Closed-loop stability analysis of a gantry crane with heavy chain and payload

In this paper, we analyse a systematically designed and easily tunable backstepping-based boundary control concept for a gantry crane with heavy chain and payload. The corresponding closed-loop system is formulated as an abstract evolution equation in an appropriate Hilbert space. Non-restrictive conditions for the controller coefficients are derived, under which the solutions are described by a C₀-semi-group of contractions, and are asymptotically stable. Moreover, by applying Huang's theorem we can finally even show that under these conditions the controller renders the closed-loop system exponentially stable.     

Energy-efficient and high-precision control of hydraulic robots

In addition to high-precision closed-loop control performance, energy efficiency is another vital characteristic in field-robotic hydraulic systems as energy source(s) must be carried on board in limited space. This study proposes an energy-efficient and high-precision closed-loop controller for the highly nonlinear hydraulic robotic manipulators. The proposed method is twofold: 1) A possibility for energy consumption reduction is realized by using a separate meter-in separate meter-out (SMISMO) control set-up, enabling an independent metering (pressure control) of each chamber in hydraulic actuators. 2) A novel subsystem-dynamics-based and modular controller is designed for the system actuators, and it is integrated to the previously designed state-of-the-art controller for multiple degrees-of-freedom (n-DOF) manipulators. Stability of the overall controller is rigorously proven. The comparative experiments with a three-DOF redundant hydraulic robotic manipulator (with a payload of 475 kg) demonstrate that: 1) It is possible to design the triple objective of high-precision piston position, piston force and chamber pressure trackings for the hydraulic actuators. 2) In relation to the previous SMISMO-control methods, unprecedented motion and chamber pressure tracking performances are reported. 3) In comparison to the state-of-the-art motion tracking controller with a conventional energy-inefficient servovalve control, the actuators’ energy consumption is reduced by 45% without noticeable motion control (position-tracking) deterioration.     

A robust Markov game controller for nonlinear systems

This paper proposes a reinforcement learning (RL)-based game-theoretic formulation for designing robust controllers for nonlinear systems affected by bounded external disturbances and parametric uncertainties. Based on the theory of Markov games, we consider a differential game in which a ‘disturbing’ agent tries to make worst possible disturbance while a ‘control’ agent tries to make best control input. The problem is formulated as finding a min–max solution of a value function. We propose an online procedure for learning optimal value function and for calculating a robust control policy. Proposed game-theoretic paradigm has been tested on the control task of a highly nonlinear two-link robot system. We compare the performance of proposed Markov game controller with a standard RL-based robust controller, and an H_∞ theory-based robust game controller. For the robot control task, the proposed controller achieved superior robustness to changes in payload mass and external disturbances, over other control schemes. Results also validate the effectiveness of neural networks in extending the Markov game framework to problems with continuous state–action spaces.     

Intelligent mixed H2/H∞ adaptive tracking control system design using self-organizing recurrent fuzzy-wavelet-neural-network for uncertain two-axis motion control system

In this paper, an intelligent adaptive tracking control system (IATCS) based on the mixed H₂/H_∞ approach under uncertain plant parameters and external disturbances for achieving high precision performance of a two-axis motion control system is proposed. The two-axis motion control system is an X–Y table driven by two permanent-magnet linear synchronous motors (PMLSMs) servo drives. The proposed control scheme incorporates a mixed H₂/H_∞ controller, a self-organizing recurrent fuzzy-wavelet-neural-network controller (SORFWNNC) and a robust controller. The combinations of these control methods would insure the stability, robustness, optimality, overcome the uncertainties, and performance properties of the two-axis motion control system. The SORFWNNC is used as the main tracking controller to adaptively estimate an unknown nonlinear dynamic function that includes the lumped parameter uncertainties, external disturbances, cross-coupled interference and frictional force. Moreover, the structure and the parameter learning phases of the SORFWNNC are performed concurrently and online. Furthermore, a robust controller is designed to deal with the uncertainties, including the approximation error, optimal parameter vectors and higher order terms in Taylor series. Besides, the mixed H₂/H_∞ controller is designed such that the quadratic cost function is minimized and the worst case effect of the unknown nonlinear dynamic function on the tracking error must be attenuated below a desired attenuation level. The mixed H₂/H_∞ control design has the advantage of both H₂ optimal control performance and H_∞ robust control performance. The sufficient conditions are developed for the adaptive mixed H₂/H_∞ tracking problem in terms of a pair of coupled algebraic equations instead of coupled nonlinear differential equations. The coupled algebraic equations can be solved analytically. The online adaptive control laws are derived based on Lyapunov theorem and the mixed H₂/H_∞ tracking performance so that the stability of the proposed IATCS can be guaranteed. Furthermore, the control algorithms are implemented in a DSP-based control computer. From the experimental results, the motions at X-axis and Y-axis are controlled separately, and the dynamic behaviors of the proposed IATCS can achieve favorable tracking performance and are robust to parameter uncertainties.     

