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Extended Kalman Filters (EKFs), Phase Locked Loops (PLLs), and Stator Flux Observers (SFOs) are widely used for sensorless control of Permanent Magnet Synchronous Motors (PMSMs) drives. Their use (in their most advanced version) is here extended, on the basis of model analogies and suitably-guaranteed closed loop stability properties, to the sensorless speed regulation control of Hybrid Stepper Motors (HSMs), in which position and speed sensors are not employed to reduce costs and increase robustness with respect to high temperature and high-vibration environments. Both realistic simulations and experimental results demonstrate the feasibility of the proposed methods in terms of closed-loop performance and robustness to parameters mismatch.

In this brief, the exponential rotor position tracking/regulation problem for position-sensorless (nonsalient-pole surface) PMSMs with unknown constant load torque and stator resistance is addressed. The requirement of persistency of excitation conditions involving a non-definitely zero rotor speed reference is removed, owing to the design of an innovative (speed measurement-based) adaptive observer that relies on a local version of the persistency of excitation lemma and does not involve straightforward adaptations of previous ideas.

The adaptive learning control theory is extended to include the case of non-minimum phase (time-invariant) linear systems with uncertain parameters. The existence of two approximate solutions to the related output tracking problem is proved. Exponential tracking of periodic output reference signals is guaranteed, along with the exponential estimation of the constant system parameters and of the constant coefficients characterizing the truncated Fourier series expansion for the periodic input reference signal.

A harmonically self-similar temporal partition, which turns out to be subtly exhibited by elite swimmers at middle distance pace, is formally defined for one of the most technically advanced swimming strokes—the butterfly. This partition relies on the generalized Fibonacci sequence and the golden ratio. Quantitative indices, named ϕ-bonacci butterfly stroke numbers, are proposed to assess such an aforementioned hidden time-harmonic and self-similar structure. An experimental validation on seven international-level swimmers and two national-level swimmers was included. The results of this paper accordingly extend the previous findings in the literature regarding human walking and running at a comfortable speed and front crawl swimming strokes at a middle/long distance pace.

The heart rate regulation problem is addressed for the well-known second order nonlinear model of the human heart rate response during treadmill/cycle-ergometer exercises. The mainly restrictive stability & global attractivity constraint in the literature, being constituted by an inequality involving four constant parameters of such a nonlinear model, is definitely removed. Nonlinear analytical arguments and design steps are innovatively presented to achieve heart rate regulation when model parameters satisfy the so-called ‘instability constraint’, with just stability & local attractivity properties being involved. Experimental results are included to illustrate all the theoretical derivations.

A master–slave synchronisation control problem is addressed for current-fed DC and permanent magnet synchronous motors with all uncertain parameters. A measurable exogenous rotor position reference signal, which belongs to the class of biased sinusoidal signals with uncertain bias, amplitude, angular frequency, phase, is to be tracked without assuming its a priori knowledge. An innovative modification of disturbance cancellation techniques allows to prove that an output feedback adaptive nonlinear control scheme, which simply generalises the classical internal-model-based input law, solves the aforementioned problem, with an overall stability proof concerning the entire closed-loop system. The practical effectiveness of the proposed approach is illustrated by experimental results.

A generalization of the PID ź - 1 control has been recently presented in Marino etźal. (2012), which guarantees the output tracking of smooth periodic reference signals (with known period) for uncertain minimum phase nonlinear systems in output feedback form with any relative degree ź ź 1 . In this note, we show that the repetitive learning control proposed in Marino etźal. (2012) also solves the same output tracking problem for a larger class of uncertain nonlinear systems in normal form, provided that the inverse system dynamics satisfy the Demidovich condition on suitable compact sets.

The paper poses the basis for the application of the Pade-based-repetitive learning control to power converters, in all the scenarios where a periodic reference signal is to be tracked. Compared to standard repetitive schemes, the new relevant feature of the proposed control is that the learning scheme is reduced to a simple intrinsically stable transfer function, whose poles lie on the left-hand-side of the complex plane. Hence, storing a considerable amount of samples is no longer required, while resetting procedures are no longer involved. The Pade-based-repetitive control has a simple structure, while being able to automatically compensate for any periodic disturbance signals coming from external generators and dead-time. A stability analysis is reported, providing a useful guidance to tune the control parameters. Simulation results are presented to illustrate the effectiveness of the proposed algorithm.

