Systems control theory applied to natural and synthetic musical sounds

Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute

Design of Algebraic Observers for Brass Instruments

International audiencePhysical high-fidelity models of brass instruments are available in the literature, but controlling them to obtain a proper musical restitution is still a challenge. The inversion of the model from a unique observation, namely the sound produced by the instrument, is therefore a natural way to deal with this situation. The observer design problem consisting in an estimation of the vibro-acoustic state of the system is essential for that purpose. The observer design problem was addressed in [@AN10] for an elementary brass system using elastic player lips and straight pipe models. A neutral system representation of the system and Lyapunov methods were used ; a proof of the observer stability was obtained and simulations have demonstrated that the estimation method is robust in the presence of noisy measurements. However no adaptation to the noise power was performed, leading to a rate of convergence of the observer that was suboptimal. Moreover, as the observer dynamics was related to the uncoupled lips dynamics, the response could be slow and oscillatory. Using a representation of the same brass model as a delay-differential algebraic system [@B13], together with a sensitivity analysis and Kalman filter theory, we address these limitations through a new observer design resulting in a substantial improvement of the observer rate of convergence

Some remarks on wheeled autonomous vehicles and the evolution of their control design

Recent investigations on the longitudinal and lateral control of wheeled autonomous vehicles are reported. Flatness-based techniques are first introduced via a simplified model. It depends on some physical parameters, like cornering stiffness coefficients of the tires, friction coefficient of the road, ..., which are notoriously difficult to identify. Then a model-free control strategy, which exploits the flat outputs, is proposed. Those outputs also depend on physical parameters which are poorly known, i.e., the vehicle mass and inertia and the position of the center of gravity. A totally model-free control law is therefore adopted. It employs natural output variables, namely the longitudinal velocity and the lateral deviation of the vehicle. This last method, which is easily understandable and implementable, ensures a robust trajectory tracking problem in both longitudinal and lateral dynamics. Several convincing computer simulations are displayed.Comment: 9th IFAC Symposium on Intelligent Autonomous Vehicles (Leipzig, Germany, 29.06.2016 - 01.07.2016

A new model-free design for vehicle control and its validation through an advanced simulation platform

A new model-free setting and the corresponding "intelligent" P and PD controllers are employed for the longitudinal and lateral motions of a vehicle. This new approach has been developed and used in order to ensure simultaneously a best profile tracking for the longitudinal and lateral behaviors. The longitudinal speed and the derivative of the lateral deviation, on one hand, the driving/braking torque and the steering angle, on the other hand, are respectively the output and the input variables. Let us emphasize that a "good" mathematical modeling, which is quite difficult, if not impossible to obtain, is not needed for such a design. An important part of this publication is focused on the presentation of simulation results with actual and virtual data. The actual data, used in Matlab as reference trajectories, have been obtained from a properly instrumented car (Peugeot 406). Other virtual sets of data have been generated through the interconnected platform SiVIC/RTMaps. It is a dedicated virtual simulation platform for prototyping and validation of advanced driving assistance systems. Keywords- Longitudinal and lateral vehicle control, model-free control, intelligent P controller (i-P controller), algebraic estimation, ADAS (Advanced Driving Assistance Systems).Comment: in 14th European Control Conference, Jul 2015, Linz, Austria. 201

An acoustic model to control an experimental slide flute

International audienceWe consider the problem of modeling and control of a slide flute: a kind of recorder without finger holes but ended by a piston to modify the length of the resonator. To control dynamical systems, it is important to elaborate a realistic model, so that control laws can be tested efficiently before they are implemented on real size prototypes. The dynamical model we have elaborated takes into account the coupling effects between the jet and the pipe which is a linear acoustic resonator. The jet is obtained by blowing through a flue channel and formed by flow separation at the flue exit, and finally directed towards a sharp edge, called the labium. A modal analysis is then performed using the linearized boundary conditions to compute the suitable blowing pressure and the suitable pipe length to obtain a desired pitch. This will constitute the "feedforward" part of our control algorithm. The Proportional-Integral feedback term is then elaborated to regulate the system to the desired set point, using the length of the piston measured by an encoder and the blowing pressure measured by a pressure sensor. First experimental results, obtained on a "mechatronic" prototype developed at Mines ParisTech will be presented

