Stefano Scalzi

Nonlinear Control Techniques for the Heart Rate Regulation in Treadmill Exercises

It has been recently shown in the literature that a robust output feedback controller for the heart rate regulation can be designed for an experimentally validated second order nonlinear model of the human heart rate response during long-duration treadmill exercises: It is based on piecewise linear approximations of the original nonlinear model and involves (local) robust linear control techniques. In this letter, we resort to recent nonlinear advanced control techniques in order to illustrate the existence of a nonlocal and nonswitching control which guarantees heart rate regulation with no exact knowledge of model parameters and nonlinearities: It simply generalizes to the nonlinear framework the classical proportional-integral control design for linear models of heart rate response during treadmill exercises. Simulation and experimental results demonstrate the effectiveness of the proposed approach in typical training exercises involving warm up/holding/cool down phases.

Asymptotic sideslip angle and yaw rate decoupling control in four-wheel steering vehicles

This paper shows that, for a four-wheel steering vehicle, a proportional-integral (PI) active front steering control and a PI active rear steering control from the yaw rate error together with an additive feedforward reference signal for the vehicle sideslip angle can asymptotically decouple the lateral velocity and the yaw rate dynamics; that is the control can set arbitrary steady state values for lateral speed and yaw rate at any longitudinal speed. Moreover, the PI controls can suppress oscillatory behaviours by assigning real stable eigenvalues to a widely used linearised model of the vehicle steering dynamics for any value of longitudinal speed in understeering vehicles. In particular, the four PI control parameters are explicitly expressed in terms of the three real eigenvalues to be assigned. No lateral acceleration and no lateral speed measurements are required. The controlled system maintains the well-known advantages of both front and rear active steering controls: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres and improved manoeuvrability. In particular, zero lateral speed may be asymptotically achieved while controlling the yaw rate: in this case comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced. Also zero yaw rate can be asymptotically achieved: in this case additional stable manoeuvres are obtained in obstacle avoidance. Several simulations, including step references and moose tests, are carried out on a standard small SUV CarSim model to explore the robustness with respect to unmodelled effects such as combined lateral and longitudinal tyre forces, pitch, roll and driver dynamics. The simulations confirm the decoupling between the lateral velocity and the yaw rate and show the advantages obtained by the proposed control: reduced lateral speed or reduced yaw rate, suppressed oscillations and new stable manoeuvres.

A nested PID steering control for lane keeping in vision based autonomous vehicles

In this paper a nested PID steering control for lane keeping in vision based autonomous vehicles is designed to perform path following in the case of roads with an uncertain curvature. The control input is the steering wheel angle: it is designed on the basis of the yaw rate, measured by a gyroscope, and the lateral offset, measured by the vision system as the distance between the road centerline and a virtual point at a fixed distance from the vehicle. No lateral acceleration and no lateral speed measurements are required. A PI active front steering control on the yaw rate tracking error is used to reject constant disturbances and the overall effect of parameter variations while improving vehicle steering dynamics. The yaw rate reference is viewed as the control input in an external control loop: it is designed using a PID control on the lateral offset to reject the disturbances on the curvature which increase linearly with respect to time. The robustness is investigated with respect to speed variations and uncertain vehicle physical parameters: it is shown that the controlled system is asymptotically stable for all perturbations in the range of interest. Several simulations are carried out on a standard big sedan CarSim vehicle model to explore the robustness with respect to unmodelled effects such as combined lateral and longitudinal tire forces, pitch and roll. The simulations show reduced lateral offset and new stable μ-split braking manoeuvres in comparison with the CarSim model predictive steering controller implemented by CarSim.

Dynamic controller for lane keeping and obstacle avoidance assistance system

This paper presents the design and simulation tests of a steering assistance for passenger vehicles based on a dynamic state feedback controller. Its main purpose is to avoid unintended lane departure and collisions. The design of the proposed lane keeping system takes into account the road curvature, considered as an exogenous input, into its internal model. The computation of the control law has been achieved by linking Lyapunov theory of stability to Bilinear Matrix Inequalities which considers bounds in the control input and minimises the reachable set of the vehicle after activation. This control strategy ensures convergence of the lateral offset to zero, even in curvy roads. Simulations show the performance of the controller and an extended application for collision avoidance.

