for a class of time-delayed nonlinear dynamic systems with Lipschitz nonlinearity conditions. Based on the Lyapunov–Krasovskii stability theory, the asymptotic stabilization criterion is derived in the linear matrix inequality form and the coefficients of the nonlinear state-feedback controller are determined. Meanwhile, an appropriate criterion to find the proper feedback gain matrix F is also provided. The robustness purpose against nonlinear functions and time delays is guaranteed in this scheme. Moreover, the problem of robust H∞ performance analysis for a class of nonlinear time-delayed systems with external disturbance is studied in this paper. Simulations are presented to demonstrate the proficiency of the offered technique. For this purpose, an unstable nonlinear numerical system and a rotary inverted pendulum system have been studied in the simulation section. Moreover, an experimental study of the practical rotary inverted pendulum system is provided. These results confirm the expected satisfactory performance of the suggested method.

Closed‐form solution of discrete‐time optimal control and its convergence

The convergence of a new closed-form solution for the discrete-time optimal control is presented. First, a new time optimal control law with simple structure is constructed in the form of the state feedback for a discrete-time double-integral system by using the state backstepping approach. The control signal sequence in this approach is determined by the linearised criterion according to the position of the initial state point on the phase plane. This closed-form non-linear state feedback control law clearly shows that time optimal control in discrete time is not necessarily the bang-bang control. Second, the convergence of the time optimal control law is proved by demonstrating the convergence path of the state point sequence driven by the corresponding control signal sequence. Finally, numerical simulation results demonstrate the effectiveness of this new discrete-time optimal control law.

Robust State and Output Feedback Control of Launched MAVs with Unknown Varying External Loads

The operation of launched micro aerial vehicles (MAVs) with coaxial rotors is usually subject to unknown varying external disturbance. In this paper, a robust controller is designed to reject such uncertainties and track both position and orientation trajectories. A complete dynamic model of coaxial-rotor MAV is firstly established. When all system states are available, a nonlinear state-feedback control law is proposed based on feedback linearization and Lyapunov analysis. Further, to overcome the practical challenge that certain states are not measurable, a high gain observer is introduced to estimate unavailable states and an output feedback controller is developed. Rigid theoretical analysis verifies the stability of the entire closed-loop system. Additionally, extensive simulation studies have been conducted to validate the feasibility of the proposed scheme.

Robust properties of systems with negative degree of homogeneity with respect to delay

The paper considers robustness problems of a class of weighted homogeneous systems with negative homogeneity degree in relation to the delay. It is shown that in the case of global asymptotic stability of a nonlinear weighted homogeneous system with negative homogeneity degree, in the presence of a delay in the system, all the trajectories converge asymptotically to some compact set containing the origin. In the absence of delay, such systems reach their equilibrium position in a finite time. The robustness analysis also covers cases of variable and multiple delays. The presented analysis is based on the application of the Lyapunov methods for delayed systems (the Lyapunov-Razumikhin function method) and the theory of weighted homogeneous systems. Computer simulation was performed to verify the analysis of system robustness with a negative degree of homogeneity in relation to the delay. A stabilizing system that represents a double integrator is used as an example. This system is weighted homogeneous with a negative degree when using a nonlinear state feedback control law that ensures that the system achieves its equilibrium position for the desired finite time. During computer simulation, the state vector was available for measurement with some delays. The computer simulation has confirmed the effectiveness of the presented theoretical results.

Maneuvering Support System for an Amphibian Vehicle – Warning Display to Prevent Rough Maneuvers –

[abstFig src='/00290003/14.jpg' width='300' text='Amphibian vehicle maneuvering simulator' ] This study proposes a maneuvering support system for an amphibian vehicle by applying a nonlinear state feedback control law for vehicle trajectory control. We consider that the vehicle should not drift sideways for good driving performance. To derive a nonlinear state feedback control law, we have defined ‘Maneuvering Trajectory’ as an additional reference trajectory that is generated by the driver’s maneuver. We have constructed a Lyapunov-like function for the trajectory control system. In this paper, we construct a vehicle-maneuvering simulator and set a clockwise circular reference trajectory. The efficiency of the proposed maneuvering support system is shown in the maneuvering simulations. We consider the case where the propulsive forces of the vehicle have limited influence on maneuverability. A new warning display system is proposed so that the driver can recognize if his or her maneuver is not suitable. Then, we examine the feasibility of the proposed warning display system through several simulations.

