A Globally Stable High-Performance Adaptive Robust Control Algorithm With Input Saturation for Precision Motion Control of Linear Motor Drive Systems

This paper focuses on the synthesis of nonlinear adaptive robust controller with saturated actuator authority for a linear motor drive system, which is subject to parametric uncertainties and uncertain nonlinearities such as input disturbances as well. Global stability with limited control efforts is achieved by breaking down the overall uncertainties to state-linearly-dependent uncertainties (such as viscous friction) and bounded nonlinearities (such as Coulomb friction, cogging force, etc.), and dealing with them via different strategies. Furthermore, a guaranteed transient performance and final tracking accuracy can be obtained by incorporating the well-developed adaptive robust control strategy and effective parameter identifier. Asymptotic output tracking is also achieved in the presence of parametric uncertainties only. Meanwhile, in contrast to the existing saturated control structures that are designed based on a set of transformed coordinates, the proposed saturated controller is carried out in the actual system states, which have clear physical meanings. This makes it much easier and less conservative to select the design parameters to meet the dual objective of achieving global stability with limited control efforts for rare emergency cases and the local high-bandwidth control for high performance under normal running conditions. Real-time experimental results are obtained to illustrate the effectiveness of the proposed saturated adaptive robust control strategy     

Adaptive robust motion control of single-rod hydraulic actuators:theory and experiments

High-performance robust motion control of single-rod hydraulic actuators with constant unknown inertia load is considered. The two chambers of a single-rod actuator have different areas, so the dynamic equations describing the pressure changes in them cannot be combined into a single load pressure equation. This complicates controller design since it not only increases the system dimension but also brings in the stability issue of the added internal dynamics. A discontinuous projection-based adaptive robust controller (ARC) is constructed. The controller takes into account not only the effect of parameter variations coming from the inertia load and various hydraulic parameters but also the effect of hard-to-model nonlinearities such as uncompensated friction forces and external disturbances. It guarantees a prescribed output tracking transient performance and final tracking accuracy in general while achieving asymptotic output tracking in the presence of parametric uncertainties. In addition, the zero error dynamics for tracking any nonzero constant velocity trajectory is shown to be globally uniformly stable. Experimental results are obtained for the swing motion control of a hydraulic arm and verify the high-performance nature of the proposed strategy. In comparison to a state-of-the-art industrial motion controller, the proposed algorithm achieves more than a magnitude reduction of tracking errors. Furthermore, during the constant velocity portion of the motion, it reduces the tracking errors almost down to the measurement resolution level     

Robust adaptive control of sawyer motors without current measurements

We address nonlinear robust adaptive dynamic output feedback of voltage-fed dual-axis linear stepper (Sawyer) motors using a detailed motor model with electrical dynamics and significant uncertainties and disturbances. A coordinate transformation is proposed to decouple the model into three third-order subsystems along with an appended fifth-order subsystem. The controller utilizes only position and velocity measurements in each axis and achieves practical stabilization of position tracking errors. Adaptations are utilized so as not to require any knowledge of electromechanical system parameters. The controller is robust to load torques, friction, cogging forces, and other disturbances satisfying certain bounds. The controller corrects for the yaw rotation to achieve synchrony of motor and platen teeth.     

Adaptive robust precision motion control of linear motors withnegligible electrical dynamics: theory and experiments

This paper studies the high performance robust motion control of an epoxy core linear motor, which has negligible electrical dynamics due to the fast response of the electrical subsystem. A discontinuous projection based adaptive robust controller (ARC) is first constructed. The controller theoretically guarantees a prescribed transient performance and final tracking accuracy in general, while achieving asymptotic tracking in the presence of parametric uncertainties. A desired compensation ARC scheme is then presented, in which the regressor is calculated using the reference trajectory information only. The resulting controller has several implementation advantages such as less online computation time, reduced effect of measurement noise, a separation of robust control design from parameter adaptation, and a faster adaptation rate. Both schemes are implemented and compared on an epoxy core linear motor. Extensive comparative experimental results are presented to illustrate the effectiveness and the achievable control performance of the two ARC designs     