Nonlinear H ∞ control of a Quadrotor (UAV), using high order sliding mode disturbance estimator

A nonlinear H _∞ output feedback controller is proposed and coupled to a high-order sliding mode estimator to regulate an UAV in the presence of the unmatched perturbations. The plant to be controlled is a Quadrotor helicopter described by nonlinear dynamics with plant uncertainties due to the variations of inertia moments and payload operation. A robust state estimation is considered under model uncertainties as well as external/measurement disturbances. Performance issues of the controller are illustrated in a simulation study made for an UAV prototype.     

A novel trajectory planning-based adaptive control method for 3-D overhead cranes

A three-dimensional (3-D) overhead crane is a complicated nonlinear underactuated mechanical system, for which high-speed positioning and anti-sway control are the kernel objective. Existing trajectory-based methods for 3-D overhead cranes focus on combining efficient and smooth trajectories with anti-sway tracking controllers without regard for payload motion; moreover, the exact value of plant parameters is required for accurate compensation during the control process. Motivated by these facts, we present a two-step design tracking strategy which consists of a trajectory planning stage and an adaptive tracking control design stage for 3-D overhead cranes. As shown by Lyapunov techniques and Barbalat's Lemma, the proposed controller guarantees asymptotic swing elimination and trolley positioning result in the presence of system uncertainties including unknown parameters and external disturbances. Simulation results also showed the applicability of the proposed method with good robustness against parameter uncertainties and external disturbances.     

Robust control of multistage printing systems

Printing errors (e.g. doubling) in multistage printing machines are mainly caused by web tension fluctuations, which arise from excessive rotation non-synchronization errors among the driven rollers in different stages (units). Therefore, the critical task in printing quality control is to attenuate web tension variations. In this paper, a robust H_∞ control strategy is proposed to attenuate tension fluctuations when the system is subject to disturbances and variations in speed or other operating conditions. Three system robustness properties are analyzed by using structured singular value analysis (μ-analysis). A systematic investigation is taken to analyze the impacts of different parameter variations on system robustness, with a purpose of providing a reference for achieving robust stability in a multistage printing system. The effectiveness of the proposed robust H_∞ controller is evaluated by both simulation and experimental tests.     

Finite-time fault-tolerant control for flutter of wing

In this paper, we use the radial basis function neural network and the finite-time H_∞ adaptive fault-tolerant control technique to deal with the flutter problem of wings with propulsion system, which is affected by input saturation, time delay, time-varying parameter uncertainties and external disturbances. Then sensor and actuator faults are both considered in the control design. The theory content of this article includes the trajectory optimization, modeling of wing flutter and fault-tolerant controller design. The stability of the finite-time H_∞ adaptive fault-tolerant controller is theoretically proved. Finally, simulation results are given to demonstrate the effectiveness of the scheme.     

