Unknown Periodic Disturbances Research Articles

Iterative-learning-based tracking control of a two-wheeled mobile robot with model uncertainties and unknown periodic disturbances

In this paper, we develop an adaptive iterative learning approach to investigate the trajectory tracking control issue for a class of two-wheeled mobile robots subject to model uncertainties and unknown disturbances. First, we derive the nonlinear velocity error dynamics. Then a parameterization-based adaptive iterative learning control scheme is adopted to achieve precise tracking, along with logic-based update law for the estimated period and bound of the disturbance. Moreover, the boundness of all the closed-loop signals is rigorously analyzed based on the Lyapunov stability theory to provide the theoretical foundation for the proposed method. The experimental results show the efficacy and viability of our results.

Neural networks-based adaptive tracking control for full-state constrained switched nonlinear systems with periodic disturbances and actuator saturation

In this paper, an adaptive tracking control approach is developed for full-state constrained switched nonlinear systems that have actuator saturation, periodic disturbances and unknown control direction. To deal with the full-state constraints, the Barrier Lyapunov functions are introduced to limit the state variables within the corresponding constraint conditions. Meanwhile, the Fourier series expansion technology is employed to deal with unknown periodic disturbances and unknown nonlinear dynamics jointly. Additionally, a Nussbaum-type function is used in the controller design to cope with the and unknown control gain and input saturation. On the basis of the Lyapunov stability theory, it is demonstrated rigorously that all signals of the closed-loop system are uniformly ultimately bounded, and the proposed controller ensures that the tracking error is kept within a compact set close to zero. In the end, the validity of the designed control protocol is verified by a simulation example.

An infinite-order integral disturbance observer for improved estimation of periodic disturbances in motion control systems

ABSTRACT In this paper, a disturbance observer is devised for motion control systems suffering unknown periodic disturbances. In the proposed scheme, the structure of a so-called integral disturbance observer is utilized for its error-feedback form, and the repetitive learning control theory is applied to the observer design, constituting an infinite-order integral disturbance observer to obtain an enhanced estimation of a periodic disturbance. A comparative study of different disturbance observers is performed, and experimental results are reported, practically showing the effectiveness of the proposed scheme.

Partial source separation from unknown correlation mixture for eliminating unknown periodic disturbances from random measured signals

Separating and eliminating periodic disturbances from measured signals are a key problem to obtain original responses used for further system identification and evaluation. Actual periodic disturbances are partial unknown sources in measured signals and have certain correlation with random noise sources in time domain. In this paper, a separation problem on partial unknown sources such as periodic sources correlated with random noises is introduced. A partial unknown source separation technique is proposed by combining signal eigenspace transformation, covariance joint diagonalization and decorrelation of correlation sources. The partial source separation procedure has two main stages: obtain uncorrelated sources by eigenspace transformation and joint diagonalization; and obtain partial periodic sources correlated with random noises from the uncorrelated sources by decorrelation. The proposed partial source separation technique is supported by several theorems. Under given assumptions, the separation technique will result in accurate partial sources. The separation technique has main features such as partial unknown sources separated from measured signals, separated periodic sources correlated with random noise sources, and being suitable for dominant random noises and non-dominant periodic disturbance sources in measured signals. Numerical results are presented to illustrate the effectiveness of the separation technique.

Supervised Output Regulation via Iterative Learning Control for Rejecting Unknown Periodic Disturbances

The internal model principle (IMC) in linear robust output regulation theory states that a dynamical controller needs to incorporate a copy of the model generating the periodic signals in order to achieve perfect rejection/tracking, robustly with respect to plant’s parameters. On the other hand Iterative Learning Control (ILC) is a data-based approach which not requires any a priori knowledge, and can be used to find the required control action for attenuating periodic disturbances or tracking periodic references. The control signal generated by ILC includes the frequency and amplitude information of the disturbance and can be used to build the internal model needed for a linear output regulator problem. The objective of this work is therefore that of trying to combine the two approaches, that is IMC and ILC, in order to retain the advantages of each methodology. The proposed methodology, denoted as Supervised Output Regulation via Iterative Learning Control (SOR-ILC), allows to address the problem of output regulation in presence of unknown frequencies. The performances of SOR-ILC are validated through numerical simulations in case of complex periodic disturbances and parameter uncertainties.