Robust Adaptive Control of Coupled Parallel Piezo-Flexural Nanopositioning Stages

Precision control of multiple-axis piezo-flexural stages used in a variety of scanning probe microscopy systems suffers not only from hysteresis nonlinearity, but also from parametric uncertainties and the cross-coupled motions of their axes. Motivated by these shortfalls, a Lyapunov-based control strategy is proposed in this article for simultaneous multiple-axis tracking control of piezo-flexural stages. A double-axis stage is considered for system analysis and controller validation. Hysteresis and coupling nonlinearities are studied through a number of experiments, and it is demonstrated that the widely used proportional-integral (PI) controller lacks accuracy in high-frequency tracking. Adopting the variable structure control method, a robust adaptive controller is then derived with its stability guaranteed through the Lyapunov criterion. It is shown that a parallelogram-type zone of attraction can be explicitly formed for the closed-loop system to which the error phase trajectory converges. Practical implementation of the controller demonstrates effective double-axis tracking control of the stage in the presence of hysteresis and coupling nonlinearities and despite parametric uncertainties for low-and high-frequency trajectories. Moreover, good agreements are achieved between the experiments and theoretical developments.      

Adaptive robust motion control of SISO nonlinear systems with implementation on linear motors

For the purpose of controlling an X–Y table driven by linear motors with a high precision, an adaptive robust motion tracking control method is first introduced. The controller is developed based upon a class of SISO nonlinear systems whose nonlinear part can be linearly parameterized. The advantage of such a controller is that parametric uncertainties and unknown disturbances can be dealt with, which is essential for a high precision of the control of linear-motor-driven X–Y table. With the prior knowledge of the bounds of the system parameters, a discontinuous projection is utilized in the adaptive law to ensure the boundedness of the parameters estimates. The algorithm is then implemented on a real X–Y table driven by the linear motors. In the modeling of such a system, fiction effects are also considered, which is useful for the derivation of the adaptive law. Experiments on the X–Y table are carried out and the results show excellent tracking performance of the system.     

Nonlinear adaptive control of direct-drive brushless DC motors andapplications to robotic manipulators

Robust adaptive nonlinear control of brushless DC (BLDC) motors is considered. A controller is designed for the plant that is robust to parametric and dynamic uncertainties in the entire electromechanical system. These uncertainties are shown to be bounded by polynomials in the states. In addition, the controller can reject any bounded unmeasurable disturbances entering the system. A model for the motor incorporating magnetic saturation is used to design voltage-level control inputs for the motor. The design methodology is based on our earlier work on adaptive control of nonlinear systems. The overall stability of the system is shown using Lyapunov techniques. The tracking error is shown to be globally uniformly bounded. The design procedure is shown to be also applicable to multilink manipulators actuated by BLDC motors. The performance of the controller is verified through simulations and comparisons with a proportional-integral-derivative-type controller are made     

Adaptive robust pressure control of variable displacement axial piston pumps with a modified reduced-order dynamic model

Variable displacement axial piston pumps (VDAPPs) are wildly used in mobile working machines and they play a key role in machine’s energy-saving load sensing (LS) systems. Typically, electric load sensing (ELS) systems utilize traditional linear control methods, which only can realize limited control flexibility and performance. This study proposes and experimentally verifies an adaptive robust pressure control strategy for a VDAPP system. To facilitate the model-based controller design, a modified reduced-order dynamic modeling of VDAPPs is proposed. Furthermore, an adaptive robust backstepping control strategy is designed to deal with the dynamic nonlinearities and parametric uncertainties of the VDAPP system for achieving accurate pressure tracking. The controller design consists of two steps, processing the pump pressure tracking and the axial angle control, respectively. Comparative experiments and simulations with different working conditions were performed to validate the advantages of the proposed control strategy. The proposed controller achieved higher pressure tracking accuracy and it showed great capability in dealing with dynamic nonlinearities, uncertainties, and time-varying disturbances.     