Autonomous vehicles, that are equipped with an artificial vision system, are considered in this paper. A new space-learning control is proposed for the tracking of planar curves, whose uncertain curvature is $L$-periodic in the curvilinear abscissa $s$. Differently from the related results in the literature, the new control does not rely on the time derivative of $s.$ Experimental results illustrate the effectiveness of the proposed approach.

A new speed reference generator for electric vehicles with fixed transmission gear ratio powered by centralized electric motors is presented. On the basis of a contraction mapping algorithm and without requiring any a priori knowledge of the external conditions, a sequence of speed reference values is provided. They converge to a steady-state operating point with a safe tire longitudinal slip. CarSim simulations illustrate the effectiveness of the proposed approach, even in the presence of uncertain parameters and complex vehicle dynamics, which are neglected in the control design.

We show how the design of repetitive learning controls, which typically require perfect knowledge of the period T characterizing the periodic reference signals to be tracked, can be generalized, through the design of novel recursive add-on period identifiers, to face sufficiently small period uncertainties in synchronization problems. Exponential period identification is achieved so that the asymptotic convergence properties guaranteed by the classical learning controls are preserved. Simulation results concerning multi-link robot synchronization tasks are included. Copyright © 2015 John Wiley & Sons, Ltd.

Summary We discuss the use of [m,m]-Pade approximants in the implementation of repetitive learning controls solving the output tracking problem (via output error feedback) in the presence of uncertain periodic reference and/or disturbance signals with known common period. The aim is to address the stability issues concerning those approximants when a linear learning controller—designed through a detailed stability proof (involving the use of a suitable Lyapunov-like function) and described by a transfer function exhibiting all its poles with negative real part—is to be obtained as well as to evaluate the corresponding closed-loop performances: robustness (for instance with respect to additive disturbance noises due to unmodeled sensor dynamics) is consequently achieved with improvements in the output tracking errors appearing as the approximation order m increases. Even though the case of any relative degree may be explicitly addressed, in this paper, for the sake of clarity, we restrict our attention to the learning problem for the class of single-input, single-output, minimum phase, time-invariant systems with known relative degree ρ = 2, uncertain parameters and uncertain output-dependent nonlinearities. Numerical simulation results illustrate the theoretical derivations. Copyright © 2014 John Wiley & Sons, Ltd.

The heart rate can be effectively used as a measure of the exercise intensity during long duration cycle-ergometer exercises: precisely controlling the heart rate (HR) becomes crucial especially for athletes or patients with cardiovascular/obesity problems. The aim of this letter is to experimentally show how the nonlocal and nonswitching nonlinear control that has been recently proposed in the literature for the HR regulation in treadmill exercises can be effectively applied to cycle-ergometer exercises at constant cycling speed. The structure of the involved nonlinear model for the HR dynamics in cycle-ergometer exercises is mathematically inspired by the structure of a recently identified and experimentally validated nonlinear model for the HR dynamics in treadmill exercises: the role played by the treadmill speed is played here by the work load while the zero speed case for the treadmill exercise is here translated into the cycling operation under zero work load. Experimental results not only validate the aforementioned nonlinear model but also demonstrate the effectiveness--in terms of precise HR regulation--of an approach which simply generalizes to the nonlinear framework the classical proportional-integral control design. The possibility of online modifying the HR reference on the basis of the heart rate variability (HRV) is also suggested and experimentally motivated.

The nonlinear learning control techniques, based on Fourier approximation theory and used by Verrelli (2011) [2] to solve the synchronization problem for uncertain permanent magnet synchronous motors (performing repetitive tasks of uncertain repetition period), are considered in this paper. We show that, if the exogenous rotor position reference signal (which is to be globally tracked without assuming its foreknowledge) is restricted to the class of sinusoidal signals with uncertain bias, amplitude, frequency and phase, a stronger result can be derived by resorting to nonlinear advanced identification techniques. In contrast to Verrelli (2011) [2] , neither availability of the rotor speed reference signal is required nor infinite memory identification schemes are used. The application to the problem of synchronizing a drumming robotic arm with a drumming human arm is presented: simulation results show satisfactory closed loop performances and confirm the effectiveness of the proposed solution.

