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This work presents a novel nonlinear control scheme for simultaneous state tracking and mitigation of undesired deflection effects in flexible robotic manipulators. The presented method directly incorporates the partial differential equations (PDEs) used for describing dynamics of the mechanism into the corresponding control calculations and assumes no form of reduction in PDEs (which in this work have been derived according to extended Hamilton principle for a rigid-flexible manipular when considering the flexible arm as an Euler-Bernoulli beam). Hence, the presented methodology should be considered as considerably more feasible for a wide range of applications in comparison with the conventional strategies which use assumed modes to analyze link flexibility dynamics or vibration effects. Furthermore, the proposed controller ensures state tracking and link-deflection boundedness only using standard control inputs to the mechanism without incorporating additional boundary inputs (which essentially represents satisfaction of more control objectives than the limited number of inputs would allow in conventional controllers), which would render it a viable choice for robotic applications where additional inputs cannot be easily exerted to end effector or cases where this strategy would require significant modifications in existing devices. Numerical simulations indicate the effectiveness of the presented control scheme. acceptedVersion

This article presents a novel scheme for model-based control of multi-input–multi-output (MIMO) systems considering input nonaffinity, nonlinear dynamical effects, and bounded modeling uncertainty. Commonly, model-based control of a nonaffine system is conducted based on an equivalent pseudo-affine expression. However, validity of this approximation necessitates boundedness of inputs and states. Furthermore, existence of truncation errors is inevitable when obtaining the pseudo-affine model. Therefore, robustness to bounded uncertainty should be ensured even in cases where the original system is deterministic. To address the expressed issues, in this study the boundedness assumptions are incorporated in a constrained robust model predictive control (MPC) algorithm. The corresponding MPC scheme is based on construction of cost according to predicted sliding functions over a finite prediction horizon. It should be noted that for the considered class of uncertain nonlinear nonaffine system, obtaining the perquisite robust stability and feasibility conditions is non-trivial. To attain the aforementioned qualities, it is proposed that sliding functions can be expressed as the sum of input-based terms (using pseudo-affine approximation of input gains based on Taylor expansion) and dynamical variation terms. Subsequently, robust stability is ensured by constructing a Lyapunov-based terminal cost. Constraints satisfaction conditions are determined based on calculation of the corresponding feasible region. Numerical simulations for a nonlinear nonaffine mechanical system indicate efficiency of the presented control model. Comparisons with other applicable schemes highlight significant features of the presented algorithm and the attained improvements regarding stability and control feasibility are discussed.

In this paper, a novel multiobjective algorithm for simultaneous path-following control (PFC) of multivariable flexible dynamical systems and maintaining boundedness of transverse vibrational effects is proposed. This method is specifically designed for control of complicated dynamical systems where obtaining precise mathematical models describing vibrational and translational dynamics is difficult or unattainable. To facilitate the control task, the proposed scheme is constructed such that it would be capable of stabilizing the closed-loop system solely using a rigid approximation of system dynamics while considering vibrational effects as unstructured uncertainties. This permits the designer to forgo the troublesome task of precisely modeling and numerically analyzing the flexible vibrational system, prioritizing important path-following and closed-loop stability characteristics. The proposed control algorithm incorporates a discrete sliding mode control (DSMC) scheme constructed on the basis of calculation of input bounds. This method does not introduce additional chattering effects as generation of control inputs is not directly dependent on switching functions. Unstructured uncertainties are estimated using one-step approximation technique which removes the need for employing difficult techniques used in the existing literature. The control algorithm is constructed in two distinct modes, the first of which considers appropriate path following as its objective. The second control mode halts the tracking task unless an assigned cost function resides in an acceptable interval, resulting in gradual reduction of intensity of vibrational effects. The control algorithm is numerically simulated in ANSYS® Mechanical APDL environment. The obtained results express the accuracy and efficiency of the control algorithm despite the use of considerably simpler procedure in comparison with existing works.