DISSIPATIVE BOUNDARY CONDITIONS FOR ONE-DIMENSIONAL NONLINEAR HYPERBOLIC SYSTEMS

International audienceWe give a new sufficient condition on the boundary conditions for the exponential stability of one-dimensional nonlinear hyperbolic systems on a bounded interval. Our proof relies on the construction of an explicit strict Lyapunov function. We compare our sufficient condition with other known sufficient conditions for nonlinear and linear one-dimensional hyperbolic systems

Asymptotic observers for a simplified brass instrument model

International audienceIn this paper, a simplified model of a brass instrument is introduced. It is composed of a valve (including the mechanics of the lips), a jet (coupled with the valve dynamics), and a straight acoustic pipe excited by the jet, radiating in the air, and with frequency independent losses. This model couples an ordinary differential equation (valve) to a partial differential equation (acoustic pipe) through a static nonlinear function (Bernoulli relation on the jet). In fact, the overall system can be described by a ''so-called'' nonlinear neutral state space representation, the state of which being the position and velocity of the valve aperture and the ingoing wave of pressure at the entrance of the pipe. The measured output is the pressure at the open end of the pipe and the control is the mouth pressure. In this paper, methods of control engineering are applied to recover the state from the input and the measured output, assuming that propagation characteristics and player expression parameters are constant: a nonlinear state observer is built.} The robustness to wrong initial conditions and to noise on the measured output are analyzed

An acoustic model for automatic control of a slide flute

International audienceIn this paper, we consider the problem of modeling and control of a slide flute : a kind of recorder without finger holes but which is ended by a piston mechanism to modify the length of the resonator. A previous study has been done (see [3]), but with a very simple boundary condition for the mouth, corresponding to an ideal situation assuming that the acoustic pressure is zero at the entrance of the resonator. In this work, we have taken into account a more realistic model, describing the coupling effects between the jet and the pipe. The jet is obtained by blowing through a flue channel and formed by flow separation at the flue exit, and finally directed towards a sharp edge, called the labium. The resulting structure can then be seen as a nonlinear oscillator coupled with the pipe which is a linear acoustic resonator. The pressure obtained through this model has been compared to the pressure measured on an actual instrument, a recorder closed at its end. A modal analysis is then performed using the linearized boundary conditions which can also be used to compute the suitable blowing pressure and the suitable pipe length to obtain a desired fundamental frequency or equivalently a desired pitch. This will constitute the basis of our control algorithm. A possible musical application of such a device is to build a flue instrument with a pitch independent of the dynamical level

Robust grey-box closed-loop stop-and-go control

International audienceThis paper presents a robust stop-and-go control law, especially well adapted to car following scenarios in urban environments. Since many vehicle/road interaction factors (road slope, rolling resistance, aerodynamic forces) are very poorly known and measurements are quite noisy, a robust strategy is proposed within an algebraic framework. On the one hand, noisy signals will be processed in order to obtain accurate derivatives, and thereafter, variable estimates. On the other hand, a grey-box closed-loop control will be implemented to compensate all kind of unmodeled dynamics or parameter uncertainties

Coupled nonlinear vehicle control: Flatness-based setting with algebraic estimation techniques

International audienceA combined nonlinear longitudinal and lateral vehicle control is investigated. Flatness-based nonlinear control and new algebraic estimation techniques for noise removal and numerical differentiation are the main theoretical tools. An accurate automatic path-tracking via vehicle steering angle and driving/braking wheel torque is thus ensured. It combines the control of the lateral and longitudinal motions in order to track straight or curved trajectories and to perform a combined lane-keeping and steering control during critical driving situations such as obstacle avoidance, stop-and-go control, lane-change maneuvers or any other maneuvers. Promising results have been obtained with noisy experimental data, which were acquired by a laboratory vehicle with high dynamic loads and high lateral accelerations