A refined disturbance rejection control for vibration suppression of smart structures under unknown disturbances

Vibrations are usually caused by continuous disturbances with large amplitudes. Different from other control methods, disturbance rejection control is a potential method, which considers the unknown disturbances in the control design. To remedy the shortcomings of the existing disturbance rejection control in the vibration reduction of structures especially under high-frequency periodic disturbances, this paper aims to improve the control ability of the current disturbance rejection control for the vibration suppression of smart structures under any unknown periodic disturbances with high-order frequency or random disturbances varying fast. Afterwards, the refined disturbance rejection control is compared with the previously designed disturbance rejection control with proportional–integral observer and disturbance rejection control with generalized proportional–integral observer on both theoretical and numerical levels.

Subspace identification of Hammerstein-type nonlinear systems subject to unknown periodic disturbance

In this paper, a subspace identification method is proposed for Hammerstein-type nonlinear systems subject to periodic disturbances with unknown waveforms. By separating the periodic disturbance response from the deterministic system response using the superposition principle, an orthogonal projection is established to eliminate the disturbance influence, while an instrumental variable is introduced to eliminate the noise effect for consistent estimation. The overall disturbance period could be exactly estimated by minimising an objective function of output prediction error. A singular value decomposition algorithm is developed to simultaneously estimate the observability matrix and the triangular block-Toeplitz matrix. The system matrices are subsequently retrieved via a shift-invariant algorithm. Sufficient conditions for consistent estimation of the observability matrix and the triangular block-Toeplitz matrix are established with a proof. An illustrative example is presented to demonstrate the effectiveness and merit of the proposed identification method.

Nonlinear Systems With Uncertain Periodically Disturbed Control Gain Functions: Adaptive Fuzzy Control With Invariance Properties

This paper proposes a novel adaptive fuzzy dynamic surface control (DSC) method for an extended class of periodically disturbed strict-feedback nonlinear systems. The peculiarity of this extended class is that the control gain functions are not bounded a priori but simply taken to be continuous and with a known sign. In contrast with existing strategies, controllability must be guaranteed by constructing appropriate compact sets ensuring that all trajectories in the closed-loop system never leave these sets. We manage to do this by means of invariant set theory in combination with the Lyapunov theory. In other words, boundedness is achieved a posteriori as a result of stability analysis. The approximator composed of fuzzy logic systems and Fourier series expansion is constructed to deal with the unknown periodic disturbance terms.

Reference tracking control and attenuation of unknown periodic disturbances in the presence of noise for unknown minimum‐phase LTI plants

SummaryThe rejection of unknown periodic disturbances in the plant output through adaptive feedback has been an active area of research. In most successful efforts, it is assumed that the plant model is a known LTI stable system. In this paper, we relax the assumption of stable known plant and consider the case where the plant model can be unstable with unknown parameters. We do assume, however, that the plant model is minimum phase and use the model reference adaptive control structure to meet the objectives of reference tracking and unknown periodic disturbance rejection without amplifying the effect of broadband noises. The cost of achieving these objectives is the use of overparameterization that adds to the number of computations. The main contribution of this paper is that it shows that the problem of rejecting unknown periodic disturbances can be solved for unstable plants with unknown parameters as long as they are minimum phase. Numerical examples illustrate the effectiveness of the proposed control methodology.

Output feedback control for unknown LTI systems driven by unknown periodic disturbances

This paper considers unknown minimum-phase LTI systems with known relative degree and system order. The main aim is to reject the unknown, unmatched sinusoidal disturbances and make the output track a given trajectory with the output feedback. The essence of the control design is composed of disturbance parametrization, K-filter technique and adaptive backstepping procedure. Firstly, the unmeasured system states are represented in terms of filtered input and output signals. Then, the disturbance information in the output signal is parametrized and the problem is converted to an adaptive control problem. After that, the K-filter approach is employed to redefine the system states that enable to use a backstepping technique. An adaptive output feedback controller is designed recursively. It is proven that the equilibrium at the origin is globally uniformly stable and the output signal tracks the reference signal asymptotically. Finally, the effectiveness of the controller is illustrated with a numerical simulation. The robustness of the closed loop system with respect to an additive unmodelled noise is also discussed.

