Additive-Decomposition-Based Output Feedback Tracking Control for Systems with Measurable Nonlinearities and Unknown Disturbances

In this paper, a new control scheme, called as additive-decomposition-based tracking control, is proposed to solve the output feedback tracking problem for a class of systems with measurable nonlinearities and unknown disturbances. By the additive decomposition, the output feedback tracking task for the considered nonlinear system is decomposed into three independent subtasks: a pure tracking subtask for a linear time invariant (LTI) system, a pure rejection subtask for another LTI system and a stabilization subtask for a nonlinear system. By benefiting from the decomposition, the proposed additive-decomposition-based tracking control scheme i) can give a potential way to avoid conflict among tracking performance, rejection performance and robustness, and ii) can mix both design in time domain and frequency domain for one controller design. To demonstrate the effectiveness, the output feedback tracking problem for a single-link robot arm subject to a sinusoidal or a general disturbance is solved respectively, where the transfer function method for tracking and rejection and backstepping method for stabilization are applied together to the design.Comment: 23 pages, 6 figure

Improved Transients in Multiple Frequencies Estimation via Dynamic Regressor Extension and Mixing

A problem of performance enhancement for multiple frequencies estimation is studied. First, we consider a basic gradient-based estimation approach with global exponential convergence. Next, we apply dynamic regressor extension and mixing technique to improve transient performance of the basic approach and ensure non-strict monotonicity of estimation errors. Simulation results illustrate benefits of the proposed solution.Comment: This paper is submitted for the ALCOSP 2016 conferenc

A parallel prefiltering approach for the identification of a biased sinusoidal signal: theory and experiments

The problem of estimating the amplitude, frequency, and phase of an unknown sinusoidal signal from a noisy-biased measurement is addressed in this paper by a family of parallel prefiltering schemes. The proposed methodology consists in using a pair of linear filters of specified order to generate a suitable number of auxiliary signals that are used to estimate\u2014in an adaptive way\u2014the frequency, the amplitude, and the phase of the sinusoid. Increasing the order of the prefilters improves the noise immunity of the estimator, at the cost of an increase of the computational complexity. Among the whole family of estimators realizable by varying the order of the filters, the simple parallel prefilters of orders 2 C 2 and 3 C 3 are discussed in detail, being the most attractive from the implementability point of view. The behavior of the two algorithms with respect to bounded external disturbances is characterized by input-to-state stability arguments. Finally, the effectiveness of the proposed technique is shown both by comparative numerical simulations and by a real experiment addressing the estimation of the frequency of the electrical mains from a noisy voltage measurement

Adaptive rejection of finite band disturbances - theory and applications

Le chapitre présente les techniques de rejection adpative de perturbation inconnue mais de bande finie. Plusieurs exemples sont mentionnés et l'application au rejet adaptatifs de perturbation inconnues sur une suspension active est décrite en détailThe techniques for adaptive rejection of unknown finite band disturbances are reviewed. Several applications are mentionned and the application to the adaptive rejection of unknown disturbances on an active suspension is presented in detail

An Adaptive Periodic-Disturbance Observer for Periodic-Disturbance Suppression

Repetitive operations are widely conducted by automatic machines in industry. Periodic disturbances induced by the repetitive operations must be compensated to achieve precise functioning. In this paper, a periodic-disturbance observer (PDOB) based on the disturbance observer (DOB) structure is proposed. The PDOB compensates a periodic disturbance including the fundamental wave and harmonics by using a time delay element. Furthermore, an adaptive PDOB is proposed for the compensation of frequency-varying periodic disturbances. An adaptive notch filter (ANF) is used in the adaptive PDOB to estimate the fundamental frequency of the periodic disturbance. Simulations compare the proposed methods with a repetitive controller (RC) and the DOB. Practical performances are validated in experiments using a multi-axis manipulator. The proposal provides a new framework based on the DOB structure to design controllers using a time delay element.Comment: 11 pages, 22 figures, journa

Nonlinear adaptive estimation with application to sinusoidal identification

Parameter estimation of a sinusoidal signal in real-time is encountered in applications in numerous areas of engineering. Parameters of interest are usually amplitude, frequency and phase wherein frequency tracking is the fundamental task in sinusoidal estimation. This thesis deals with the problem of identifying a signal that comprises n (n ≥ 1) harmonics from a measurement possibly affected by structured and unstructured disturbances. The structured perturbations are modeled as a time-polynomial so as to represent, for example, bias and drift phenomena typically present in applications, whereas the unstructured disturbances are characterized as bounded perturbation. Several approaches upon different theoretical tools are presented in this thesis, and classified into two main categories: asymptotic and non-asymptotic methodologies, depending on the qualitative characteristics of the convergence behavior over time. The first part of the thesis is devoted to the asymptotic estimators, which typically consist in a pre-filtering module for generating a number of auxiliary signals, independent of the structured perturbations. These auxiliary signals can be used either directly or indirectly to estimate—in an adaptive way—the frequency, the amplitude and the phase of the sinusoidal signals. More specifically, the direct approach is based on a simple gradient method, which ensures Input-to-State Stability of the estimation error with respect to the bounded-unstructured disturbances. The indirect method exploits a specific adaptive observer scheme equipped with a switching criterion allowing to properly address in a stable way the poor excitation scenarios. It is shown that the adaptive observer method can be applied for estimating multi-frequencies through an augmented but unified framework, which is a crucial advantage with respect to direct approaches. The estimators’ stability properties are also analyzed by Input-to-State-Stability (ISS) arguments. In the second part we present a non-asymptotic estimation methodology characterized by a distinctive feature that permits finite-time convergence of the estimates. Resorting to the Volterra integral operators with suitably designed kernels, the measured signal is processed, yielding a set of auxiliary signals, in which the influence of the unknown initial conditions is annihilated. A sliding mode-based adaptation law, fed by the aforementioned auxiliary signals, is proposed for deadbeat estimation of the frequency and amplitude, which are dealt with in a step-by-step manner. The worst case behavior of the proposed algorithm in the presence of bounded perturbation is studied by ISS tools. The practical characteristics of all estimation techniques are evaluated and compared with other existing techniques by extensive simulations and experimental trials.Open Acces

