Finite-time sliding mode controller for perturbed second-order systems

Observer-based proportional-retarded controller for payload swing attenuation of 2D-crane systems including load hoisting-lowering

Crane systems are essential systems utilized in industry and for research. Nevertheless, they are always affected by endogenous and exogenous disturbances, which may generate undesirable payload oscillations, compromising people's security and the system itself. Thus, to deal with these issues and control these mechatronic systems efficiently, this manuscript develops a novel robust observer-based proportional-retarded controller for perturbed two-dimensional cranes, considering variation in the rope length. This novel scheme makes the trolley follow a desired reference signal while reducing the payload variations. The controller structure allows for compensating disturbances, while a new control approach introduces artificial delays that stabilize the closed-loop system and attain the desired control objective. A formal theoretical analysis demonstrates the validity of the new proposal. Then, experimental results show the outstanding performance of the proposed control scheme and its superior performance against other methodologies from the literature.

An Adaptive Control Scheme Based on Non-Interference Nonlinearity Approximation for a Class of Nonlinear Cascaded Systems and Its Application to Flexible Joint Manipulators

Control design for the nonlinear cascaded system is challenging due to its complicated system dynamics and system uncertainty, both of which can be considered some kind of system nonlinearity. In this paper, we propose a novel nonlinearity approximation scheme with a simplified structure, where the system nonlinearity is approximated by a steady component and an alternating component using only local tracking errors. The nonlinearity of each subsystem is estimated independently. On this basis, a model-free adaptive control for a class of nonlinear cascaded systems is proposed. A squared-error correction procedure is introduced to regulate the weight coefficients of the approximation components, which makes the whole adaptive system stable even with the unmodeled uncertainties. The effectiveness of the proposed controller is validated on a flexible joint system through numerical simulations and experiments. Simulation and experimental results show that the proposed controller can achieve better control performance than the radial basis function network control. Due to its simplicity and robustness, this method is suitable for engineering applications.

Designing a fixed-time observer-based adaptive non-singular sliding mode controller for flexible spacecraft

This paper investigates the stabilization problem with a fixed-time approach for a flexible spacecraft subject to vibrations of flexible modes, unknown bounded disturbance, and inherent uncertainty. To estimate the modal variables of a flexible spacecraft which are often unmeasurable in practice, an observer with guaranteed fixed-time convergence is designed. Using the estimated modal variables, a fixed-time non-singular sliding mode controller is designed so that the desired attitude can be reached before a pre-specified time threshold regardless of the spacecraft's initial attitude. By incorporating the estimated modal variables in the control design, significant reduction in the steady-state error of the system response is achieved. The proposed control system is further enhanced with an adaptive law to increase robustness against unknown external disturbances and uncertainties. Stability analysis based on Lyapunov theory guarantees the convergence of observer estimation error and spacecraft attitude error to a pre-determined set before a fixed threshold. Simulation results validate the promising performance of the proposed control system, highlighting its effectiveness in achieving accurate and robust attitude control for flexible spacecraft.

An Output Feedback Controller for a Second-Order System Subject to Asymmetric Output Constraint Based on Lyapunov Function with Unlimited Domain

In this work, a new robust controller is designed for a second-order plant model, considering asymmetric output constraints. The tracking error convergence and output constraint are achieved by using a control law whose output feedback term is user-defined and bounded: it takes on large but finite and user-defined values for tracking error values equal to or higher than the constraint boundary, and it comprises a previously known user-defined function for tracking error values far from the constraint boundary. This is a significant contribution that remedies two important limitations of common output constraint control designs: the infinite control effort for tracking error equal to or higher than the constraint boundary, and the impossibility of using previously known user-defined functions in the output feedback function for tracking error values far from the constraint boundary. As another contribution, the control design is based on the dead-zone Lyapunov function, which facilitates the achievement of convergence to a compact set with user-defined size, avoidance of discontinuous signals in the controller, and robustness to model uncertainty or disturbances. The proposed output feedback term consists of the product between two functions of the tracking error, an increasing function and a sigmoid function, whose exact expressions are user-defined. Finally, the effectiveness of the developed controller is illustrated by the simulation of substrate concentration tracking in a continuous flow stirred bioreactor.