Active Unmatched Disturbance Cancellation and Estimation by State--Derivative Feedback for Plants Modeled as an LTI System

We design adaptive algorithms for both cancellation and estimation of unknown periodic disturbance, by feedback of state--derivatives ( i.e.,} without position information for mechanical systems) for the plants which are modeled as a linear time invariant system. We consider a series of unmatched unknown sinusoidal signals as the disturbance.The first step of the design consists of the parametrization of the disturbance model and the development of observer filters.The result obtained in this step allows us to use adaptive control techniques for the solution of the problem.In order to handle the unmatched condition, a backstepping technique is employed. Since the partial measurement of the virtual inputs is not available, we design a state observer and the estimates of these signals are used in the backstepping design.Finally, the stability of the equilibrium of the adaptive closed loop system with the convergence of states is proven.As a numerical example, a two-degree of freedom system is considered and the effectiveness of the algorithms are shown.

An acceleration-based hybrid learning-adaptive controller for robot manipulators

The robust periodic trajectory tracking problem is tackled by employing acceleration feedback in a hybrid learning-adaptive controller for n-rigid link robotic manipulators subject to parameter uncertainties and unknown periodic dynamics with a known period. Learning and adaptive feedforward terms are designed to compensate for periodic and aperiodic disturbances. The acceleration feedback is incorporated into both learning and adaptive controllers to provide higher stiffness to the system against unknown periodic disturbances and robustness to parameter uncertainties. A cascaded high gain observer is used to obtain reliable position, velocity and acceleration signals from noisy encoder measurements. A closed-loop stability proof is provided where it is shown that all system signals remain bounded and the proposed hybrid controller achieves global asymptotic position tracking. Results obtained from a high fidelity simulation model demonstrate the validity and effectiveness of the developed hybrid controller.

Identification of Linear Time‐Invariant Systems under Periodic Disturbance with Its Estimation

SUMMARYIn this paper, we propose a new method for identification of linear time‐invariant systems and estimation of unknown periodic disturbances. We assume that a disturbance to be considered here is unknown except its period. In this method, by stacking not only the unknown coefficients of a mathematical model but also the unknown disturbance as a parameter vector, we modify the equation error method so as to treat the unknown disturbance in the identification scheme. In particular, we also explain how the periodicity of the disturbance is utilized. In order to show the validity of this method, we give an illustrative numerical example.

Robust adaptive attenuation of unknown periodic disturbances in uncertain multi-input multi-output systems

In high-performance high-accuracy systems, the attenuation of vibrational disturbances is essential. In this paper, we design and analyze a robust output-feedback adaptive control scheme to attenuate noise-corrupted vibrational disturbances with unknown characteristics for multi-input multi-output linear time-invariant systems in the presence of plant unstructured modeling uncertainties. The conditions and the design parameters that contribute to the performance of the closed-loop system are investigated. The main ingredients of the proposed scheme include the use of a compensator to properly shape the singular values of the plant model, a robust adaptive law to handle unmodeled dynamics and output random noise, as well as an over-parametrization in the estimated parameters in order to provide flexibility for performance improvement. Analysis and simulations together with practical design considerations are presented to demonstrate the efficacy of the proposed scheme.

Rejection of unknown periodic disturbances for continuous‐time MIMO systems with dynamic uncertainties

SummaryRejection of unknown periodic disturbances in multi‐channel systems has several industrial applications that include aerospace, consumer electronics, and many other industries. This paper presents a design and analysis of an output‐feedback robust adaptive controller for multi‐input multi‐output continuous‐time systems in the presence of modeling errors and broadband output noise. The trade‐off between robust stability and performance improvement as well as practical design considerations for performance improvements are presented. It is demonstrated that proper shaping of the open‐loop plant singular values as well as over‐parameterizing the controller parametric model can significantly improve performance. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme. Copyright © 2016 John Wiley & Sons, Ltd.