In this paper, the problem of stabilization and tracking control of uncertain flexible multivariable continuum mechanism systems with additional appendage considering boundedness of undesired vibrational effects are investigated. It is proposed that rather than controlling the entire dynamical system through installation of additional actuators on appendage, it is more desirable to stabilize the core system while considering undesired vibrational effect in the appendage as optimization cost. To this end, the nonlinear programming problem corresponding to a predictive control scheme is presented based on a cost defined according to magnitude of accelerations of undesired vibrations in the appendage. Stabilization of control algorithm is conducted based on demonstration of existence of feasible Lyapunov functions. Candidate Lyapunov functions are defined based on sliding functions analysis. The associated sliding functions are defined for core subsystems which correspond to degrees of freedom of dynamical system that are associated with reference signals. Undesired vibrations caused by other degrees of freedom corresponding to appendage are considered as segments of control cost in the optimization problem. To ensure the feasibility of control model in real-time applications, the control algorithm is obtained in discrete-time basis. Based on investigation of monotonically decreasing Lyapunov functions and expression of sliding functions as a combination of dynamical terms, reference inputs and control input terms, stabilizing constraints of closed-loop system are calculated. Similarly, based on combination of sliding surfaces with considered control and vibrational constraints, additional constraints for boundedness of vibrational terms in nonlinear programming problem are obtained. Numerical comparisons with a sliding control algorithm for core mechanical system and a reaching law method indicate improvements regarding reduction of undesired vibrational effects in appendage. Furthermore, regulation of appendage dynamics is conducted without installation of additional actuators, which reduces the implementation cost in comparison with a full-control scheme for core system and appendage.

In this article, a new control method is proposed based on finite-time discrete sliding mode control for uncertain multi-input multi-output systems which are affine to their inputs considering uncertain input multipliers in the case where signs of input gains remain constant over uncertainty spaces. In addition, a method for solving a set of convex control inequalities is introduced. The proposed control strategy is based on merging data obtained from investigation of common candidate Lyapunov functions assigned to various subsystems and their subsequent decoupling based on matrix elementary row operations. Initially, separate sliding functions corresponding to a single degree of freedom are assigned to each subsystem in the overall multi-input multi-output system, which results in obtaining a convex inequality corresponding to input bounds. Stacking the data obtained from various subsystems, the product of the uncertain input gain matrix in input vector is obtained as the middle term in a set of convex inequalities. Subsequently, the convex inequality is solved according to a set of matrix elementary row operations transforming the corresponding input matrix to row echelon form such that the bounds of each input are clearly expressed. Then, based on assigning input bounds proximity factors to each lower bound–upper bound duo, appropriate control inputs are generated. Chattering effects are eliminated as no switching term is included in construction of the control model. Effectiveness of the proposed method is demonstrated using numerical simulations. The implementation of control algorithm using microprocessors is also illustrated, indicating the feasibility of digital application.

This paper proposes a novel method for simultaneous estimation of unknown switched external disturbance and precise position control of dynamical systems which employ worm gear drive reducers. This algorithm is based on an improved discrete sliding mode control (DSMC) design which ensures convergence to the desired sliding set without introducing chattering effects to the dynamical system. In order to improve the performance of DSMC and to obtain an accurate estimation of gearbox model, a new method for incorporation of switched friction is proposed in the presence of external disturbance. To this end, the dynamical response of worm gear drive reducer is investigated in distinct switched disturbance modes of resistive disturbances, assistive disturbances and no disturbance to obtain approximate functions describing system dynamics in aforementioned configurations. In comparison with the feedback data, the obtained models permit appropriate incorporation of friction into the improved DSMC scheme. Based on multiple common Lyapunov functions and calculation of virtual reference signals for armature currents, the feasibility of control algorithm is ensured in all modes of switched dynamics. The effectiveness of the proposed estimation and control schemes has been verified using an experimental setup employing a worm gear drive reducer on which multiple permanent magnet DC motors are installed, and improvements resulted from incorporation of friction estimation algorithm are analyzed.