Permanent-magnet step motors offer several advantages such as high efficiency, high power density, high torque-to-inertia ratio, and excellent durability and serviceability, as well as the absence of external rotor excitation and windings. The nonuniformity in the developed torque due to the nonsinusoidal flux distribution in the airgap is, however, the major obstacle in achieving global high-precision position tracking. When the position reference profile is a periodic signal of known period, such an obstacle may be however overcome by using recent learning control techniques, which require neither high gains in the inner speed/position control loops nor resetting procedures. An experimental comparison of two different recently designed learning position controls (“adaptive” and “iterative”) is, for the first time, carried out with reference to the same low-speed robotic application. Benefits and drawbacks of the two learning approaches are analyzed in detail.

SUMMARY In this brief note, we consider the transient stabilization and voltage regulation problem for a synchronous generator connected to an infinite bus. We show how a much simpler output feedback controller, compared with previous results, can be obtained if a different stability analysis is carried out: a suitable change of coordinates is performed so that advantageous triangularity properties of the regulation error dynamics are highlighted. A novel first order estimator for the uncertain mechanical input power is designed: it is the only adaptation scheme used by the controller. The innovative crucial step in the presented control design relies on relaxing the constraint imposed by the typically (previously) adopted back-stepping techniques and constituted by the required availability of the regulation/tracking error variables: the converging estimate of the mechanical input power directly becomes the reference value for the electrical power and allows for the straightforward computation of the uncertain power angle constant value guaranteeing voltage regulation at steady state. Copyright © 2011 John Wiley & Sons, Ltd.

On the basis of the ideas recently presented in Tomei and Verrelli (Tomei, P., and Verrelli, C.M. (2010), ‘Learning Control for Induction Motor Servo Drives with Uncertain Rotor Resistance’, International Journal of Control, 83, 1515–1528) and Marino et al. (Marino, R., Tomei, P., and Verrelli, C.M. (2011), ‘Robust Adaptive Learning Control for Nonlinear Systems with Extended Matching Unstructured Uncertainties’, International Journal of Robust and Nonlinear Control, Early View, doi: 10.1002/rnc.1720), we briefly show how the adaptive learning control design proposed in Liuzzo and Tomei (Liuzzo, S., and Tomei, P. (2009), Global Adaptive Learning Control of Robotic Manipulators by Output Error Feedback, International Journal of Adaptive Control and Signal Processing, 23, 97–109) can be extended to robotic manipulators driven by nonsalient-pole (surface) permanent magnet synchronous motors. Unstructured uncertain dynamics (that is no parameterisation is available for the uncertainties) of the rigid robot wi...

We address the tracking control problem for sensorless (nonsalient-pole surface) permanent magnet synchronous motors with unknown constant load torque. On the basis of stator current and voltage measurements only and without relying on nonrobust open loop integration of motor dynamics, a novel sixth order nonlinear adaptive control algorithm is designed, which guarantees, under persistency of excitation, local exponential rotor speed tracking. Simulation results illustrate the closed loop performance and show the effectiveness of the proposed solution even in the presence of current sensor noise and stator resistance variations.

SUMMARY The exponential output tracking problem for a class of single-input, single-output uncertain nonlinear systems, including systems with extended matching unstructured uncertainties and without a well-defined global relative degree, is addressed. Conditions on the uncertain system dynamics are derived, which allow us to design a state-feedback learning control achieving semi-global exponential output tracking of sufficiently smooth and periodic reference signals of known period, while guaranteeing ℒ2 and ℒ∞ transient performances during the learning phase. The application of the proposed learning approach to the position tracking control problem for uncertain permanent magnet step motors with non-sinusoidal flux distribution and uncertain position-dependent load torque allows us to provide a solution to a yet unsolved problem. Copyright © 2011 John Wiley & Sons, Ltd.