PID-type sliding mode-based adaptive motion control of a 2-DOF piezoelectric ultrasonic motor driven stage

This paper presents a new scheme of adaptive sliding mode control (ASMC) for a piezoelectric ultrasonic motor driven X–Y stage to meet the demand of precision motion tracking while addressing the problems of unknown nonlinear friction and model uncertainties. The system model with Coulomb friction and unilateral coupling effect is first investigated. Then the controller is designed with adaptive laws synthesized to obtain the unknown model parameters for handling parametric uncertainties and offsetting friction force. The robust control term acts as a high gain feedback control to make the output track the desired trajectory fast for guaranteed robust performance. Based on a PID-type sliding mode, the control scheme has a simple structure to be implemented and the control parameters can be easily tuned. Theoretical stability analysis of the proposed novel ASMC is accomplished using a Lyapunov framework. Furthermore, the proposed control scheme is applied to an X–Y stage and the results prove that the proposed control method is effective in achieving excellent tracking performance.     

Robust Kalman Filter Design for Markovian Jump Linear Systems with Norm-Bounded Unknown Nonlinearities

This paper considers the problems of stability and filtering for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The hybrid system under study involves a continuous-valued system state vector and a discretevalued system mode. The unknown nonlinearities in the system are time varying and norm bounded. The Markovian jump parameters are modeled by a Markov process with a finite number of states. First, we show the equivalence of the sets of norm-bounded linear and nonlinear uncertainties. Then, instead of the original hybrid linear system with nonlinear uncertainties, we consider the same system with linear uncertainties. By using a Riccati equation approach for this new system, a robust filter is designed using two sets of coupled Riccati-like equations such that the estimation error is guaranteed to have an upper bound.     

Desired Compensation Adaptive Robust Control of a Linear-Motor-Driven Precision Industrial Gantry With Improved Cogging Force Compensation

This paper proposes a new model for cogging forces of linear motor systems. Sinusoidal functions of positions are used to effectively capture the largely periodic nature of cogging forces with respect to position, while B-spline functions are employed to account for the additional aperiodic part of cogging forces. This model is experimentally demonstrated to be able to capture both the periodic and nonperiodic characteristics of cogging force while having a linear parametrization form, which makes the online adaptive compensation of cogging forces possible and effective. A discontinuous-projection-based desired compensation adaptive robust controller (DCARC) is then constructed, which makes full use of the proposed cogging force model for an improved cogging force compensation. Comparative experimental results with various cogging force compensations are obtained on both axes of a linear-motor-driven industrial gantry. The results show that DCARC with the proposed model compensation achieves the best tracking performance among all the three algorithms tested, validating the proposed cogging force model. The excellent tracking performances obtained in the experiments also verify the effectiveness of the proposed ARC control algorithms in practical applications. The proposed model and control algorithm can be applied for other types of motor control systems as well.      

Robust nonlinear control of brushless DC motors for direct-driverobotic applications

The control problem associated with brushless DC motors (BLDCMs) for direct-drive robotic applications is considered. In order to guarantee the high-performance operation of BLDCMs in such applications, the effects of reluctance variations and magnetic saturation are accounted for in the model. Such a BLDCM model constitutes a highly coupled and nonlinear dynamic system. Using the transformation theory of nonlinear systems, a feedback control law, which is shown to compensate for the system nonlinearities, is derived. Conditions under which such a control law is possible are presented. The need for the derivation of explicit commutation strategies is eliminated, resulting in reduction of the computations involved. To guarantee the high-performance operation of the system under substantial uncertainties, a robust control law is derived and appended to the overall control structure. The inclusion of the robust controller results in good tracking performance when there are modeling and measurement errors and payload uncertainties. The efficacy of the overall control law is investigated by considering a single-link direct-drive arm actuated by a BLDCM     

