Comments on `On adaptive inverse dynamics control of rigid robots'[with reply]

The commenters point out an error in the adaptive control approach for robotic manipulators given in the above-named work by M.W. Spong and R. Ortega (see ibid., vol.35, p.92-5, Jan. 1990). It is noted that the authors assert that their adaptive control scheme eliminates the restriction given in J.J. Craig (1986) on the estimated inertia matrix; however, the commenters point out that a form of the inverse of the estimated inertia matrix must be bounded for the acceleration to be bounded. In a reply, the authors acknowledge the error in their paper     

Comments on `The control of robot manipulators with bounded input'[with reply]

The present author demonstrates: (1) that the optimal decision strategy (ODS) proposed in the paper by M.W. Spong and J.S. Thorp (IEEE Trans. Automat. Contr. vol.AC-31, p.483-90 (1986)) is in fact a specific case of an optimal aim strategy (OAS) with special aim-state and system-state assignments; and (2) that the primal-dual method employed in the same paper can be replaced by a more direct, more efficient discrete-time control algorithm based on fixed-point iteration or by a more complete, more exact continuous-time control law based on fixed-point feedback. For the class of problems under discussion, however, the authors' special assignments represent a significant application of optimal-aim notions. Spong and Thorp point out that although the optimal decision strategy (ODS) that they use in their paper does not appear to be a special case of OAS as originally defined, it can be included within the framework of more recent formulations of OAS. In fact, it appears that the two methods, as currently defined, are essentially equivalent     

An output feedback globally stable controller for induction motors

We present a globally stable nonlinear dynamic output feedback controller for torque tracking and flux regulation of induction motors. The control law is globally defined, requires only measurement of stator variables and rotor speed, and does not rely on cancellation of the systems nonlinearities. Our work extends the result of the paper by Ortega et al.(1993), where the torque tracking problem was solved for a model and the variables are expressed in a frame rotating at an arbitrary angular frequency (dq model). First, we obviate the need to transfer the dq control signals of the paper by Ortega et al., to the physical input variables in the stator frame, hence providing a directly implementable control law. Second, besides the torque tracking objective, we include the practically important rotor flux regulation task. Third, by choosing a more suitable representation of the motor model, we simplify the controller structure and provide a better understanding of its derivation and behavior     

A switched priority scheduling mechanism for ATM switches with multi-class output buffers

In this paper, we propose a switched priority scheduling mechanism for an Asynchronous Transfer Mode (ATM) switch with multi-class output buffers. The switched priority scheduling mechanism is composed of a model-based linear controller, a heuristic nonlinear controller and the corresponding switching law of the controllers. The nonlinear controller is first applied to bring each class buffer into a small neighborhood of its operating point such that the linear controller can be used. The linear controller is then used to ensure that each buffer occupancy converges to its desired operating point. The service rate of each class buffer is periodically computed and dynamically adjusted. We derive the design formulae of the control mechanism such that each buffer occupancy globally converges to its desired operating point related to quality-of-service requirements.     

Robust stabilizing control laws for a class of second-order switched systems

For a class of second-order switched systems consisting of two linear time-invariant (LTI) subsystems, we show that the so-called conic switching law proposed previously by the present authors is robust, not only in the sense that the control law is flexible (to be explained further), but also in the sense that the Lyapunov stability (resp., Lagrange stability) properties of the switched system are preserved in the presence of certain kinds of vanishing perturbations (resp., nonvanishing perturbations). The analysis is possible since the conic switching laws always possess certain kinds of “quasi-periodic switching operations”. We also propose for a class of nonlinear second-order switched systems with time-invariant subsystems a switching control law which locally exponentially stabilizes the entire nonlinear switched system, provided that the conic switching law exponentially stabilizes the linearized switched systems (consisting of the linearization of each nonlinear subsystem). This switched control law is robust in the sense mentioned above.     