The class of single-input, single-output, minimum phase, nonlinear, time-invariant systems with uncertain output-dependent nonlinearities, uncertain parameters and known relative degree one or two is considered. The output regulation problem by output error feedback in the presence of periodic reference and/or disturbance signals with known common period is addressed and solved by following recent developments in the iterative learning control theory. A simple iterative learning control algorithm is derived: it can be interpreted as a generalization of the classical PID control which, for such a class of systems, solves the problem when reference and disturbance signals are constant. An application to autonomous vehicle control is presented to illustrate the potentiality of the proposed technique.

Learning control techniques, based on Fourier approximation theory, are used to solve the tracking control problem via state (rotor position and speed and stator currents) feedback for permanent magnet synchronous motors performing repetitive tasks: smooth rotor position and speed reference signals, whose foreknowledge is not assumed and which are periodic of uncertain period, are required to be tracked for any motor initial condition. The effectiveness of the proposed solution is illustrated by its successfully application to a master–slave synchronization problem. The presented result illustrates the high potentiality of merging together functional approximation theory and advanced nonlinear control techniques.

The rotor speed and flux modulus tracking problem for sensorless induction motors with uncertain constant load torque and uncertain both rotor and stator resistances is addressed. A new ninth order dynamic nonlinear adaptive control algorithm is designed: it relies on a novel closed loop observer for the unmeasured state variables (rotor speed and luxes) which is adaptive with respect to the uncertain parameters (load torque and motor resistances). Local exponential stability of the origin of the closed loop tracking and estimation error dynamics is guaranteed under suitable conditions including persistency of excitation which depends on reference signals only.

The tracking control problem for induction motor servo drives with mechanical and electrical uncertainties is addressed. Under the assumptions that the reference profile for the rotor angle is periodic of known period and the rotor flux modulus reference signal is persistently exciting, a robust adaptive learning control is designed, which is adaptive with respect to the uncertain rotor resistance and is able to ‘learn’ the periodic disturbance signal due to mechanical uncertainties by identifying the Fourier coefficients of its truncated approximation.

This paper addresses the output feedback tracking control problem for induction motor servo drives with mechanical uncertainties: rotor angle, rotor speed and stator Currents are assumed to be available for feedback. A robust adaptive learning control is designed under the assumption that the reference profile for the rotor angle is periodic with known period: it 'learns' the periodic disturbance signal by identifying the Fourier coefficients of any truncated approximation; L-2 and L-infinity transient performances are guaranteed in the 'learning phase'. It is shown that, for any motor initial condition belonging to an arbitrary given compact set, by properly setting the control parameters: (i) the rotor position and flux modulus tracking errors, exponentially converge to residual sets, which may be arbitrarily reduced by increasing the number of terms in the truncated Fourier series; (ii) when the unknown periodic disturbance can be represented by a finite Fourier series, the rotor position and flux modulus tracking errors exponentially converge to zero. As in field oriented-control, the control algorithm generates references for the magnetizing flux component and for the torque component of the stator current leading to significant simplifications for current-fed motors. Copyright (C) 2008 John Wiley & Sons, Ltd.

The problem of controlling sensorless induction motors with uncertain constant load torque and rotor resistance on the basis of stator current measurements only is addressed. A new eighth-order dynamic nonlinear adaptive control algorithm is designed, which relies on a closed loop adaptive observer for the unmeasured state variables (rotor speed and fluxes) and for the uncertain parameters and is not based on non-robust open loop integration of flux dynamics. Local exponential stability of the closed loop tracking and estimation error dynamics is achieved under persistency of excitation conditions which restrict the reference signals and may be interpreted in terms of motor observability and rotor resistance identifiability.

We propose a novel nonlinear tracking control algorithm for induction motors with uncertain load torque in which only stator currents are used for feedback: rotor speed and flux sensors are not required; no open-loop integration of flux dynamics is used. For a class of reference signals, for sufficiently small computable time-varying load torque uncertainty and for any initial condition belonging to an explicitly computed region, closed-loop boundedness is guaranteed while, under persistency of excitation, local exponential rotor speed and flux modulus tracking are achieved in the case of constant load torque. Copyright © 2007 John Wiley & Sons, Ltd.

