Nonlinear Feedback Control Law Research Articles

Design of Robust Controller for a Class of Uncertain Discrete-Time Systems Subject to Actuator Saturation

This technical note studies the robust output tracking controller design for a class of uncertain discrete-time systems subject to actuator saturation. To achieve this capability, a new controller is proposed by robustifying the discrete-time composite nonlinear feedback (DCNF) control law. Since, the proposed controller may be saturated; a precise analysis is done to show its robust performance in spite of presence of actuator saturation and time-varying external disturbances. Additionally, a theorem is given and proved which guarantees the disturbance attenuation via the proposed control law for three different cases of the saturation function and it is shown that even if the control signal is saturated, the proposed controller achieves steady-state error of order $O(T)$ for state regulation. Finally, computer simulations are performed for a practical system and the applicability of the proposed controller is shown.

An IPEM for optimal control of uncertain beam-moving mass systems with saturation nonlinearity

This paper addresses the vibration control of single-span beams subjected to a moving mass by coupling the saturated nonlinear control and an improved point estimation method (IPEM). An optimal nonlinear feedback control law, for a kind of uncertain linear system with actuator nonlinearities, is derived using the combination of Pontryagin's maximum principles and the improved point estimation method. The stability of the feedback system is guaranteed using a Lyapunov function. In order to obtain the instantaneously probabilistic information of output responses, a novel moment approach is presented by combining the improved point estimation method, the maximum entropy methodology and the probability density evolution theory. In addition to the consideration of stochastic system parameters, the external loadings are considered as a nonstationary random excitation and a moving sprung mass, respectively. The proposed strategy is then used to perform vibration suppression analysis and parametric sensitivity analysis of the given beam. From numerical simulation results, it is deduced that the improved point estimation method is a priority approach to the optimal saturated nonlinear control of stochastic beam systems. This observation has widespread applications and prospects in vehicle–bridge interaction and missile–gun systems.

Fault-tolerant control with mixed aerodynamic surfaces and RCS jets for hypersonic reentry vehicles

This paper proposes a fault-tolerant strategy for hypersonic reentry vehicles with mixed aerodynamic surfaces and reaction control systems (RCS) under external disturbances and subject to actuator faults. Aerodynamic surfaces are treated as the primary actuator in normal situations, and they are driven by a continuous quadratic programming (QP) allocator to generate torque commanded by a nonlinear adaptive feedback control law. When aerodynamic surfaces encounter faults, they may not be able to provide sufficient torque as commanded, and RCS jets are activated to augment the aerodynamic surfaces to compensate for insufficient torque. Partial loss of effectiveness and stuck faults are considered in this paper, and observers are designed to detect and identify the faults. Based on the fault identification results, an RCS control allocator using integer linear programming (ILP) techniques is designed to determine the optimal combination of activated RCS jets. By treating the RCS control allocator as a quantization element, closed-loop stability with both continuous and quantized inputs is analyzed. Simulation results verify the effectiveness of the proposed method.

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.

Anti‐windup for a class of partially linearisable non‐linear systems with application to wave energy converter control

This paper studies the anti-windup (AW) problem for a certain class of non-linear systems, in which the plant is globally quadratically stable and also partially linearisable by a suitably chosen non-linear feedback control law. Three types of AW compensators are proposed for this type of non-linear system: the first one is a non-linear extension of the popular linear internal model control (IMC) scheme; the second one has a similar structure to the IMC AW compensator yet is of reduced order and has entirely linear dynamics; and the third one is again a linear AW compensator, but can endow the closed-loop system with some sub-optimal performance properties. All three AW compensators are able to provide global exponential stability guarantees for the aforementioned class of systems. This work was inspired by a wave energy application whose dynamics fall into the class of systems studied in this study. Simulation results show the efficacy of the three AW compensators when applied to the wave energy application.

Passivity control with practically finite-time convergence for large space structures

A nonlinear output feedback control law based on passivity is proposed to reduce the vibration of large space structures. The considered system is assumed to be equipped with collocated actuators and sensors. The concept of practically finite-time stability is first developed to describe the finite-time convergence of a passive system. Then, an output feedback is introduced to drive the trajectories of a passive system into a small set around the origin in finite time. Finally, the proposed control strategy is applied to the vibration suppression of large space structures with distributed thrusters and velocity sensors or torque outputting devices and angular rate sensors. Numerical simulations are conducted to validate the effectiveness of the proposed controller.

Finite-Time Adaptive Synchronisation of a Class of Master-Slave Systems with Different Unknown Parameters

This paper is concerned with the finite-time chaotic synchronization and dynamic errors in finite-time stabilization of master-slave systems. We suggest solving these issues using a virtual recursive adaptive nonlinear controller when different unknown parameters occur. Therefore, a systematic design approach is defined for constructing both virtual adaptive nonlinear feedback control laws and associated Lyapunov functions. The corresponding sufficient conditions to achieve synchronization between two chaotic systems are obtained based on the Lyapunov stability theory. Then, two applications are evaluated using our approach: Genesio-Tesi and Coullet systems which are two topologically dissimilar systems, known as difficult to synchronize. The results presented in this paper demonstrate both effectiveness and feasibility of our control laws.