Improved closed‐loop stability for fixed‐point controller realizations using the delta operator

A stable discrete‐time control system may achieve a lower than predicted performance or even become unstable when the discrete‐time control law is implemented with a fixed‐point digital control processor due to the finite word length (FWL) effects, which depends on the control law state‐space realization and the discrete‐time operator (e.g., the delta operator or the forward‐shift operator) used to represent the control law. To improve the closed‐loop stability (and as a byproduct, performance) when the control law is implemented, a state‐space approach that selects the control law realization to optimize a stability‐related objective function is developed using the delta operator. Analytical and numerical comparison of the fixed‐point performance of delta control laws with the performance of the corresponding forward‐shift control laws quantifies the improved closed‐loop stability of the delta realizations over those of the corresponding forward‐shift realizations. It is also shown that there exists a simple mapping between the optimal FWL forward‐shift control law realizations and the optimal FWL delta control law realizations. The results are illustrated by delta and forward‐shift control law realizations of a discrete‐time H_∞ control law designed for a teleoperation motion‐scaling system. Copyright © 2001 John Wiley & Sons, Ltd.     

无人机空中加油过程中分数阶滑模会合导引控制

针对带末端角度和末端速度约束的无人机空中加油自主会合问题,设计了一种3维分数阶滑模导引律,使无人机在无加油机主动配合的情况下具备自主会合能力.首先,根据无人机与加油机之间的相对运动关系,设计了3维比例导引规律,使无人机能够到达期望的加油位置.其次,利用滑模控制的强鲁棒性特点以及分数阶微积分的精细控制特性,基于变结构理论和李雅普诺夫稳定性理论设计了一种带有末端角度约束的3维分数阶滑模变结构控制律,并用所设计的分数阶滑模控制律对3维比例导引指令进行重构,使无人机能以期望的末端追踪角度到达加油位置.然后,构造了速度指令生成器,对无人机的末端速度进行约束.最后,对所设计的导引律进行了仿真验证,仿真结果表明所设计出来的导引律能满足追踪角度和速度约束的要求.     

Stability analysis of a multi-model predictive control algorithm with application to control of chemical reactors

We study a stabilizing multi-model predictive control strategy for controlling nonlinear process at different operating conditions. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function that has finite and infinite horizon cost components. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and steers the system to the desired operating point. The system is represented by a sequence of piecewise linear models. Based on the condition of the system states, the sequence of piecewise linear models is updated and the controller’s objective function switches form quasi-infinite to infinite horizon objective function. This results in a hybrid control structure. A recent approach in the analysis of hybrid systems that uses multiple Lyapunov functions is employed in the stability analysis of the closed-loop system. The stabilizing hybrid control strategy is illustrated on two examples and their closed-loop stability properties are studied.     

Nonlinear control of induction motors: torque tracking with unknownload disturbance

Ortega and Espinosa (1993) presented a globally stable controller for torque regulation of a complete induction motor model with partial state feedback, i.e., no assumption of flux measurement. The result was established under the assumptions that both the desired and load torques are constant, that the former does not exceed certain bounds which depend on the systems natural damping, and that the motor parameters are known. In the present contributions the authors extend these results in several directions. First, by “adding mechanical damping” to the closed-loop system the authors relax the upper bound condition on the desired torque. Second, the authors use a new controller structure that allows them to treat the case of time-varying desired torque. Finally, a new estimator is proposed to handle time-varying (linearly parameterized) unknown loads     

Controller designs for bilateral teleoperation with input saturation

Input saturation raises a stability issue in a bilateral teleoperation system when a master robot whose motion is induced by a human operator moves fast in abnormal situation and a slave robot cannot follow the motion command due to the input saturation. In this paper, we conduct rigorous stability analyses of the teleoperation system under the input saturation. We first extend analysis of teleoperation scheme proposed in Chopra and Spong (2004) to a case of the input saturation, in which analysis is valid for a local operation region whose size is dependent on the input capacity. We further develop a new control scheme that guarantees the stability for a global operation region. Therefore, the proposed control scheme can deal with extreme cases, e.g., the speed of motion of the master robot can be substantially greater than the actuator capability of the slave robot. Simulations and experiments are subsequently conducted to verify the effectiveness of the analyses.     

Hybrid modelling and control of the common rail injection system

We present an industrial case study in automotive control of significant complexity: the new common-rail fuel-injection system for Diesel engines under development at Magneti Marelli Powertrain. In this system, an inlet metering valve, inserted before the high pressure (HP) pump, regulates the fuel flow that supplies the common rail according to the engine operating point (e.g., engine speed and desired torque). The standard approach in automotive control based on a mean-value model for the plant does not provide a satisfactory solution as the discrete-continuous interactions in the fuel injection system, due to the slow time-varying frequency of the HP pump cycles and the fast sampling frequency of sensing and actuation, play a fundamental role. We present a design approach based on a hybrid model of the Magneti Marelli Powertrain common-rail fuel-injection system for four-cylinder multi-jet engines and a hybrid approach to the design of a rail pressure controller. The hybrid controller performs significantly better when compared with the classical mean-value based approach.     

