A passive repetitive controller for discrete-time finite-frequency positive-real systems

This work proposes and studies a new internal model for discrete-time passive or finite-frequency positive-real systems which can be used in repetitive control designs to track or to attenuate periodic signals. The main characteristic of the proposed internal model is its passivity. This property implies closed-loop stability when it is used with discrete-time passive plants, as well as the broader class of discrete-time finite-frequency positive real plants. This work discusses the internal model energy function and its frequency response. A design procedure for repetitive controllers based on the proposed internal model is also presented. Two numerical examples are included.Peer Reviewe

A new passive repetitive controller for discrete-time finite-frequency positive-real systems

This work proposes a new repetitive controller for discrete-time finite-frequency positive-real systems which are required to track periodic references or to attenuate periodic disturbances. The main characteristic of the proposed controller is its passivity. This fact implies closed-loop stable behavior when it is used with discrete-time passive plants, but additional conditions must be fulfilled when it is used with a discretetime finite-frequency positive-real plant. These conditions are analyzed and a design procedure is proposed.Peer Reviewe

A repetitive controller for discrete-time passive systems

This work proposes and studies a new repetitive controller for discrete-time systems which are required to track or to attenuate periodic signals. The main characteristic of the proposed controller is its passivity. This fact implies closed-loop stable behaviour when it is used with discrete-time passive plants. The work also discusses the energetic structure, the frequency response and the time response of the proposed controller structure. Some examples are included to illustrate its practical use

Measurements, Models, Systems and Design

531 s.

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Switched Kinematic and Force Control for Lower-Limb Motorized Exoskeletons and Functional Electrical Stimulation

Millions of people experience movement deficits from neurological conditions (NCs) that impair their walking ability and leg function. Exercise-based rehabilitation procedures have shown the potential to facilitate neurological reorganization and functional recovery. Lower-limb powered exoskeletons and motorized ergometers have been combined with functional electrical stimulation (FES) to provide repetitive movement, partially reduce the burden of therapists, improve range of motion, and induce therapeutic benefits. FES evokes artificial muscles contractions and can improve muscle mass and strength, and bone density in people with NCs. Stationary cycling is recommended for individuals who cannot perform load-bearing activities or have increased risks of falling. Cycling has been demonstrated to impart physiological and cardiovascular benefits. Motorized FES-cycling combines an electric motor and electrical stimulation of lower-limb muscles to facilitate coordinated, long-duration exercise, while mitigating the inherent muscle fatigue due to FES. Lower-limb exoskeletons coupled with FES, also called neuroprostheses or hybrid exoskeletons, can facilitate continuous, repetitive motion to improve gait function and build muscle capacity. The human-robot interaction during rehabilitative cycling and walking yield a mix of discrete effects (i.e., foot impact, input switching to engage lower-limb muscles and electric motors, etc.) and continuous nonlinear, uncertain, time-varying dynamics. Switching control is necessary to allocate the control inputs to lower-limb muscle groups and electric motors involved during assisted cycling and walking. Kinematic tracking has been the primary control objective for devices that combine FES and electric motors. However, there are force interactions between the machine and the human during cycling and walking that motivate the design of torque-based controllers (i.e., exploit torque or force feedback) to shape the leg dynamics through controlling joint kinematics and kinetics. Technical challenges exist to develop closed-loop feedback control strategies that integrate kinematic and force feedback in the presence of switching and discontinuous effects. The motivation in this dissertation is to design, analyze and implement switching controllers for assisted cycling and walking leveraging kinematic and force feedback while guaranteeing the stability of the human-robot closed-loop system. In Chapter 1, the motivation to design closed-loop controllers for motorized FES-cycling and powered exoskeletons is described. A survey of closed-loop kinematic and force feedback control methods is also introduced related to the tracking objectives presented in the subsequent chapters of the dissertation. In Chapter 2, the dynamics models for walking and assisted cycling are described. First, a bipedal walking system model with switched dynamics is introduced to control a powered lower-limb exoskeleton. Then, a stationary FES-cycling model with nonlinear dynamics and switched control inputs is introduced based on published literature. The muscle stimulation pattern is defined based on the kinematic effectiveness of the rider, which depends on the crank angle. The experimental setup for lower-limb exoskeleton and FES-cycling are described. In Chapter 3, a hierarchical control strategy is developed to interface a cable-driven lower-limb exoskeleton. A two-layer control system is developed to adjust cable tensions and apply torque about the knee joint using a pair of electric motors that provide knee flexion and extension. The control design is segregated into a joint-level control loop and a low-level loop using feedback of the angular positions of the electric motors to mitigate cable slacking. A Lyapunov-based stability analysis is developed to ensure exponential tracking for both control objectives. Moreover, an average dwell time analysis computes an upper bound on the number of motor switches to preserve exponential tracking. Preliminary experimental results in an able-bodied individual are depicted. The developed control strategy is extended and applied to the control of both knee and hip joints in Chapter 4 for treadmill walking. In Chapter 4, a cable-driven lower-limb exoskeleton is integrated with FES for treadmill walking at a constant speed. A nonlinear robust controller is used to activate the quadriceps and hamstrings muscle groups via FES to achieve kinematic tracking about the knee joint. Moreover, electric motors adjust the knee joint stiffness throughout the gait cycle using an integral torque feedback controller. A Lyapunov-based stability analysis is developed to ensure exponential tracking of the kinematic and torque closed-loop error systems, while guaranteeing that the control input signals remain bounded. The developed controllers were tested in real-time walking experiments on a treadmill in three able-bodied individuals at two gait speeds. The experimental results demonstrate the feasibility of coupling a cable-driven exoskeleton with FES for treadmill walking using a switching-based control strategy and exploiting both kinematic and force feedback. In Chapter 5, input-output data is exploited using a finite-time algorithm to estimate the target desired torque leveraging an estimate of the active torque produced by muscles via FES. The convergence rate of the finite-time algorithm can be adjusted by tuning selectable parameters. To achieve cadence and torque tracking for FES-cycling, nonlinear robust tracking controllers are designed for muscles and motor. A Lyapunov-based stability analysis is developed to ensure exponential tracking of the closed-loop cadence error system and global uniformly ultimate bounded (GUUB) torque tracking. A discrete-time Lyapunov-based stability analysis leveraging a recent tool for finite-time systems is developed to ensure convergence and guarantee that the finite-time algorithm is Holder continuous. The developed tracking controllers for the muscles and electric motor and finite-time algorithm to compute the desired torque are implemented in real-time during cycling experiments in seven able-bodied individuals. Multiple cycling trials are implemented with different gain parameters of the finite-time torque algorithm to compare tracking performance for all participants. Chapter 6 highlights the contributions of the developed control methods and provides recommendations for future research extensions