Adaptive robust control of fully-constrained cable driven parallel robots

In this paper, adaptive robust control (ARC) of fully-constrained cable driven parallel robots is studied in detail. Since kinematic and dynamic models of the robot are partly structurally unknown in practice, in this paper an adaptive robust sliding mode controller is proposed based on the adaptation of the upper bound of the uncertainties. This approach does not require pre-knowledge of the uncertainties upper bounds and linear regression form of kinematic and dynamic models. Moreover, to ensure that all cables remain in tension, proposed control algorithm benefit the internal force concept in its structure. The proposed controller not only keeps all cables under tension for the whole workspace of the robot, it is chattering-free, computationally simple and it does not require measurement of the end-effector acceleration. The stability of the closed-loop system with proposed control algorithm is analyzed through Lyapunov second method and it is shown that the tracking error will remain uniformly ultimately bounded (UUB). Finally, the effectiveness of the proposed control algorithm is examined through some experiments on a planar cable driven parallel robot and it is shown that the proposed controller is able to provide suitable tracking performance in practice.     

Nonlinear control of mechatronic systems with permanent-magnet DC motors

The current trends in development and deployment of advanced electromechanical systems have facilitated the unified activities in the analysis and design of state-of-the-art motion devices, electric motors, power electronics, and digital controllers. This paper attacks the motion control problem (stabilization, tracking, and disturbance attenuation) for mechatronic systems which include permanent-magnet DC motors, power circuity, and motion controllers. By using an explicit representation of nonlinear dynamics of motors and switching converters, we approach and solve analysis and control problems to ensure a spectrum of performance objectives imposed on advanced mechatronic systems. The maximum allowable magnitude of the applied armature voltage is rated, the currents are limited, and there exist the lower and upper limits of the duty ratio of converters. To approach design tradeoffs and analyze performance (accuracy, settling time, overshoot, stability margins, and other quantities), the imposed constraints, model nonlinearities, and parameter variations are thoroughly studied in this paper. Our goal is to attain the specified characteristics and avoid deficiencies associated with linear formulation. To solve these problems, an innovative controller is synthesized to ensure performance improvements, robust tracking, and disturbance rejection. One cannot neglect constraints, and a bounded control law is designed to improve performance and guarantee robust stability. The offered approach uses a complete nonlinear mechatronic system dynamics with parameter variations, and this avenue allows one to avoid the conservative results associated with linear concept when mechatronic system dynamics is mapped by a linear constant-coefficient differential equation. To illustrate the reported framework and to validate the controller, analytical and experimental results are presented and discussed. In particular, comprehensive analysis and design with experimental verification are performed for an electric drive. A nonlinear bounded controller is designed, implemented, and experimentally tested.     

Adaptive Fuzzy Output-Feedback Tracking Control for a Class of Switched Stochastic Nonlinear Time-Delay Systems

In this paper, a design scheme for an adaptive fuzzy tracking controller is proposed for a class of switched stochastic nonlinear time-delay systems via dynamic output-feedback. First, a reduced-order observer is introduced to estimate the unmeasurable states of the switched system. During the adaptive controller design procedure, an appropriate stochastic Lyapunov–Krasovskii functional deals with the time-delay terms, and fuzzy logic systems are employed to approximate the unknown nonlinearities. Based on the designed controller, the semi-globally uniform ultimate boundedness of all the closed-loop signals is guaranteed and the tracking error converges to a small neighborhood of the origin. Finally, a simulation example is given to illustrate the validity of the proposed approach.     

Adaptive integral robust control of hydraulic systems with asymptotic tracking

In this paper, an adaptive integral robust controller is developed for high accuracy motion tracking control of a double-rod hydraulic actuator. We take unknown constant parameters including the load and hydraulic parameters, and lumped unmodeled disturbances in inertia load dynamics and pressure dynamics into consideration. A discontinuous projection-based adaptive control law is constructed to handle parametric uncertainties, and an integral of the sign of the extended error based robust feedback term to attenuate unmodeled disturbances. Moreover, the present controller does not require a priori knowledge on the bounds of the lumped disturbances and the gain of the designed robust control law can be tuned itself. The major feature of the proposed full state controller is that it can theoretically guarantee global asymptotic tracking performance with a continuous control input, in the presence of various parametric uncertainties and unmodeled disturbances such as unmodeled dynamics as well as external disturbances via Lyapunov analysis. Comparative experimental results are obtained for motion control of a double-rod hydraulic actuator and verify the high-performance nature of the proposed control strategy.     