An advanced fuzzy logic gain scheduling trajectory control for nonlinear systems

This paper investigates a novel fuzzy control approach developed for a class of nonlinear continuous systems. We combine an input–output feedback linearization (IOFL) method and a gain scheduling (GS) approach to obtain a tracking control structure. The latter is mainly based on the reversing trajectory method which allows us to estimate the asymptotic stability region around operating points. Needless to say that the limitation of this analytical approach lies in the challenge of determining the intermediate operating points in order to ensure a smooth transition from actual operating conditions to desired ones. This happens when there is no intersection between successive stability regions. The proposed fuzzy logic controller (FLC) is synthesized in order to determine the intermediate operating points which, in turn, will allows us to online implement the tracking control for nonlinear systems. Finally, the effectiveness of the fuzzy gain scheduling schema is demonstrated through its simulation to a temperature control problem in a CSTR.     

A semiglobally stable output feedback PI2D regulator forrobot manipulators

Provides an answer to the long-standing question of designing asymptotically stable proportional plus integral regulators with only position feedback for robots with uncertain payload. It has previously been shown in Kelly (1993) and Ailon and Ortega (1993) that globally asymptotically stable set-point regulators for robot manipulators without velocity measurement can be obtained replacing the velocity feedback of a proportional plus derivative controller by a filtered position feedback. In these schemes, the only robot prior information required is the evaluation of the gravity forces at the reference (constant) position. This prior knowledge is used to shape the robot potential energy to have a unique minimum at the desired position. A mismatch in the estimation of the gravity forces leads to a position steady-state error. The authors' main contribution in this paper is to obviate the need of this prior information via the inclusion of two integral terms, around the position error and the filtered position, respectively. Semiglobal stability of the resulting control law is established     

Robust SVC controller design and analysis for uncertain power systems

A Static Var Compensator (SVC) installed in a power transmission network can be effectively used to enhance the damping of electromechanical oscillations [Schweickardt, H. E., Romegialli, G., & Reichert, K. (1978). Closed loop control of static VAR sources (SVS) on EHV transmission lines. IEEE Pes winter power meeting, (paper no A78, pp. 135–136), New York, Jan. 29–Feb. 3]. An adequately designed robust controller, which takes into account variations in the operating conditions, can help to achieve the desired damping control. The proposed approach described in this paper is aimed to achieve damping of electromechanical oscillations by considering a systematic approach, based on interval systems theory and Kharitonov's Theorem. The method presented allows for the design of a fixed-parameter, low-order controller, given a supposed stability degree of the system. The synthesis of a robust SVC controller is divided into two tasks. The first is the determination of the region of stability in the controller parameter plane by plotting the stability boundary locus. The second task is the optimization of the selected controller parameters from the obtained solutions to the first task. Examples of eigenvalue analysis and time simulation demonstrate the effectiveness and robustness of the designed controller.     

Clustering based multiple model control of hybrid dynamical systems using HJB solution

This paper deals with Hamilton–Jacobi–Bellman (HJB) equation based stabilized optimal control of hybrid dynamical systems (HDS). This paper presents the fuzzy clustering based event wise multiple linearized modeling approaches for HDS to describe the continuous dynamic in each event. In the present work a fuzzy clustering validation approach is presented for the selection of number of linearized models which span entire HDS. The method also describes how to obtain event wise operating point using fuzzy membership function, which is used to find the event wise model bank by linearizing the first principles model. The event wise linearized models are used for the formulation of the optimal control law. The HJB equation is formulated using a suitable quadratic term in the objective function. By use of the direct method of Lyapunov stability, the control law is shown to be optimal with respect to objective functional and stabilized the event wise linearized models. The global Lyapunov function is proposed with discrete variables which stabilized the HDS. The proposed modeling and control algorithm have been applied on two HDSs. Necessary theoretical and simulation experiments are presented to demonstrate the performance and validation of the proposed algorithm.     