ADAPTIVE ROBUST DISTURBANCE COMPENSATION IN LINEAR SYSTEMS WITH DELAY

Subject of Research. The paper considers the problem of disturbance compensation for the class of linear time-invariant plants with known parameters and delay.Method. The disturbance is presented as a sum of irregular and regular components. An irregular component is treated as an unknown bounded time function. A regular component is described as unmeasurable output of linear autonomous model (exosystem) with known order and unknown parameters. The problem is resolved with the use of parametrized representation of disturbance designed by means of exosystem state observer and predictor of this state that finally allows applying certainty equivalence principle. In order to remove undesirable influence of delay, a modified adaptation algorithm is created. The algorithm is based on augmentation of the plant state vector and generates advanced adjustable parameters for control. Robust modification of adaptive algorithm is used for keeping stability of closed-loop system in the presence of irregular disturbance. As distinct from widespread approaches the proposed algorithm does not require identification of disturbance parameters and gives the possibility to discard from the control system such restrictions as adaptation gain margin and time delay margin. Main Results. Simulation results obtained in MATLAB/Simulink environment are presented to demonstrate the performance of the proposed approach. The results illustrate the boundedness of all signals in the closed-loop system in the presence of external disturbance. It is shown that the proposed idea enables keeping system stability for different values of input delay. Practical Relevance. Thealgorithm of adaptive compensation is recommended for application in such problems as: the problem of control for active vibration protection devices wherein several dominating harmonics can be taken from the spectrum of vibration signal, control problems of robotic systems with periodical behavior, the problems of ship roll compensation, control problems of space plants in the presence of uncontrollable rotation

Frequency Estimation for Periodical Signal with Noise in Finite Time

International audienceThe frequency estimation technique with guaranteed finite time of convergence to a given accuracy of identification is presented. The approach for a high frequency noise rejection is proposed. The possibility of switching algorithm introduction for estimation quality improvement is discussed. The proposed solution has order three, that is smaller than in other existent solutions. Efficiency of the approach is demonstrated on examples of computer simulation

ALGORITHM OF MULTIHARMONIC DISTURBANCE COMPENSATION IN LINEAR SYSTEMS WITH ARBITRARY DELAY: INTERNAL MODEL APPROACH

Subject of Research. The problem of multiharmonic disturbance compensation for the class of linear time-invariant plants with known parameters and delay is considered. Method. The disturbance is presented as unmeasurable output of linear autonomous model (exosystem) with known order and unknown parameters. The problem is resolved with the use of parametrized representation of disturbance designed by means of exosystem state observer and predictor of this state that finally enables applying certainty equivalence principle. In order to remove undesirable influence of delay a modified adaptation algorithm is created. The algorithm is based on augmentation of the plant state vector and generates advanced adjustable parameters for control. As distinct from widespread approaches, the proposed algorithm does not require identification of disturbance parameters and gives the possibility to remove such restrictions as adaptation gain margin and time delay margin. Main Results. Simulation results obtained in MATLAB/Simulink environment are presented to demonstrate the performance of proposed approach. Results illustrate the boundness of all signals in the closed-loop system and complete compensation of harmonic signal. It is shown that the proposed idea makes it possible to increase the adaptation gain for different delays without system stability loss. Practical Relevance. The algorithm of adaptive compensation is recommended for the use in such problems as: the problem of control for active vibration protection devices wherein several dominating harmonics can be taken from the spectrum of vibration signal; the problems of control of robotics systems with periodical behavior; the problems of ship roll compensation; the problems of space plants control in the presence of uncontrollable rotation

Controlling rigid formations of mobile agents under inconsistent measurements

Despite the great success of using gradient-based controllers to stabilize rigid formations of autonomous agents in the past years, surprising yet intriguing undesirable collective motions have been reported recently when inconsistent measurements are used in the agents' local controllers. To make the existing gradient control robust against such measurement inconsistency, we exploit local estimators following the well known internal model principle for robust output regulation control. The new estimator-based gradient control is still distributed in nature and can be constructed systematically even when the number of agents in a rigid formation grows. We prove rigorously that the proposed control is able to guarantee exponential convergence and then demonstrate through robotic experiments and computer simulations that the reported inconsistency-induced orbits of collective movements are effectively eliminated.Comment: 10 page