Adaptive fuzzy sliding mode control for uncertain nonlinear underactuated mechanical systems

Sliding mode control has been shown to be a robust and effective control approach for stabilization of nonlinear systems. However the dynamic performance of the controller is a complex function of the system parameters, which is often uncertain or partially known. This paper presents an adaptive fuzzy sliding mode control for a class of underactuated nonlinear mechanical systems. An adaptive fuzzy system is used to approximate the uncertain parts of the underactuated system. The adaptive law is designed based on the Lyapunov method. The proof for the stability and the convergence of the system is presented. Robust performance of the adaptive fuzzy sliding mode control is illustrated using a gantry crane system. Simulation results demonstrate that the system output can track the reference signal in the presence of modelling uncertainties, external disturbances and parameter variation. © 2013 IEEE

Observer-based integral sliding mode control for sensorless PMSM drives using FPGA

This paper presents the design and evaluation of an observer-based integral sliding mode controller for sensorless Permanent Magnet Synchronous Motor (PMSM) drive based on the Field Programmable Gate Array (FPGA) technology. For enhancement of robustness, a flux angle estimator using an improved sliding mode observer is proposed to estimate the current and back electromotive force (EMF) as well as to derive the flux angle. These estimated values together with the computed rotor speed of the motor are fed back for the control purpose in both the current loop and the speed loop. To increase the performance of PMSM speed control, an integral sliding mode control (ISMC) is designed with integral operation to improve steady state accuracy against parameter variations and external disturbances. The developed controller has been implemented in an FPGA-based environment and the very high speed integrated circuit-hardware description language (VHDL) is adopted to show advantages of the proposed control system. By integrating the observer-based and integral sliding mode control techniques into speed control of a PMSM drive, the system performance can be substantially enhanced while improving its cost-effectiveness and reliability. The validity of the proposed approach is verified through simulation results based on Modelsim and Simulink co-simulation method. © 2013 IEEE

Discrete-time sliding mode control with state bounding for linear systems with time-varying delay and unmatched disturbances

© The Institution of Engineering and Technology 2015. This study is concerned with the problem of quasi-sliding mode control design for a class of discrete-time systems with time-varying delay and unmatched disturbances. On the basis of the Lyapunov-Krasovskii method, combined with the reciprocally convex approach, sufficient conditions for the existence of a stable sliding surface are first derived in terms of matrix inequalities. These conditions also guarantee that the state trajectories of the reduced-order system are exponentially convergent within a ball whose radius can be minimised to deal with the effects of time-varying delay and disturbances. A robust quasi-sliding mode control scheme is then developed to drive the system state trajectories towards that ball in a finite time and maintain them therein after subsequent time. A numerical example is given to illustrate the effectiveness of the proposed approach

Offshore container crane systems with robust optimal sliding mode control

Open-sea ship-to-ship transfer operation is an alternative way to avoid port congestion. This process involves a relatively small vessel which transports containers between the harbour and a large cargo ship equipped with a container crane. However, the presence of disturbances and uncertainties caused by harsh open-sea conditions can produce an excessive sway to the hoisting ropes of the crane system. This paper addresses the problem of robust sliding mode control for offshore container crane systems subject to bounded disturbances and uncertain parameters. The mathematical model of an offshore container crane is first derived whereas the effects of ocean waves and gusty winds are taken into account. Then, based on the linear quadratic regulator (LQR) design, a sliding surface is obtained to meet the required performance and stable dynamics for the closed-loop system. Finally, a robust sliding mode controller is proposed to drive the state trajectories of the offshore container crane system towards the sliding surface in finite time and maintain them subsequently on that surface. Simulation results are given to show that the proposed controller can significantly suppress the effects of uncertainties and disturbances from the vessel's wave-and wind-induced motion and wind drag force on the payload

Decentralised predictive controllers with parameterised quadratic constraints for nonlinear interconnected systems