An Adaptive Controller Dominant-Type Hybrid Adaptive and Learning Controller for Trajectory Tracking of Robot Manipulators

This paper proposes a new hybrid adaptive and learning control method based on combining model-based adaptive control, repetitive learning control (RLC) and proportional–derivative control to consider the periodic trajectory tracking problem of robot manipulators. The aim of this study is to obtain a high-accuracy trajectory tracking controller by developing a simpler adaptive dominant-type hybrid controller by using only one vector for estimation of the unknown dynamical parameters in the control law. The RLC input is adopted using the original learning control law, adding a forgetting factor to achieve the convergence of the learning control input to zero. We will improve and prove that the adaptive dominant-type controller could be applied for tracking a periodic desired trajectory in which adaptive control input increases and becomes dominant of the control input, whereas the other control inputs decrease close to zero. The domination of the adaptive control input gives the advantage that the proposed controller could adjust the feed-forward control input immediately and it does not spend much time relearning the learning control input when the periodic desired trajectory is switched over from the first trajectory to another trajectory. We utilize the Lyapunovlike method to prove the stability of the proposed controller and computer simulation results to validate the effectiveness of the proposed controller in achieving the accurate tracking to the periodic desired trajectory.     

Control of a non-linear PDE system arising from non-burning tokamak plasma transport dynamics

The control of kinetic profiles is among the most important problems in fusion reactor research. It is strongly related to a great number of other problems in fusion energy generation such as burn control, transport reduction, confinement time improvement, MHD instability avoidance and high-β or high-confinement operating modes access. We seek a controller which is able to make the kinetic profiles converge to their desired equilibrium profiles. We are interested in constructing a stabilizing controller that achieves stability for unstable equilibrium profiles and increases performance for stable equilibrium profiles. As a first approach, we consider in this work a set of non-linear partial differential equations (PDEs) describing approximately the dynamics of the density and energy profiles in a non-burning plasma. This nonlinear PDE model represents the one-dimensional transport equations for the kinetic variables, density and energy, in cylindrical geometry. The transport coefficients in this model are in turn non-linear functions of the kinetic variables. The original set of PDEs is discretized in space using a finite difference method which gives a high order set of coupled nonlinear ordinary differential equations (ODEs). Applying a backstepping design we obtain a discretized coordinate transformation that transforms the original system into a properly chosen target system that is asymptotically stable in l²-norm. To achieve such stability for the target system, convenient boundary conditions are chosen. Then, using the property that the discretized coordinate transformation is invertible for an arbitrary (finite) grid choice, we conclude that the discretized version of the original system is asymptotically stable and obtain a non-linear feedback boundary control law for the energy and density in the original set of coordinates. Numerical simulations show that the feedback control law designed using only one step of backstepping can successfully control the kinetic profiles.     

Robust design of adaptive control systems using conic sector theory

This paper presents a design approach for discrete adaptive control systems which provides a quantitative measure of the effect of design alternatives such as (i) adaptive gain, (ii) model order, and (iii) sampling rate, on stability in the presence of unmodeled plant dynamics. The proposed method, based on the conic conditions developed by Ortega et al. (1985, IEEE Trans. Aut. Control, AC-30, 1179–1187), is illustrated using a benchmark example. The results demonstrate that the sector conditions permit design tradeoffs to be made such that stability is maintained despite the model-plant mismatch.     

Robust arm configuration of manipulator mounted on flexible base

In this paper, the robustness of a manipulator mounted on a flexible base with a task-space feedback control to a fixed desired point is considered. We define the robust arm configuration (RAC), which is a special configuration where the linearized system is positive real. Lyapunov indirect method and the passivity theory guarantee a local asymptotic stability of the original nonlinear system. A finite but high closed-loop gain can be applied in the neighborhood of the RAC without considering the base flexibility, i.e., an additional sensor or a solution of whole inverse dynamics is not necessary. Considering the positive semidefiniteness of the residue matrices, a measure is proposed that measures the distance from the RAC. This measure represents the controllability of the manipulator itself, and does not depend on the underlying control law. The validity of the proposed approach is confirmed by a numerical example and experiments.     

Bearing‐only control of directed cycle formations: Almost global convergence and hardware implementation

In this article, we study bearing‐only control of directed cyclic formations. First, we provide a necessary and sufficient condition on the bearing constraints so that the directed cycle formation of n‐agents in (n?1)‐dimensional space is infinitesimally bearing rigid. Second, a bearing‐only control law which only allows motions perpendicular to the desired bearing vector is proposed. Under this control law, the agents globally asymptotically converge to a desired formation which is fully determined from their initial positions and desired bearing vectors. Finally, the proposed formation control law is implemented on mobile robots to support the analysis.