Robustness and Performance of Adaptive Suppression of Unknown Periodic Disturbances

In recent years, a class of adaptive schemes has been developed for suppressing periodic disturbance signals with unknown frequencies, phases, and amplitudes. The stability and robustness of these schemes with respect to inevitable unmodeled dynamics and noise disturbances in the absence of persistently exciting signals has not been established despite successful simulation results and implementations. The purpose of this technical note is to propose a robust adaptive scheme for rejection of unknown periodic components of the disturbance and analyze its stability and performance properties. First, we consider the ideal case (non-adaptive) when complete information about the characteristics of the disturbance is available. We show that the rejection of periodic terms may lead to amplification of output noise and in some cases lead to a worse output performance. The way to avoid such undesirable noise amplification is to increase the size of the feedback control filter in order to have the flexibility to achieve rejection of the periodic disturbance terms while minimizing the effect of the noise on the output. The increased filter order leads to an over-parameterized scheme where persistence of excitation is no longer possible, and this shortcoming makes the use of robust adaptation essential. With this important insight in mind, the coefficients of the feedback filter whose size is over parameterized are adapted using a robust adaptive law. We show analytically that the proposed robust adaptive control scheme guarantees stability, performance and robustness with respect to unmodeled dynamics and bounded broadband noise disturbances. We use numerical simulations to demonstrate the results.

Fuzzy Approximation-Based Adaptive Backstepping Control of an Exoskeleton for Human Upper Limbs

This paper presents fuzzy approximation-based adaptive backstepping control of an exoskeleton for human upper limbs to provide forearm movement assistance so that a human forearm can track any continuous desired trajectory (or constant setpoint) in the presence of parametric/functional uncertainties, unmodeled dynamics, actuator dynamics, and/or disturbances from environments. Given the desired trajectories of human forearm positions, in the developed control, adaptive fuzzy approximators are used to estimate the dynamical uncertainties of the human–robot system, and an iterative learning scheme is utilized to compensate for unknown time-varying periodic disturbances. With the synthesis of the backstepping, iterative learning, and Lyapunov function approaches, the developed controller does not require exact knowledge of the exoskeleton model, and the close-loop system can be proven to be semiglobally uniformly bounded. Three comparison experiments are conducted to illustrate the effectiveness of the proposed control scheme by tracking periodic/repeated trajectories.

Robust disturbance rejection in modified repetitive control system

This study concerns disturbance rejection for a modified repetitive control system (MRCS) that contains a strictly proper plant with time-varying uncertainties. Since an MRCS is affected by both periodic and aperiodic disturbances, and since the disturbances are often unknown, an equivalent-input-disturbance (EID)-based estimator was added to an MRCS to yield an EID-based MRCS that compensates for all types of disturbances. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of an EID estimate into the control input enables rejection of unknown periodic and aperiodic disturbances. A robust stability condition for the MRCS was established in the form of a linear matrix inequality, and the condition was used to design the parameters of the controller. This design method handles uncertainties and enables the preferential adjustment of the tracking and control performance of the MRCS. Simulation results demonstrate the validity of the method.

Data-driven Controller Tuning for Attenuation of the Effect of Unknown Periodic Disturbance

In this paper, we provide a novel method of controller parameter tuning for attenuating the effect of unknown exogenous periodic disturbances. Our approach is based on the direct use of one-shot experimental data obtained in the actual closed loop. By utilizing such a data, we tune the off-line disturbance observer with a nominal model of a plant to achieve the desired closed loop property. We also illustrate a numerical example to show the validity of our proposed method.

Identification of Linear Time-Invariant Systems under Periodic Disturbance with its Estimation

In this paper, we propose a new method for identification of linear time-invariant systems and estimation of unknown periodic disturbances. We assume that a disturbance to be considered here is unknown except its period. In this method, by stacking not only the unknown coefficients of a mathematical model but also the unknown disturbance as a parameter vector, we modify the equation error method so as to treat the unknown disturbance in the identification scheme. In particular, we also explain how the periodicity of the disturbance is utilized. In order to show the validity of this method, we give an illustrative numerical example.