High precision position control of electro-hydrostatic actuators in the presence of parametric uncertainties and uncertain nonlinearities

Characterized by high power-to-weight ratio, modularity and energy efficiency, electro-hydrostatic actuators (EHAs) have been successfully applied to aircrafts and submarines, where high precision and repeatability are in high demand. The position tracking performance, however, can be inevitably affected by parametric uncertainties and uncertain nonlinearities. Model inaccuracy or system variations normally require a large loop gain to achieve robust performance, which leads to over-design. Leakage in the fluid power system decreases steady-state accuracy, and friction in the actuator degrades the transient performance or even causes stick-slip motion at low speeds. Furthermore, the system may exhibit limit cycle (or hunting) due to Stribeck friction and integral action. This paper proposes a robust high precision position control strategy incorporating leakage and friction compensation for EHAs. Quantitative feedback theory (QFT) is applied to design a robust controller that satisfies the prescribed performance specifications without over-design, considering model inaccuracy and system variations. The internal leakage is subsequently compensated based on experimental data instead of incorporating an integrator in the controller; hence, limit cycle is avoided, and response speed is improved. Friction in the actuator is identified based on the LuGre friction model and compensated through an observer in the loop. Friction variation and load fluctuation are considered to be output disturbances to be suppressed by the QFT controller. The QFT controller with leakage and friction compensation scheme is verified through experiments on a typical EHA. Both the steady-state and transient position tracking performances are greatly improved.     

Adaptive Iterative Learning Control for a Class of Uncertain Nonlinear Systems with Second-Order Sliding Mode Technique

This paper addresses the problem of robust adaptive iterative learning control for a chain of uncertain integral nonlinear systems, whose aim is to stabilize the tracking error of the system and improve convergence speed in the presence of uncertainties. In response to unknown bounded disturbances, a continuous second-order sliding mode adaptive iterative learning control scheme is proposed, in which an integral term is to attenuate the effects of the disturbances and achieve fast convergence performance. By designing a suitable controller and composite energy function, it is proved that the tracking error along iterative learning horizon will converge to a small neighborhood of zero. Numerical examples are provided to validate the efficacy of the proposed method.     

Robust Dichotomy Analysis and Synthesis With Application to an Extended Chua's Circuit

Dichotomy, or monostability, is one of the most important properties of nonlinear dynamic systems. For a dichotomous system, the solution of the system is either unbounded or convergent to a certain equilibrium, thus periodic or chaotic states cannot exist in the system. In this paper, a new methodology for the analysis of dichotomy of a class of nonlinear systems is proposed, and a linear matrix inequality (LMI)-based criterion is derived. The results are then extended to uncertain systems with real convex polytopic uncertainties in the linear part, and the LMI representation for robust dichotomy allows the use of parameter-dependent Lyapunov function. Based on the results, a dynamic output feedback controller guaranteeing robust dichotomy is designed, and the controller parameters are explicitly expressed by a set of feasible solutions of corresponding linear matrix inequalities. An extended Chua's circuit with two nonlinear resistors is given at the end of the paper to demonstrate the validity and applicability of the proposed approach. It is shown that by investigating the convergence of the bounded oscillating solutions of the system, our results suggests a viable and effective way for chaos control in nonlinear circuits.     

Robust H/sub 2/ filtering for a class of systems with stochastic nonlinearities

This paper addresses the robust H/sub 2/ filtering problem for a class of uncertain discrete-time nonlinear stochastic systems. The nonlinearities described by statistical means in this paper comprise some well-studied classes of nonlinearities in the literature. A technique is developed to tackle the matrix trace terms resulting from the nonlinearities, and the well-known S-procedure technique is adopted to cope with the uncertainties. A unified framework is established to solve the addressed robust H/sub 2/ filtering problem by using a linear matrix inequality approach. A numerical example is provided to illustrate the usefulness of the proposed method.