Robust adaptive boundary control of a perturbed hybrid Euler-Bernoulli beam with coupled rigid and flexible motion

In this paper, a robust adaptive boundary controller is proposed to stabilize the coupled rigid-flexible motion of an Euler-Bernoulli beam in presence of boundary and distributed perturbations. Applying Hamilton’s principle, the dynamics of the hybrid beam model, including the actuators hub and the payload at its ends, is represented through four nonhomogeneous nonlinear partial differential equations (PDEs) subject to ordinary differential equations (ODEs) of boundary conditions. Using a Lyapunov-based control synthesis procedure, a robust nonlinear boundary controller is established that asymptotically stabilizes the perturbed beam vibration while regulating the rigid motion coordinates. A redesign of the proposed control laws produces a robust adaptive boundary controller that achieves control objectives in the presence of both parametric and modelling uncertainties. Control design is directly based on system PDEs without truncating the model so that instabilities from spillover effects are mitigated. The control inputs to the beam consist of three forces/torque applied to the actuators hub and a transverse force applied to the tip payload. Simulation results are used to investigate the efficiency of the proposed approach.

     

Multi-frequency disturbance rejection via blending control technique for hard disk drives

This paper is concerned with the rejection of multiple narrowband disturbances in hard disk drives (HDDs). Inspired by a control blending idea, the multi-frequency disturbance rejection is formulated as a blending control problem. Each disturbance rejection is accomplished by using the H₂ optimal control method. Based on all H₂ optimal controllers, the blending technique is applied to yield a single controller which is capable of achieving rejection of all disturbances. Rejections of two and three disturbances for a 1.8-inch HDD VCM actuator are taken as application examples in the paper. Simulation and experimental results show that the ultimate controller results in a simultaneous attenuation of disturbances with frequencies higher or lower than the closed-loop system bandwidth. Moreover, the method turns out to be able to lift phase and thus prevent phase margin loss when it is used to deal with disturbances near bandwidth.     

Adaptive output feedback tracking control of robot manipulators using position measurements only

In this paper, a new adaptive neuro controller for trajectory tracking is developed for robot manipulators without velocity measurements, taking into account the actuator constraints. The controller is based on structural knowledge of the dynamics of the robot and measurements of joint positions only. The system uncertainty, which may include payload variation, unknown nonlinearities and torque disturbances is estimated by a Chebyshev neural network (CNN). The adaptive controller represents an amalgamation of a filtering technique to generate pseudo filtered tracking error signals (for the elimination of velocity measurements) and the theory of function approximation using CNN. The proposed controller ensures the local asymptotic stability and the convergence of the position error to zero. The proposed controller is robust not only to structured uncertainty such as payload variation but also to unstructured one such as disturbances. Moreover the computational complexity of the proposed controller is reduced as compared to the multilayered neural network controller. The validity of the control scheme is shown by simulation results of a two-link robot manipulator. Simulation results are also provided to compare the proposed controller with a controller where velocity is estimated by finite difference methods using position measurements only.     

Inertia‐free saturated output feedback attitude stabilization for uncertain spacecraft

In this article, the problem of robust output feedback attitude stabilization control for a class of uncertain spacecraft is investigated, which contains external disturbances, model parameter uncertainty, unknown and uncertain inertia, controller's gain perturbations, measurement errors, and input saturation. The aim of this work is to design a dynamic output feedback controller such that the closed‐loop attitude system is stabilized, while the H_∞ norm of the transfer function from the lumped disturbance and measurement error to output is ensured to be less than a pre‐specified disturbance attenuation level, and the actual control input is confined into a certain range simultaneously. Based on the Lyapunov theory, the existence conditions of such controller are derived in terms of linear matrix inequalities. It is worth mentioning that the controller's additive and multiplicative perturbations are accounted for respectively. An illustrative example is given to demonstrate the effectiveness and advantage of the proposed control design method.     

Design of decentralized robust controller for voltage regulation and stabilization of multimachine power systems

This paper presents a decentralized state-feedback controller design based on robust control theory to ensure system stability and voltage regulation in multimachine power systems. The power system is decomposed in n subsystems each represented by a state-space model with bounded parameter uncertainties and unknown input disturbances of class L _∞ which model couplings with the generators of the others subsystems. The proposed controller designed according to a Riccati-based approach is robust with respect to uncertain network parameters and counteracts the effects of the disturbances. A stability analysis in presence of L _∞ disturbances is also given. The control law is straightforward and cost effective because it is function of constant gains and of local measurable machine variables. Numerical simulations give evidence of the achievements in terms of system transient stability as well as voltage regulation, also in comparison with another design technique.     