Assuming that only stator currents and voltages are available for feedback, a nonlinear adaptive speed tracking control algorithm is proposed for a permanent magnet step motor with unknown constant load torque. It relies on three new theoretical results: the ‘s-alignment’ and ‘c-alignment’ procedures, in which the motor is forced to reach certain known equilibrium points, and an output feedback controller which guarantees asymptotic speed tracking for every initial condition belonging to an explicitly computed domain of attraction (global exponential convergence is achieved in the case of known constant load torque). Numerical simulation results illustrate the effectiveness of the proposed solution. Copyright © 2007 John Wiley & Sons, Ltd.

Two different nonlinear dynamic control algorithms are presented for synchronous motors with damping windings: (i) an adaptive speed-sensorless controller for rotor position tracking in the presence of unknown constant load torque, on the basis of rotor angle, stator and field windings currents measurements; (ii) an adaptive control law for rotor speed tracking in the presence of uncertain constant load torque and motor inertia, which is based on measurements of mechanical variables (rotor angle and speed) and stator windings currents but does not require field current. As in classical field oriented control, the three voltage inputs are designed so that the direct axis component of the stator current vector is driven to zero; the controllers generate, as an intermediate step, the reference signals for the field current and for the quadrature axis component of the stator current vector, which respectively determine the direct axis component of the damping winding flux vector and the electromagnetic torque. Simulation results are provided for a 20-KW synchronous machine, which show the effectiveness of the two proposed control algorithms.

The position estimation problem is addressed for (nonsalient-pole surface) permanent magnets synchronous machines. Rotor speed and stator currents/voltages measurements are assumed to be available for feedback. Two novel adaptive observers are compared and experimental results concerning pump-fan and generating applications are provided.

A master-slave synchronization control problem is addressed for current-fed permanent magnets synchronous machines with uncertain parameters and no speed sensor. An exogenous rotor position reference signal, which belongs to the class of biased sinusoidal signals with uncertain bias, amplitude, angular frequency, phase, is to be tracked without assuming its foreknowledge. An innovative output feedback adaptive nonlinear control scheme, which solves the aforementioned problem and simply generalizes the classical internal model-based input law, is presented. The effectiveness of the proposed approach is validated by experimental results.

We address the master-slave synchronization control problem for a current-fed DC motor with uncertain parameters: an exogenous rotor position reference signal, which belongs to the class of biased sinusoidal signals with uncertain bias, amplitude, frequency, phase, is to be tracked without assuming its foreknowledge. An innovative use of adaptive disturbance cancellation techniques allows to obtain an output feedback adaptive nonlinear control scheme which simply represents a generalization of the classical internal model- based input law. Analyses from both theoretical and experimental points of view illustrate the effectiveness of the proposed approach.

We propose a novel tracking control for induction motors in which only stator currents are used for feedback. Local exponential rotor speed and flux modulus tracking are achieved for any constant reference value and for restricted time-varying reference signals; any known motor parameters values (including constant load torque) and any initial condition, including rotor speed and fluxes, belonging to an explicitly computed domain of attraction are allowed.

The adaptive learning approach proposed in Del Vecchio, Marino, and Tomei (2003) and Liuzzo, Marino, and Tomei (2007a), which guarantees output tracking of sufficiently smooth periodic reference signals (of known period) for classes of time-invariant nonlinear systems with sufficiently smooth unstructured uncertainties, is considered. By using a slightly different analysis (and in particular less conservative bounds), we show how improved convergence properties can be established while maintaining the same learning control structures. The delayed first arithmetic mean of the Fourier series of the uncertain periodic time function f (of known period) can be used instead of the partial sums of the Fourier series of f to further improve the result: a trigonometric polynomial, whose approximation to f is almost as good as the best approximation of f, is obtained.

We present the use of [m, m]-Pade approximants in the implementation of repetitive learning controls for the asymptotic link position tracking in robotic manipulators with uncertain dynamics and periodic position reference signals (with known period). The resulting linear learning controllers are described by transfer functions exhibiting all their poles with negative real part. Analyses from both theoretical and experimental points of view are carried out.