A decentralised model predictive control scheme for nonlinear interconnected systems is developed with parameterised stabilising constraints in this paper. Both control and state constraints are inclusive in the problem formulation. An extension to the input-to-state stabilisation framework is given with a newly derived input-to-power-and-state stabilisability (IpSS) condition for interconnected systems. In this work, we consider C1 continuous nonlinear input-affine state-space models with unknown but bounded input disturbance, and develop an LMI-based robust stabilisability condition for the global system. The interactive signals are also unknown and bounded in this development. With an open-loop perspective, the stabilising constraint for model predictive control in this approach is a dynamic quadratic constraint on the initial control vector, which is converted from a dissipation-based constraint using compound output signals. Numerical simulation for three dynamically-coupled subsystems is provided to illustrate the theoretical development. © 2012 IEEE

Further results on exponential stability of linear discrete-time systems with time-varying delay

© 2015 IEEE. This note addresses the exponential stability problem of a class of discrete-time systems with interval time-varying delay. Based on the Lyapunov-Krasovskii method, a set of appropriate Lyapunov-Krasovskii functionals, containing an augmented vector and some triple summation terms is first proposed. By utilizing the combination of the reciprocally convex approach and the delay-decomposition technique, improved delay-dependent conditions for exponential stability of the system are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed approach

APRC-based decentralised model predictive control for parallel splitting systems with a matrix annihilation

A decentralised model predictive control strategy for interconnected process systems having parallel-splitting structure based on the asymptotically positive realness constraint (APRC) is presented in this paper. Parallel masking and transform descriptor approaches have been employed in previous work for this type of interconnection processes. A robust control perspective has been brought to light in this work to resolve the issue of multiple subprocess parallelised-ly decoupled in a mixed connection configuration of dynamically coupled units. An annihilation is employed to cancel out the interactive vectors between interconnected processing units. Simulation for a parallel redundant process system in mining industry is provided to demonstrate the effectiveness of the presented robust control approach to parallelised interconnected systems. © 2013 IEEE

On sliding dynamics bounding for discrete-time systems with state delay and disturbances

This paper addresses the problem of bounding the reachable set of the sliding dynamics in discrete-time systems subject to time-varying state delay and bounded external disturbances. The sliding motion is determined from the equivalent dynamics chosen from a desired eigen-structure via the pole placement technique. New delay-dependent conditions are derived to guarantee that the trajectories in the sliding mode are prescribed in an ellipsoid with a minimal bound on each coordinate. Finally, the proposed approach is illustrated by a numerical example of a quasi-sliding mode controller. © Institution of Engineers Australia 2012

Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances

This paper addresses the problem of reachable set bounding for linear discrete-time systems that are subject to state delay and bounded disturbances. Based on the Lyapunov method, a sufficient condition for the existence of ellipsoid-based bounds of reachable sets of a linear uncertain discrete system is derived in terms of matrix inequalities. Here, a new idea is to minimize the projection distances of the ellipsoids on each axis with different exponential convergence rates, instead of minimization of their radius with a single exponential rate. A smaller bound can thus be obtained from the intersection of these ellipsoids. A numerical example is given to illustrate the effectiveness of the proposed approach. © 2012 Springer Science+Business Media New York

Modelling and robust trajectory following for offshore container crane systems

© 2015 Elsevier B.V. In stevedoring operations, the ship-to-ship transfer of containers in open-sea is becoming an alternative way to avoid port congestion and subsequently can increase port efficiency. This process involves a large container ship or a barge, equipped with a crane, and a smaller vessel which transports containers between the ship and the harbour. However, the harsh open-sea conditions can produce exogenous disturbances to the crane system during the load transfer. Besides, the uncertainties and disturbances in the crane system may degrade the control performance. Hence, one of the requirements of offshore container cranes is to enhance robustness of the crane control system. This paper addresses the problem of robust sliding mode control for offshore container crane systems subject to bounded disturbances and uncertainties. The mathematical model of the control plant is first derived whereas the effects of ocean waves and strong winds are taken into account. Then, a robust sliding mode controller is proposed to track an optimal trajectory of the crane system during load transfer. Extensive simulation results are given to show that the proposed controller can significantly suppress the effects of disturbances from the vessel's wave- and wind-induced motion