Observer-based saturated proportional derivative control of perturbed second-order systems: Prescribed input and velocity constraints

This study introduces a new methodology for controlling second-order nonlinear systems in point-to-point tasks with simultaneous input and velocity saturation constraints. The proposed approach utilizes a robust disturbance observer for compensating for the unknown dynamics and disturbances affecting the system. Then, the disturbance observer is combined with a saturated proportional derivative (PD) controller. The resulting control signal allows solving the regulation problem and generating input values and velocities with some prescribed bounds defined by the user. Based on the Lyapunov-theory, asymptotic stability of the origin of the closed-loop error dynamics is attained, which implies that the position regulation objective is achieved while keeping the input and velocity values within prescribed bounds defined by the user. The new control scheme is assessed through numerical simulations, which corroborate the new saturated controller's feasibility.

Composite prescribed performance control of small unmanned aerial vehicles using modified nonlinear disturbance observer

An integrated control scheme composed of modified nonlinear disturbance observer and predefined-time prescribed performance control is proposed to address the high-accuracy tracking problem of the unmanned aerial vehicles (UAVs) subjected to external mismatched disturbances. By utilizing the transformation technique that incorporates the desired performance characteristic and the newly predefined-time performance function, the original controlled system can be transformed into a new unconstrained one to achieve the fixed-time convergence of the tracking error. Then, by virtual of the transformed unconstrained system, a modified nonlinear disturbance observer (NDO) which possesses fast convergence speed is established to estimate the external disturbance. With the application of the precise estimation value to compensate the normal control design in each back-stepping step, a novel composite control scheme is constructed. The light spot of the proposed scheme is that it not only has the superior capability to attenuate unknown mismatched disturbances, but also can guarantee that the output tracking errors converge to their prescribed regions within predefined time. Finally, simulation studies verify the effectiveness of the proposed control scheme.

A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions

In this study, a novel robust observer-based adaptive controller was formulated for systems represented by second-order input–output dynamics with unknown second state, and it was applied to concentration tracking in a chemical reactor. By using dead-zone Lyapunov functions and adaptive backstepping method, an improved control law was derived, exhibiting faster response to changes in the output tracking error while avoiding input chattering and providing robustness to uncertain model terms. Moreover, a state observer was formulated for estimating the unknown state. The main contributions with respect to closely related designs are (i) the control law, the update law and the observer equations involve no discontinuous signals; (ii) it is guaranteed that the developed controller leads to the convergence of the tracking error to a compact set whose width is user-defined, and it does not depend on upper bounds of model terms, state variables or disturbances; and (iii) the control law exhibits a fast response to changes in the tracking error, whereas the control effort can be reduced through the controller parameters. Finally, the effectiveness of the developed controller is illustrated by the simulation of concentration tracking in a stirred chemical reactor.

Integrated guidance and control for missile with narrow field-of-view strapdown seeker

Due to the removal of the mechanically stable platform in the conventional gimbaled seeker, the strapdown seeker's measurement is coupled with the missile body attitude motion, such that the inertial line-of-sight (LOS) angular rate required to implement traditional guidance laws cannot be measured, and the field-of-view (FOV) limit must be considered when designing guidance and control systems for a strapdown homing missile. To address these practical problems, an integrated guidance and control (IGC) scheme with considering the FOV limit is proposed in this paper. A novel IGC model is first derived based on the body-LOS (BLOS) angle that a strapdown seeker can directly measure, and then an IGC controller is designed using the dynamic surface control technique. A great merit of this design is that the inertial LOS angle and its angular rate are not needed, and thus the filters/estimators required to extract this guidance information in previous studies can be canceled. Next, by using the output to input saturation transformation (OIST) technique, the FOV limit, which is always considered as a state/output constraint, is transformed to a time-varying boundary limitation on the control input, and then is handled simultaneously with the actuator saturation constraint. Finally, extensive numerical simulations against both stationary and moving targets are performed to fully demonstrate the efficiency of the proposed IGC law.

Robust control design for an industrial wind turbine with HIL simulations

This paper describes the design and implementation of a H_∞-based robust controller for a commercial 2MW variable-speed variable-pitch wind turbine. The single controller is able to deliver specification performance for the entire full load region. Various aspects of modeling and design procedures including reduced order model validation, torsional mode damping of drivetrain and uncertainty estimation are explained in detail. To make the design more reliable and industrially attractive, simple routines for the derivation of required weighting functions are introduced. To investigate the benefits of the suggested design, its closed-loop performance is compared with the wind turbine's baseline controller and an alternative state-space controller proposed in the literature. This is first evaluated using a FAST-based simulator under IEC-61400 compatible scenarios. It is then verified by a real-life hardware in the loop simulator using an industrial PLC.