Nonlinear state feedback control design to eliminate subcritical limit cycle oscillations in aeroelastic systems

A strictly nonlinear state feedback control law is designed for an aeroelastic system to eliminate subcritical limit cycle oscillations. Numerical continuation techniques and harmonic balance methods are employed to generate analytical estimates of limit cycle oscillation commencement velocity and its sensitivity with respect to the introduced control parameters. The obtained estimates are used in a multiobjective optimization framework to generate optimal control parameters which maximize the limit cycle oscillation commencement velocity while minimizing the control cost. Numerical simulations are used to show that the assumed nonlinear state feedback law with the optimal control parameters successfully eliminates any existing subcritical limit cycle oscillations by converting it to supercritical limit cycle oscillations, thereby guaranteeing safe operation of the system in its flight envelope.

Suppression of Low-Frequency Oscillation in Traction Network of High-Speed Railway Based on Auto-Disturbance Rejection Control

The traction blockade in the depots of multiple electric multiple units (EMUs) is caused by the low-frequency oscillation (LFO) of high-speed railway traction network overvoltage. To suppress LFO, a strategy for optimizing the load characteristics of EMUs rectifier using the auto-disturbance rejection control (ADRC) is put forward. First, a first-order mathematical model is established to describe the characteristics of EMUs rectifier. Second, the nonlinear state observer and feedback control law are designed for state observation and disturbance estimation. By constructing a new nonlinear state-error feedback function, the ADRC is improved. This function’s convergence effect is better than the linear state-error feedback function, and it can solve the problem of the jitter problem of control force to some extent. Third, the outer-loop controller for pulsewidth modulation (PWM) rectifier voltage is designed. The improved ADRC can effectively deal with the contradiction between overshoot and rapidity. Its performance is better than the traditional proportional integral (PI) controller, which is applied in all of the EMUs at present. Finally, the full model of EMUs-traction network electrical coupling system (ETNECS) is constructed. Compared with multivariable controller, the simulation results show that the improved ADRC can ensure the ETNECS stability and suppress the LFO more efficiently.

Energy Shaping for Tracking Control of 4-DOF Crane

In this paper the nonlinear tracking control methodology is proposed for 4–DOF (degree of freedom) overhead crane system using energy shaping. The 4–DOF underactuated overhead crane system has an extra DOF compared with the popular 3–DOF variant. The 4-DOF crane modeling represents strong state coupling and more complicated system dynamics which makes it challenging control problem. The control methodology begins with the first step of decoupling the crane dynamics into two subsystems using collocated partial feedback linearization. The passivating outputs of the modified subsystems are identified which are further utilized for energy shaping to obtain the nonlinear state feedback control law which effectively achieves the objective of trajectory tracking with fast elimination of payload swings. The energy shaping procedure obviates the need for solving PDEs to derive the control law. The trajectory tracking control law represents generalization of the position regulation problem. The simulation results are presented to validate the control law and superior performance is demonstrated over the existing control methodologies.

水陸両用レスキュー車の浮行時における操縦支援システムの検討

In this report, we focus on a maneuvering problem of an amphibian vehicle for rescue, and a novel manueuvering support system for the vehicle on the surface of water is proposed by applying a nonlinear state feedback control law for trajectory control. To simplify the problem, we consider only viscous friction among the external forces and ignore other external forces which are applied to the vehicle on the surface of water. We consider that the vehicle should not drift sideways for an excellent driving performance. Thereby, we propose to employ three ducted fans as additional propulsion devices. Each of the two ducted fans, which are attached symmetrically to the left and right side of the vehicle, has a swiveling function in order to generate a lateral force. The other ducted fan, which is attached to the center rear of the vehicle, generates a longitudinal propulsive force. To design a nonlinear state feedback control law, we define ‘Maneuvering Trajectory’ as a trajectory which is generated by the maneuver of the vehicle's pilot and we construct a Lyapunov-like function for the trajectory control system. Then the feasibility of the proposed system is verified by evaluating the tracking error against a reference trajectory through several numerical simulations.

