Follow the bouncing ball: global results on tracking and state estimation with impacts

peer reviewedIn this paper we formulate tracking and state- estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous trajectories arising from the impacts, we use hybrid systems stability analysis tools to establish the results. Using a novel concept of mirrored images of the target mass we prove that 1) a tracking control algorithm, and 2) an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards, including rectangles. Moreover, we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking. The results are illustrated via simulations

State observer with Round-Robin aperiodic sampled measurements with jitter

A sampled-data observer is proposed for linear continuous-time systems whose outputs are sequentially sampled via non-uniform sampling intervals repeating a prescribed Round-Robin sequence. With constant sampling intervals (jitter-free case) we provide constructive necessary and sufficient conditions for the design of an asymptotic continuous–discrete observer whose estimation error is input-to-state stable (ISS) from process disturbances and measurement noise. We use a time-varying gain depending on the elapsed time since the last measurement. With non-constant sampling intervals (jitter-tolerant case), our design conditions are only sufficient. A suspension system example shows the effectiveness of the proposed approach

An almost Anti-Windup scheme for plants with magnitude, rate and curvature saturation

peer reviewedWe address the anti-windup augmentation problem for plants with saturations on the magnitude, rate and curvature of the control input. To this aim, given an unconstrained closed-loop, we generate a slightly modified strictly proper controller for which the derivatives of the control signal are available and we solve the anti-windup problem for this modified control scheme (namely, an almost anti-windup for the original closed-loop). Based on this “almost” approach, we revisit an existing Model Recovery anti-windup solution for rate and magnitude saturated plants and then we extend the results to the case of rate, magnitude and curvature saturation, by providing a Model Recovery solution to this additional problem. An example illustrates the peculiarities and the effectiveness of the proposed solutions

Unsafe Point Avoidance in Linear State Feedback

International audienceWe propose a hybrid solution for the stabilization of the origin of a linear time-invariant stabilizable system with the property that a suitable neighborhood of a pre-defined unsafe point in the state space is avoided by the closed-loop solutions. Hybrid tools are motivated by the fact that the task at hand cannot be solved with continuous feedback, whereas the proposed hybrid solution induces nominal and robust asymptotic stability of the origin. More specifically, we formulate a semiglobal version of the problem at hand and describe a fully constructive approach under the assumption that the unsafe point to be avoided does not belong to the equilibrium subspace induced by the control input on the linear dynamics. The approach is illustrated on a numerical exampl

Enhanced Bounded Integral Control of Input-to-State Stable Nonlinear Systems

The bounded integral controller (BIC) was recently proposed to replace the traditional integral controller (IC) for the regulation of any input-to-state stable (ISS) nonlinear system and guarantee closed-loop system stability with a bounded control output. In this paper, an enhanced version of the BIC is presented to provide a better approximation of the traditional IC in the entire bounded range of the control output and relax the assumption on the selection of the initial conditions of the original BIC. Using Lyapunov methods, it is analytically proven that the enhanced BIC maintains the zero-gain property and guarantees closed-loop stability of any nonlinear ISS plant with a given bound at the control output, without suffering from integrator windup issues. The plant dynamics and structure can be unkown as long as the plant is ISS. Hence, the proposed enhanced version of the BIC can replace the traditional IC in many applications where closed-loop stability cannot be proven, without changing the controller operation. A practical example is simulated to verify the performance of the proposed enhanced BIC compared to the original version and the traditional IC

A hybrid observer for localization from noisy inertial data and sporadic position measurements

We propose an asymptotic position and speed observer for inertial navigation in the case where the position measurements are sporadic and affected by noise. We cast the problem in a hybrid dynamics framework where the continuous motion is affected by unknown continuous-time disturbances and the sporadic position measurements are affected by discrete-time noise. We show that the peculiar hybrid cascaded structure describing the estimation error dynamics is globally finite-gain exponentially ISS with gains depending intuitively on our tuning parameters. Experimental results, as well as the comparison with an Extended Kalman Filter (EKF), confirm the effectiveness of the proposed solution with an execution time two orders of magnitude faster and with a simplified observer tuning because our bounds are an explicit function of the observer tuning knob

Localization from inertial data and sporadic position measurements

A novel estimation strategy for inertial navigation in indoor/outdoor environments is proposed with a specific attention to the sporadic nature of the non-periodic measurements. After introducing the inertial navigation model, we introduce an observer providing an asymptotic estimate of the plant state. We use a hybrid dynamical systems representation for our results, in order to provide an effective, and elegant theoretical framework. The estimation error dynamics with the proposed observer shows a peculiar cascaded interconnection of three subsystems (allowing for intuitive gain tuning), with perturbations occurring either on the jump or on the flow dynamics (depending on the specific subsystem under consideration). For this structure, we show global exponential stability of the error dynamics. Hardware-in-the-loop results confirm the effectiveness of the proposed solution

Appendix to "Torque setpoint tracking for parallel hybrid electric vehicles using dynamic input allocation", published on IEEE Transactions on Control Systems Technology

A dynamic allocator is proposed in order to generalize a previously introduced strategy for input redundant plants, which applies to linear plants with multiple and redundant inputs. The theory is extended here to the case of multiple linear actuators, each of them with its own dynamics, acting on a nonlinear plant with strong input redundancy. In the HEV case the two redundant inputs are the ICE and EM torques and the two actuators with different dynamics are the two propulsion systems