Modeling and Control of Robot-Structure Coupling During In-Space Structure Assembly

This paper considers the problem of robot-structure coupling dynamics during in-space robotic assembly of large flexible structures. A two-legged walking robot is used as a construction agent, whose primary goal is to stably walking on the flexible structure while carrying a substructure component to a designated location. The reaction forces inserted by the structure to the walking robot are treated as bounded disturbance inputs, and a trajectory tracking robotic controller is proposed that combines the standard full state feedback motion controller and an adaptive controller to account for the disturbance inputs. In this study, a reduced-order Euler-Bernoulli beam structure model is adapted, and a finite number of co-located sensors and actuators are distributed along the span of the beam structure. The robot-structure coupling forces are treated as a bounded external forcing function to the structure, and hence an output covariance constraint problem can be formulated, in terms of linear matrix inequality, for optimal structure control by utilizing the direct output feedback controllers. The numerical simulations show the effectiveness of the proposed robot-structure modeling and control methodology

Multi-Input Multi-Output Repetitive Control Theory And Taylor Series Based Repetitive Control Design

Repetitive control (RC) systems aim to achieve zero tracking error when tracking a periodic command, or when tracking a constant command in the presence of a periodic disturbance, or both a periodic command and periodic disturbance. This dissertation presents a new approach using Taylor Series Expansion of the inverse system z-transfer function model to design Finite Impulse Response (FIR) repetitive controllers for single-input single-output (SISO) systems, and compares the designs obtained to those generated by optimization in the frequency domain. This approach is very simple, straightforward, and easy to use. It also supplies considerable insight, and gives understanding of the cause of the patterns for zero locations in the optimization based design. The approach forms a different and effective time domain design method, and it can also be used to guide the choice of parameters in performing in the frequency domain optimization design. Next, this dissertation presents the theoretical foundation for frequency based optimization design of repetitive control design for multi-input multi-output (MIMO) systems. A comprehensive stability theory for MIMO repetitive control is developed. A necessary and sufficient condition for asymptotic stability in MIMO RC is derived, and four sufficient conditions are created. One of these is the MIMO version of the approximate monotonic decay condition in SISO RC, and one is a necessary and sufficient condition for stability for all possible disturbance periods. An appropriate optimization criterion for direct MIMO is presented based on minimizing a Frobenius norm summed over frequencies from zero to Nyquist. This design process is very tractable, requiring only solution of a linear algebraic equation. An alternative approach reduces the problem to a set of SISO design problems, one for each input-output pair. The performances of the resulting designs are studied by extensive examples. Both approaches are seen to be able to create RC designs with fast monotonic decay of the tracking error. Finally, this dissertation presents an analysis of using an experiment design sequence for parameter identification based on the theory of iterative learning control (ILC), a sister field to repetitive control. This is suggested as an alternative to the results in optimal experiment design. Modified ILC laws that are intentionally non-robust to model errors are developed, as a way to fine tune the use of ILC for identification purposes. The non-robustness with respect to its ability to improve identification of system parameters when the model error is correct is studied. It is demonstrated that in many cases the approach makes the learning particularly sensitive to relatively small parameter errors in the model, but sensitivity is sometimes limited to parameter errors of a specific sign

Repetitive Control Systems: Stability and Periodic Tracking beyond the Linear Case

Periodic output regulation studies the problem of steering the output of a dynamical system along a periodic reference. This is a fundamental control problem which has a great interest from a practical point of view, since most industrial activities oriented to production are based on tasks with a cyclic nature. Nevertheless this interest extends rapidly to a theoretical framework once the problem is formalized. Mathematical tools coming from different fields can be used to provide an insight to the output regulation problem in different ways. An important control technique that is classically used to achieve periodic out- put regulation si called Repetitive Control (RC) and this thesis focuses on (but is not limited to) the development and the analysis with novel tools of RC schemes. Periodic output regulation for nonlinear dynamical systems is a challenging topic. This thesis, besides of providing consistent and practically useful results in the linear case, introduces promising tools dealing with the nonlinear periodic output regulation problem, whose solution is presented for particular classes of systems. The contribution of this research is mainly theoretical and relies on the use of mathematical tools like infinite-dimensional port-Hamiltonian systems and autonomous discrete-time systems to study stability and tracking properties in RC schemes and periodic regulation in general. Differently from the classical continuous-time formulation of RC, internal model arguments are not directly used is this work to study asymptotic tracking. In this way the linear case can be reinterpreted under a new light and novel strategies to consistently attack the nonlinear case are presented. Furthermore an application-oriented chapter with experimental results is present which describes the possibility of implementing a discrete-time RC scheme involving trajectory generation and non-minimum phase systems