Nonlinear Anti-swing Control of Underactuated Tower Crane Based on Improved Energy Function

The control system of tower crane exhibits strong nonlinearity in the process of control execution, which is prone to the problems of inaccurate positioning control of the payload and difficult anti-swing control. Aiming at the problems, this paper proposes a control law based on improved energy coupling analysis for suppressing the payload swing in the tower cranes. A three-dimensional dynamic model of tower crane system with considering friction is established, and an improved energy coupling signal is designed. The coupling relationship of trolley movement and payload swing, jib rotation and payload swing are considered, then a nonlinear anti-swing controller is established in order to reduce the swing. The closed-loop stability of the system with the controller is verified by the Lyapunov method and LaSalle invariance principle, simulations and experimental analyses are performed to verify the controller performance. The control performance of the controller is compared with other classic and typical current control methods, and the proposed controller outperformed other controllers. The anti-swing controller proposed in this paper has accurate positioning, and can achieve precise control when the payload is transported, reaching the set target position in a little time and eliminating residual swing angle. Meanwhile the proposed controller has a good control robustness, which can restore stability in around a very short time when the rope length and payload mass of the system’s inherent property are changed and external interference is added. In addition, when different target position parameters are uncertain, the proposed control law has good robust performance.

     

An Energy-based Nonlinear Coupling Control for Offshore Ship-mounted Cranes

This paper proposes a novel nonlinear energy-based coupling control for an underactuated offshore ship-mounted crane, which guarantees both precise trolley positioning and payload swing suppressing performances under external sea wave disturbance. In addition to having such typical nonlinear underactuated property, as it is well known, an offshore ship-mounted crane also suffers from much unexpected persistent disturbances induced by sea waves or currents, which, essentially different from an overhead crane fixed on land, cause much difficulty in modeling and controller design. Inspired by the desire to achieve appropriate control performance against those challenging factors, in this paper, through carefully analyzing the inherent mechanism of the nonlinear dynamics, we first construct a new composite signal to enhance the coupling behavior of the trolley motion as well as the payload swing in the presence of ship′s roll motion disturbance. Based on which, an energy-based coupling control law is presented to achieve asymptotic stability of the crane control system′s equilibrium point. Without any linearization of the complex nonlinear dynamics, unlike traditional feedback controllers, the proposed control law takes a much simpler structure independent of the system parameters. To support the theoretical derivations and to further verify the actual control performance, Lyapunov-based mathematical analysis as well as numerical simulation/experimental results are carried out, which clarify the feasibility and superior performance of the proposed method over complicated disturbances.     

Mixed H2/H∞ state-feedback design for microsatellite attitude control

Owing to a great decrease in size and weight, the pointing accuracy of microsatellite is vulnerable to space environmental disturbances and the internal uncertainty of moment-of-inertia variation. Mixed H₂/H_∞ control, giving consideration to both stability robustness and root-mean-square (rms) performance, is particularly attractive for attitude controller design of microsatellites. By using linear matrix inequality method, the numerical solution of mixed H₂/H_∞ state-feedback controller can be efficiently solved. The performance differences between mixed H₂/H_∞ controller and its two extremes—pure H₂ controller and pure H_∞ controller—are discussed in detail. Mixed H₂/H_∞ controller shows the remarkable capability of achieving a balanced compromise between H₂ and H_∞ performances.     