In this paper, a novel control scheme is proposed for model predictive control (MPC) of switched systems under arbitrarily generated undetectable switching signals. To this end, it is assigned that control scheme should simultaneously ensure reduction in optimization cost and maintain closed-loop stability. In other words, the control algorithm operates as single-mode in case corresponding conditions are satisfied, resulting in reduction of number of required calculations and ease of implementation. The proposed stabilization scheme is based on prediction of sliding hyperplane in various switched configurations, leading to reduced problem dimensions and ease of implementation of robustness analysis. To this end, an analytic gradient-descent expression of the optimization solution is obtained, shown to be robustly input-to-state stable (ISS) given the existence of a common Lyapunov function (CLF) corresponding to sliding mode controller (SMC). Furthermore, effects of dynamical variations over the prediction horizon are investigated, noting important effects on the stability criteria, which have been ignored in previous analytical studies. In case sufficient conditions are satisfied, the control scheme results in closed-loop stability and gradual convergence of sliding functions to origin in all potential modes of switched dynamics regardless of active switching state. However, the necessary conditions corresponding to sampling rate pertaining to this objective are potentially over-strict. To overcome this issue, it is proposed that control objectives and stability conditions can be relaxed such that boundedness of sliding functions in all switched modes is maintained according to the cost-reducing input update law rather than their strict convergence to the origin. The effects of state and input constraint violations are then incorporated as soft constraints. Experimental and numerical evaluations demonstrate the effectiveness of control method.

This paper proposes a new method for control of nonlinear multi input – multi output (MIMO) mechanical systems that incorporate viscoelastic dampers (VED) for reducing undesired vibrations of actuators. To this end, a control algorithm is proposed based on considering various characteristics of the described dynamical systems (namely mechanical dynamics, viscoelasticity and actuator dynamics) in generation of control inputs guaranteeing convergence of system response to desired reference signals. This procedure features three consecutive parts within the control loop which are conducted iteratively at each control sample. At each sample, initially necessary forces and moments exerted to mechanical system are calculated as virtual control inputs generated based on a MIMO discrete-time sliding mode control (DSMC) algorithm. As the aim of control model is obtaining a closed-loop system without resulting in notable vibrational effects, undesired chattering effects should be eliminated from inputs generated by DSMC. This objective is attained by calculation of appropriate input bounds. Next, an additional virtual input is assigned corresponding to viscoelastic strain such that virtual mechanical input from previous part of the control loop is generated. To this end, Maxwell model for viscoelastic material is considered. Finally, actual controller input is generated such that all virtual control objectives are satisfied. The effectiveness of control procedure is numerically illustrated for a 3-PRR manipulator.

In the current study, the behavior of a crank–slider mechanism with single and multiple clearance joints is analyzed. For this purpose nonlinear dynamics of the system are discussed, using Poincare maps and bifurcation diagrams. Subsequently, the effects of joint friction on dynamical behavior and nonlinear response of the mechanism are investigated. Afterward, a control scheme providing continuous contact in joints, with the aim of maintaining a more stable behavior, is proposed. The control scheme is easy to apply and, since continuous contact between bodies in joints is established, several undesired effects normally caused because of clearance joints are prevented or reduced. Also the limitation of the proposed control method is investigated.

Dynamical behaviors and control of planar crank–slider mechanism considering the effects of joint clearance and link flexibility are studied. A control scheme for maintaining continuous contact is proposed. It was observed that using one actuator for control scheme might cause the actuator to reach its saturation limit, a problem that was bypassed by installing an additional actuator on connecting rod. In one actuator case, only continuous contact can be obtained, while with the aid of two actuators, point contact can be achieved. Great improvements in the performance of mechanism and reduction of vibrations are observed in the case of using an additional actuator.

In this paper, a novel method for control of uncertain MIMO flexible systems is proposed. The control system is constructed such that it is capable of stabilizing a flexible dynamical system based on rigid approximation of continuum dynamics, resulting in facilitation of modeling and control procedures for complicated vibrational systems. In order to ensure system stability in real-time applications, the control system is obtained in discrete-time basis. To these ends, a sliding hyper-plane based sliding mode control (SMC) algorithm is constructed featuring sliding functions for individual subsystems. An approximated dummy model of the real system is used alongside the dynamical system in order to estimate parametric and unstructured uncertainties which are evaluated through comparisons between the dummy model, data obtained from the real system and corresponding mathematical model. Conventional SMC techniques introduce undesired effects of chattering which result in amplifying vibrations in flexible systems. To address this issue, an alternate algorithm based on selection of control signals within appropriate bounds is used in order to eliminate chattering and provide superior performance in comparison with conventional SMC techniques. The accuracy of proposed method has been verified through ANSYS® mechanical APDL-based simulations and its effectiveness has been verified in multiple operating conditions.