A globally exponentially stable speed observer for a class of mechanical systems: experimental and simulation comparison with high-gain and sliding mode designs

Abstract

It is shown in the paper that the problem of speed observation for mechanical systems that are partially linearisable via coordinate changes admits a very simple and robust (exponentially stable) solution with a Luenberger-like observer. This result should be contrasted with the very complicated observers based on immersion and invariance reported in the literature. A second contribution of the paper is to compare, via realistic simulations and highly detailed experiments, the performance of the proposed observer with well-known high-gain and sliding mode observers. In particular, to show that-due to their high sensitivity to noise, that is unavoidable in mechanical systems applications-the performance of the two latter designs is well below par.

Bias Propagation and Estimation in Homogeneous Differentiators for a Class of Mechanical Systems

“…The drawback of this approach is that it is based on the linearization of the system, and therefore it is not valid when the angle θ is not close to the desired position and the approximation sin(θ) ≈ θ does not hold. This drawback can be alleviated using linear observers with time-varying gains, e.g., with gains scheduling, or using nonlinear state observers for mechanical systems, see [10] and the references therein. However, such solutions are typically harder to design and implement.…”

“…It can be shown that the control law (8) with the finite-time observers (10) and (12) locally stabilizes the system (1). Indeed, for the observers (10) and (12) there exists the common settling time T com = T (e p (0), e r (0)), such that the control laws (5) and 8are equivalent for t ≥ T com . Since the control law (5) is stabilizing for the linearized system (4), it is locally stabilizing for the nonlinear system (1) in a neighborhood of the desired equilibrium; define this neighborhood as α .…”

“…Using y as a measurement of θ in (10) and noting that θ − y = e p,1 − d, the error dynamics (11) takes the forṁ…”

“…For nonlinear systems, state estimation can be performed based on linearization (or linear time-varying representation) of the system dynamics yielding a standard linear observer, e.g., Kalman-Bucy filter, or a nonlinear observer can be proposed [8]; for discrete-time nonlinear systems, a Newton observer can be utilized, see, e.g., [9]. Notably, an exponential nonlinear velocity observer for a class of mechanical systems has been recently proposed in [10]. The drawback of the full-state observer design is that it typically requires an accurate model and estimates the coupled state vector of the whole system, which is not reasonable in the considered robotic design with multiple degrees of freedom.…”

Feedback Control with Equilibrium Revision for CMG-Actuated Inverted Pendulum

“…The CMG for inverted pendulum balancing has been intensively studied in recent years. In work [6] there was suggested a global change of coordinates to transform the dynamics of the system into a lower nonlinear subsystem and stabilize the system with a control Lyapunov function. Another research [7] was devoted to creation of a model predictive controller (MPC) to control such a system.…”