Semi-global output regulation for discrete-time singular linear systems with input saturation via composite nonlinear feedback control

The semi-global output regulation problem of multi-variable discrete-time singular linear systems with input saturation is investigated in this paper. A composite nonlinear feedback control law is constructed by using a low gain feedback technique for semi-global stabilisation of discrete-time singular linear systems with input saturation. The sufficient solvability conditions of the semi-global output regulation problem by composite nonlinear feedback control are established. When the composite nonlinear feedback control law is reduced to a linear control law, the solvability conditions are an exact discrete-time counterpart of the semi-global output regulation problem of continuous-time singular linear systems. With the extra control freedom of the nonlinear part in the composite nonlinear feedback control law, the transient performance of the closed-loop system can be improved by carefully choosing the linear feedback gain and the nonlinear feedback gain. The design procedure of the composite nonlinear feedback control law and the improvement of the transient performance are illustrated by a numerical example.

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.

Chaos Control in Three Dimensional Cancer Model by State Space Exact Linearization Based on Lie Algebra

This study deals with the control of chaotic dynamics of tumor cells, healthy host cells, and effector immune cells in a chaotic Three Dimensional Cancer Model (TDCM) by State Space Exact Linearization (SSEL) technique based on Lie algebra. A non-linear feedback control law is designed which induces a coordinate transformation thereby changing the original chaotic TDCM system into a controlled one linear system. Numerical simulation has been carried using Mathematica that witness the robustness of the technique implemented on the chosen chaotic system.

Dual-quaternion based fault-tolerant control for spacecraft formation flying with finite-time convergence

Study results of developing control system for spacecraft formation proximity operations between a target and a chaser are presented. In particular, a coupled model using dual quaternion is employed to describe the proximity problem of spacecraft formation, and a nonlinear adaptive fault-tolerant feedback control law is developed to enable the chaser spacecraft to track the position and attitude of the target even though its actuator occurs fault. Multiple-task capability of the proposed control system is further demonstrated in the presence of disturbances and parametric uncertainties as well. In addition, the practical finite-time stability feature of the closed-loop system is guaranteed theoretically under the designed control law. Numerical simulation of the proposed method is presented to demonstrate the advantages with respect to interference suppression, fast tracking, fault tolerant and practical finite-time stability.

Adaptive control for two-spacecraft electromagnetic formation keeping

Electromagnetic spacecraft formation flying is a new type of spacecraft formation using electromagnetic forces between spacecraft to control relative motion. Primary principles of the relative motion of a two-craft electromagnetic formation were discussed. Analytical solutions of control magnetic moments according to commanded control forces for the case of two-spacecraft electromagnetic formation were developed considering the energy consumption equilibrium. Nonlinear relative motion dynamic models for a two-spacecraft electromagnetic formation were derived based on polar coordinates. Parameter uncertainties of the equations because of the approximation of the electromagnetic model and unknown disturbed forces were analyzed. Nonlinear adaptive feedback control laws for formation keeping were then designed,and the closed-loop dynamic procedure of a two-spacecraft electromagnetic formation in a low earth circular orbit was simulated. Results indicate that the relative motion equations and the adaptive control laws are valid. The formation can effectively converge to desired states and the unknown parameters are estimated accurately. The simulations demonstrate that electromagnetic forces between spacecraft can be used to realize spacecraft formation keeping and the electromagnetic formation flying is feasible.

On the Robust Trajectory Tracking Task for Flexible-Joint Robotic Arm With Unmodeled Dynamics

This paper is concerned with the design and experimental assessment of, both, feedback linearization and sliding mode control techniques to the tracking trajectory problem of a flexible-joint robotic arm for a smooth rest to rest maneuver. The robust improvement of these controllers is analyzed by means of additional integral compensation, in which an alternative sliding surface was proposed for the control of the flexible arm. A feedback linearization of the nonlinear dynamic equation of the robot arm is computed in order to get a full-state non-linear feedback control law. On the other hand, it is proposed a second order sliding mode control with an integral term in the sliding surface, which improves the robustness of the controller sliding surface. Some experimental evaluations that include the addition of external unmodeled perturbations to test the enhancement of the robustness property show the improvements and effectiveness of the proposed control laws in disturbance rejection tasks. The controllers were implemented using exclusively position measurements and time derivatives approximations.

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.