An innovative cruise control algorithm for electric vehicles (trains, cars) powered by induction motors has been recently proposed in [12]. It achieves vehicle speed regulation to a given constant reference by incorporating a suitable rotor speed generator into a highly efficient adaptive indirect field oriented control. The aim of this paper is to solve an analogous regulation problem in which automatic, feedback-based variations in the vehicle speed reference are required to be on-line performed by the control algorithm in order to take into account constraints on the tire longitudinal slip. CarSim simulations illustrate the effectiveness of the proposed approach in performing challenging manoeuvres, even in the presence of complex vehicle dynamics that have been neglected in the control design steps.

It has been recently shown in the literature that a robust output feedback controller for the heart rate regulation can be designed for an experimentally validated second order nonlinear model of the human heart rate response during long-duration treadmill exercises: It is based on piecewise linear approximations of the original nonlinear model and involves (local) robust linear control techniques. In this letter, we resort to recent nonlinear advanced control techniques in order to illustrate the existence of a nonlocal and nonswitching control which guarantees heart rate regulation with no exact knowledge of model parameters and nonlinearities: It simply generalizes to the nonlinear framework the classical proportional-integral control design for linear models of heart rate response during treadmill exercises. Simulation and experimental results demonstrate the effectiveness of the proposed approach in typical training exercises involving warm up/holding/cool down phases.

The output tracking control problem via state feedback is addressed for a class of single input-single output nonlinear systems which are affected by extended matching unstructured uncertainties. Under the assumption that the output reference signal is sufficiently smooth and periodic with known period, a robust adaptive learning control is designed, which learns the unstructured unknown periodic disturbance signals due to system uncertainties by identifying the Fourier coefficients of any truncated approximation while guaranteeing L2 and L? transient performances. For any initial condition of the system in an arbitrary given compact set, by properly setting the control parameters: i) the output tracking error exponentially converges to a residual set which may be arbitrarily reduced by increasing the number of terms in the truncated Fourier series expansions; ii) when the unknown periodic disturbances can be represented by finite Fourier series expansions, the output tracking error exponentially converges to zero.

We address the state feedback position tracking control problem for uncertain current-fed permanent magnet step motors with non-sinusoidal flux distribution. Under the assumption that the reference profile for the rotor angle is periodic with known period, a robust adaptive learning control algorithm is designed, which "learns" the non-structured unknown periodic disturbance signal due to system uncertainties by identifying the Fourier coefficients of any truncated approximation, while guaranteing L2 and Lx transient performances. It is shown that for any motor initial condition: i) the position tracking error exponentially converges to a residual set which may be arbitrarily reduced by increasing the number of terms in the truncated Fourier series; ii) when the unknown periodic disturbance can be represented by a finite Fourier series, it is exponentially reconstructed by the learning algorithm and exponential position tracking is achieved.

The problem of controlling sensorless induction motors with uncertain constant load torque and rotor resistance is addressed. A new eigth order dynamic nonlinear adaptive control algorithm is designed, which feeds back only stator current measurements and does not require open loop integration of flux dynamics. Local exponential rotor speed and flux modulus tracking of smooth bounded reference signals are guaranteed under persistency of excitation.

The output feedback tracking control problem for induction motor servo drives with mechanical uncertainties is addressed. Under the assumption that the reference profile for the rotor angle is periodic with known period, an adaptive learning control is designed, which "learns" the non-structured unknown periodic disturbance signal due to mechanical uncertainties by identifying the Fourier coefficients of any truncated approximation, while guaranteing L2 and Linfin transient performances. It is shown that, for any motor initial condition belonging to an arbitrary given compact set: i) the guaranteed output tracking precision improves by increasing the number of terms in the truncated Fourier series; ii) when the unknown periodic disturbance can be represented by a finite Fourier series, it is exponentially reconstructed by the learning algorithm and exponential output tracking is achieved. Simulation results for a digital implementation of the proposed controller are provided.

A nonlinear control for speed-sensorless synchronous motors with damping windings is designed. Assuming that flux initial values are known, exponential rotor angle tracking of arbitrary smooth bounded reference signals, rotor flux vector direct axis component tracking of suitable smooth bounded reference signals and stator current vector direct axis component regulation to zero (motor field orientation) are guaranteed for any initial condition and for any unknown constant load torque. In the case of non-exact knowledge of flux initial conditions, a local result holds.