離散化双線形モデルに基づくブーストコンバータ出力電圧の積分補償付非線形制御―II

This paper is concerned with nonlinear control with integral compensation for the output voltage of boost converters through the use of their discretized bilinear model. We first derive a nonlinear state feedback control law through Lyapunov stability theory, where we introduce a Lyapunov function candidate and maximize its decrement at each switching instant under a penalty on the control input. This approach is then modified to incorporate an integral action in the control law,and a method is provided for confirming the closed-loop stability under the modified control law. We next apply the design method of the control law with integral compensation to the identified discretized bilinear model of a boost converter. Finally, we carry out control experiments with the designed control law, through which the effectiveness of the overall scheme of the present study is demonstrated.

Local input-to-state stabilization and ℓ ∞ -induced norm control of discrete-time quadratic systems

Summary This paper addresses the problems of local stabilization and control of open-loop unstable discrete-time quadratic systems subject to persistent magnitude bounded disturbances and actuator saturation. Firstly, for some polytopic region of the state-space containing the origin, a method is derived to design a static nonlinear state feedback control law that achieves local input-to-state stabilization with a guaranteed stability region under nonzero initial conditions and persistent bounded disturbances. Secondly, the stabilization method is extended to deliver an optimized upper bound on the l ∞ -induced norm of the closed-loop system for a given set of persistent bounded disturbances. Thirdly, the stabilization and l ∞ designs are adapted to cope with actuator saturation by means of a generalized sector bound constraint. The proposed controller designs are tailored via a finite set of state-dependent linear matrix inequalities. Numerical examples are presented to illustrate the potentials of the proposed control design methods. Copyright © 2014 John Wiley & Sons, Ltd.

Cascaded energy based trajectory tracking control of a quadrotor

Abstract This paper presents a cascaded nonlinear state feedback control law for a quadrotor, which achieves asymptotic tracking of a predefined position and heading reference trajectory. The inner-loop attitude controller and the outer-loop position controller reflect the cascade structure of the quadrotor dynamics and are designed independently using an energy shaping approach. The closed loop tracking error dynamics form a nonautonomous nonlinear cascade for whose zero equilibrium we prove almost global asymptotic stability. Experimental results show the performance of the control concept.

1P2-H05 水陸両用レスキュー車の浮行時における操縦支援システムの提案(サーチ&レスキューロボット・メカトロニクス(2))

In this report, an amphibian vehicle for rescue is introduced, and a manueuvering support system for the vehicle is proposed by applying a nonlinear state feedback control law for the trajectory control of the vehicle. To simplify the problem, we consider only viscous friction among the external forces and ignore other external forces applying to the vehicle. We consider that the vehicle should not drift sideways for a good driving performance. To derive a nonlinear state feedback control law, we define 'Maneuvering Trajectory' as a trajectory which is generated by the driver's maneuver and construct a Lyapunov-like function for the trajectory control system. Then feasibility of the proposed system is verified through several numerical simulations.

Local Stabilization of Markov Jump Nonlinear Quadratic Systems

This paper investigates the problem of local stabilization of Markov jump nonlinear quadratic systems. A method is presented for the synthesis of a static nonlinear quadratic state feedback control law that ensures the local exponential mean square stability of the zero equilibrium point of the closed-loop system in some polytopic region of the state-space with a guaranteed region of stability inside this polytope. The proposed control design is tailored in terms of linear matrix inequalities together with convex optimization to achieve an enlarged stability region. A numerical example is presented to illustrate the application of the stabilization method.

Constant-yield control of the chemostat

Abstract —The present work addresses the problem of chemostat stabilization around an optimal steady state, in the sense of enlargement of its stability region. The need for stabilization becomes imperative under conditions where the growth of biomass is subject to substrate inhibition, and the primary concern is to prevent washout of the biomass in the presence of disturbances. Inspired by the empirical concept of constant-yield control, a nonlinear state feedback control law is derived, and the stability basin of resulting closed-loop system is estimated using a Lyapunov function approach. Our analysis extends previous results in the sense that it accounts for biomass decay and endogenous metabolism and, moreover, it covers the case where the product is soluble in the effluent stream.