Modelling and Design of State Estimator for a Pick and Place Robotic Arm

A robust model is essential for the design of system components such as controllers, observers state estimators, and simulators. State estimators are becoming increasingly important in modern systems, especially systems with states that may not be measured with sensors. Therefore, it is imperative to analyze the performance of different modelling and state estimator design techniques. In this research work, a parametric model of a pick and place robotic arm was obtained using system identification technique. Pick and place robotic arms have a lot of industrial applications. The parameters of the obtained model were determined using the general second-order characteristics equation and manual tuning. Furthermore, five state estimators were designed based on the developed model. The accuracy of the model, and the performance of the observers were analyzed. The model was found to provide a good representation of the system. Nonetheless, with very small divergence between the model and the real system. The performance of the observers was found to be dependent on their pole locations; the higher the magnitude of the poles, the higher the state estimators’ gain and the better the estimation provided. It was found out that the state estimators with high gains were more susceptible to measurement noise. Keywords— Modelling, pick and place robots, observers, and state estimators.

Recursive State and Parameter Estimation of COVID-19 Circulating Variants Dynamics

COVID-19 pandemic response with non-pharmaceutical interventions is an intrinsic control problem. Governments balance social distancing policies to avoid overload on health system without major economic impact. A control strategy requires reliable predictions to be efficient on long-term. SARS-CoV-2 mutability, vaccination coverage and time-varying restrictive measures change virus evolution dynamics frequently. State and parameter estimations are an option do deal with these uncertainties. In this paper, a SIR-based model is proposed considering data available and feedback corrections over time. State and parameter estimations were done on state estimators with augmented states. Three observers were implemented: Constrained Extended Kalman Filter (CEKF), CEKF and Smoother (CEKF&S) and Moving Horizon Estimator (MHE). The parameters estimated therein are based on vaccine efficacy studies regarding transmissibility, severeness of disease and lethality. Social distancing is a measured disturbance calculated with Google mobility data. Six federative units from Brazil are used to evaluate proposed strategy: Amazonas, Mato Grosso do Sul, Rio Grande do Norte, Rio Grande do Sul, Rio de Janeiro and São Paulo. State and parameter estimations were realized from October 1 st 2020 to July 1 st 2021 during which Zeta and Gamma variants emerged. Results showed an efficient detection of circulating variants from proposed parameter estimation. In addition, it asserted dynamics related to virus mutations. Zeta mutations increase lethality between 19 and 45%, and increased transmissibility between 20 and 38%. Gamma mutations, on the other hand, increased lethality between 62 and 110% while increasing transmissibility between 52 and 107%. Furthermore, parameter estimation indicated existence and temporal change of subnotification on hospitalized and deceased individuals. Overall, dynamics estimated were within expectations and are applicable to control theory.

Analysis and Prediction of Electric Power System’s Stability Based on Virtual State Estimators

The stability of bilinear systems is investigated using spectral techniques such as selective modal analysis. Predictive models of bilinear systems based on inductive knowledge extracted by big data mining techniques are applied with associative search of statistical patterns. A method and an algorithm for the elementwise solution of the generalized matrix Lyapunov equation are developed for discrete bilinear systems. The method is based on calculating the sequence of values of a fixed element of the solution matrix, which depends on the product of the eigenvalues of the dynamics matrix of the linear part and the elements of the nonlinearity matrixes. A sufficient condition for the convergence of all sequences is obtained, which is also a BIBO (bounded input bounded output) systems stability condition for the bilinear system.

Multibody-Based Input and State Observers Using Adaptive Extended Kalman Filter

The aim of this work is to explore the suitability of adaptive methods for state estimators based on multibody dynamics, which present severe non-linearities. The performance of a Kalman filter relies on the knowledge of the noise covariance matrices, which are difficult to obtain. This challenge can be overcome by the use of adaptive techniques. Based on an error-extended Kalman filter with force estimation (errorEKF-FE), the adaptive method known as maximum likelihood is adjusted to fulfill the multibody requirements. This new filter is called adaptive error-extended Kalman filter (AerrorEKF-FE). In order to present a general approach, the method is tested on two different mechanisms in a simulation environment. In addition, different sensor configurations are also studied. Results show that, in spite of the maneuver conditions and initial statistics, the AerrorEKF-FE provides estimations with accuracy and robustness. The AerrorEKF-FE proves that adaptive techniques can be applied to multibody-based state estimators, increasing, therefore, their fields of application.

Set-membership state estimators based on cooperative output injections

To estimate validated bounds on the actual state vector of uncertain non-linear systems, cooperative output injections methods are proposed in this contribution. The aim of the output injections is to design set-membership state estimators that ensure the order-preserving property between the lower, actual and upper state trajectories. Based on a special sensors placement, continuous-time and event-triggered output injections are proposed to cope with the conservatism of the classical bounding system methods. Furthermore, based on some properties of monotone dynamical systems, the convergence of the proposed set-membership state estimators is shown. It is worth pointing out that the proposed set-membership state estimation method allows one: on one hand, to avoid the conservatism related to the use of similarity transformations usually required in the framework of interval observer design approaches, and on the other hand, to circumvent the pessimism accumulation related to the wrapping effect of set-valued iterative numerical schemes.