Interval type 2 hierarchical FNN with the H-infinity condition for MIMO non-affine systems

To develop a controller that deals with noise-corrupted training data and rule uncertainties for interconnected multi-input–multi-output (MIMO) non-affine nonlinear systems with unmeasured states, an interval type-2 fuzzy system is integrated with an observer-based hierarchical fuzzy neural controller (IT2HFNC) in this paper. Also, an H_∞ control technique and a strictly positive real Lyapunov (SPR-Lyapunov) design approach are employed for attenuating the influence of both external disturbances and fuzzy logic approximation error on the tracking of errors. Moreover, the proposed hierarchical fuzzy structure can greatly reduce the number of adjusted parameters of the IT2HFNC, and then, the problem of online computational burden can be solved. According to the design of the interval type-2 fuzzy neural network and H_∞ control technique, the IT2HFNN controller can improve its robustness to noise, uncertainties, approximation errors, and external disturbances. Simulation results are reported to show the performance of the proposed control system mode and algorithms.     

Application Of H2/H∞ Technique To Aircraft Landing Control

The paper describes the automatic control of an aircraft in the longitudinal plane during landing, taking into account sensor errors and disturbances. Aircraft auto‐landing is achieved by combining H₂ and H_∞ control techniques, thereby obtaining a robust H₂/H_∞ controller. It provides good precision tracking and robust stability with respect to the uncertainties caused by different disturbances and noise‐type signals. The weights of the H₂ and H_∞ control techniques within the robust H₂/H_∞ controller are adjusted so that the aircraft accurately tracks the desired trajectory during the two main stages of the landing process. The theoretical results are validated by numerical simulations for the landing of a Boeing; the results are very good (Federal Aviation Administration accuracy requirements for Category III are met) and prove the robustness of the new auto‐landing system even in the presence of disturbances and sensor errors.     

Sliding mode control of drum water level in an industrial boiler unit with time varying parameters: A comparison with H∞-robust control approach

In steam power-plants, to prevent over-heating of drum components or flooding of steam lines, perfect control of drum water level is of great importance. But during the operation, disturbances affecting water level, model uncertainties and parameter mismatch due to variant operating conditions lead to the variation of model parameters. In this paper, under transient conditions and in the presence of model uncertainties, two control strategies are implemented to achieve desired tracking of drum water level: robust sliding mode and H_∞ control. Two transfer functions between drum water level (output variable); feed-water and steam mass rates (input variables) are considered. For the dynamic system with time varying characteristic and parametric uncertainties, a sliding mode controller is developed and an optimal H_∞ controller is designed based on μ-synthesis with DK-iteration algorithm. For different desired commands of drum water level (including a sequence of steps and ramps-steps); it is observed that both control strategies guarantee robust stability and performance of the system without actuators saturation (control signals are bounded). However, using the sliding mode controller leads to the more smooth and rapid time responses of drum water level with less oscillatory behaviour of control efforts (and consequently less energy consumption). In addition, for tracking objectives in short command times, sliding mode controller performs more appropriately.     

Non-linear output feedback tracking control for AUVs in shallow wave disturbance condition

This article presents a non-linear output feedback tracking controller deisgn for autonomous underwater vehicles (AUVs) operating in shallow water area. In a shallow water environment, significant disturbances due to shallow water waves affect the motion of marine vehicles greatly. Since it is not energy efficient to counteract the oscillatory disturbances due to waves, it is critical to obtain the wave information or wave induced disturbance information and design an energy efficient controller to reduce the action of actuators to counteract wave disturbances to avoid wear and tear on actuators. In this article, a non-linear observer is first designed to estimate the low frequency (LF) motion of AUVs and to filter out wave-frequency (WF) motion of AUVs due to shallow water wave by using position and attitude measurements. Based on the designed observer, a non-linear output feedback controller is subsequently derived by using the observer backstepping technique. By using this approach, the AUV achieves global exponential tracking without excessive energy consumption to counteract the wave disturbance and also avoids excessive wear and tear on thrusters. Global exponential stability (GES) of overall observer-controller system is proved through Lyapunov stability theory. A set of simulations is carried out by using the KAMBARA (Silpa-Anan 2001 Silpa-Anan, C. 2001. “Autonomous Underwater Robot: Vision and Control”. In Master's thesis, The Australian National University.  [Google Scholar]) AUV model to demonstrate the performance of the proposed observer and output feedback controller.