Robust trajectory tracking for quadrotor aircraft based on ADRC attitude decoupling control

An attitude decoupling algorithm based on active disturbance rejection control( ADRC) was designed for underactuated quadrotor aircraft. The algorithm can overcome some shortcomings of traditional control method for underactuated quadrotor,such as strong coupling between system states,weak anti-interference ability and high sensitivity of tracking performance to modeling errors,etc. The state coupling was tracked and estimated by extended state observer( ESO),system interference can be estimated by ESO at the same time. The interference of the system includes internal and external disturbances. The nonlinear multipleinput multiple-output( MIMO) system was transformed into linear single-input single-output( SISO) system by dynamic feedback linearization. Then using the nonlinear feedback control law to achieve high quality control of the attitude system,and study the robust trajectory tracking problem of the aircraft based on the attitude decoupling control algorithm. The simulation results show that the above attitude control algorithm can improve the robustness of the trajectory tracking system. The algorithm does not rely on the accurate system model,reduces the difficulty of practical application,and has strong anti-interference capability and practical application value as well.

Nonlinear Local Stabilization of a Viscous Hamilton-Jacobi PDE

We consider the boundary stabilization problem of the non-uniform equilibrium profiles of a viscous Hamilton-Jacobi (HJ) Partial Differential Equation (PDE) with parabolic concave Hamiltonian. We design a nonlinear full-state feedback control law, assuming Neumann actuation, which achieves an arbitrary rate of convergence to the equilibrium. Our design is based on a feedback linearizing transformation which is locally invertible. We prove local exponential stability of the closed-loop system in the $H^{1} $ norm, by constructing a Lyapunov functional, and provide an estimate of the region of attraction. We design an observer-based output-feedback control law, by constructing a nonlinear observer, using only boundary measurements. We illustrate the results on a benchmark example computed numerically.

Three-Axis Attitude Control Using Redundant Reaction Wheels with Continuous Momentum Dumping

A description of an attitude control system for a three-axis stabilized spacecraft is presented. A globally stabilizing nonlinear feedback control law is derived that enables tracking of an arbitrary time-varying reference attitude. This new control incorporates integral feedback while avoiding any quadratic rate feedback components. A redundant cluster of four or more reaction wheels is used to control the spacecraft attitude, and three magnetic torque rods are used for purposes of continuous autonomous momentum dumping. The momentum dumping strategy can employ general torque rod orientations, and it is developed to take advantage of a redundant set of reaction wheels.

Stabilisation of Timoshenko beam system with a tip payload under the unknown boundary external disturbances

This paper is concerned with the boundary stabilisation of a Timoshenko beam with a tip payload under the boundary external disturbances. Nonlinear feedback control laws are designed to reduce the effects of the external disturbances. Since the controlled system is nonlinear, the well posedness of the nonlinear closed-loop system is investigated using the theory of nonlinear maximal monotone operators and the variational principle. In addition, we show the exponential stability of the nonlinear controlled system using the Lyapunov direct method. In the end, the numerical simulations are displayed to illustrate the effectiveness of the proposed boundary controls.

Control Design Of Robot Manipulator Position Based On Pd-Fuzzy Mamdani Controlled With Computed Torque Control (Pd-Fuzzy-Ctc)

Robotics science has evolved significantly, driven by rapid advances in computer and sensor technology; and theoretical advances in control and computer vision. These development make widespread use of robot manipulators in industrial environments. Major problem in controlling a robot manipulator is to control the robot in order to achieve the desired position. Therefore the design issue of the robot control is to choose the right type controller. Computed Torque Controller (CTC) is a powerful nonlinear controllers are widely used in the control of robot manipulators. CTC controller is designed based on feedback linearization and the required torque of the robot arm by using a nonlinear feedback control law. Simulation is done by providing joint trajectory from point to point. The simulation results show that the PD-Fuzzy-CTC controller is able to follow the joint trajectory with The RMSE value of the joint angle position of PD-Fuzzy-CTC controller is 10 times smaller than that of the PD-CTC controller with the end-effector position accuracy is 0.1 mm.

Nonlinear fractional order proportion-integral-derivative active disturbance rejection control method design for hypersonic vehicle attitude control

Near space hypersonic vehicle model is nonlinear, multivariable and couples in the reentry process, which are challenging for the controller design. In this paper, a nonlinear fractional order proportion integral derivative (NFOPIλDμ) active disturbance rejection control (ADRC) strategy based on a natural selection particle swarm (NSPSO) algorithm is proposed for the hypersonic vehicle flight control. The NFOPIλDμ ADRC method consists of a tracking-differentiator (TD), an NFOPIλDμ controller and an extended state observer (ESO). The NFOPIλDμ controller designed by combining an FOPIλDμ method and a nonlinear states error feedback control law (NLSEF) is to overcome concussion caused by the NLSEF and conversely compensate the insufficiency for relatively simple and rough signal processing caused by the FOPIλDμ method. The TD is applied to coordinate the contradiction between rapidity and overshoot. By attributing all uncertain factors to unknown disturbances, the ESO can achieve dynamic feedback compensation for these disturbances and thus reduce their effects. Simulation results show that the NFOPIλDμ ADRC method can make the hypersonic vehicle six-degree-of-freedom nonlinear model track desired nominal signals accurately and fast, has good stability, dynamic properties and strong robustness against external environmental disturbances.