Experimental Heart Rate Regulation in Cycle-Ergometer Exercises

The heart rate can be effectively used as a measure of the exercise intensity during long duration cycle-ergometer exercises: precisely controlling the heart rate (HR) becomes crucial especially for athletes or patients with cardiovascular/obesity problems. The aim of this letter is to experimentally show how the nonlocal and nonswitching nonlinear control that has been recently proposed in the literature for the HR regulation in treadmill exercises can be effectively applied to cycle-ergometer exercises at constant cycling speed. The structure of the involved nonlinear model for the HR dynamics in cycle-ergometer exercises is mathematically inspired by the structure of a recently identified and experimentally validated nonlinear model for the HR dynamics in treadmill exercises: the role played by the treadmill speed is played here by the work load while the zero speed case for the treadmill exercise is here translated into the cycling operation under zero work load. Experimental results not only validate the aforementioned nonlinear model but also demonstrate the effectiveness-in terms of precise HR regulation-of an approach which simply generalizes to the nonlinear framework the classical proportional-integral control design. The possibility of online modifying the HR reference on the basis of the heart rate variability (HRV) is also suggested and experimentally motivated.

Repetitive Learning Control Design for LED Light Tracking

A lighting system composed of three color light-emitting diode (LED) strings is considered. On the basis of a simplified dynamic model (with uncertainties) for the aforementioned system, the tracking of (possibly complex) periodic reference signals (with known period) for both the light color and intensity is achieved by designing, for each LED string, a decentralized repetitive learning control. Experimental results illustrate the effectiveness of the proposed approach in a practical user-friendly scenario: the color coordinates are obtained by an external low-cost red, green, blue sensor which allows for measuring the overall lighting effects (including external disturbances) while increasing the overall energy saving. A detailed theoretical analysis of the learning control design for first-order linear systems with zero relative degree under suitable assumptions is also included.

Vehicle yaw rate control based on piecewise affine regions

This paper shows that an active front steering control, that considers the nonlinear behaviour of the tire-road forces, can be designed by parameterizing the vehicle dynamics with respect to the measurable yaw rate and taking into account the steady state behaviour of the vehicle. In order to ensure the tracking of the yaw rate reference signal on the basis of the yaw rate tracking error, despite constant disturbances and parameters uncertainties, the proposed control strategy uses a proportional integral (PI) control, in which the gains depend on the defined parametrized vehicle dynamics. The proposed control system switches depending on the yaw rate as it is a variable measured at low cost. The stability is proved by a piecewise quadratic Lyapunov function using linear matrix inequalities technique. Several simulations, including disturbances rejections and step references, are carried out on a standard nonlinear CarSim D-Class vehicle model to explore the robustness with respect to unmodelled effects such as combined lateral and longitudinal tire forces, pitch, roll and driver dynamics. The simulations confirm that the proposed piecewise linear (PWL) control can greatly improve the vehicle stability and is advantageous in very demanding manoeuvres.

Integrated Driver and Active Steering Control for Vision-Based Lane Keeping

A nested PID steering control for autonomous vehicles equipped with artificial vision systems is designed so that the driver can override the automatic lane-keeping action and obtain a complete control of the vehicle lateral dynamics without any switching strategy. The control input is the steering wheel angle: it is designed on the basis of the yaw rate, which is measured by a gyroscope, and the lateral offset, which is measured by the vision system as the distance between the road centerline and a virtual point at a fixed distance ahead from the vehicle. No lateral acceleration and no lateral speed measurements are required. A PI active front steering control on the basis of the yaw rate tracking error is designed to compensate for constant disturbances while improving vehicle steering dynamics and reducing the influence of parameter variations. The yaw rate reference is viewed as the control input in an external control loop: it is designed using a PID control based on the lateral offset measurements to reject the disturbances on the curvature during autonomous control, i.e., when the driver is not exerting any torque on the steering wheel. A third control block is designed to allow the driver to control the vehicle (for example, lane change for passing purposes or obstacle avoidance) overriding the automatic lane-keeping action while maintaining the advantages of the yaw rate feedback. Several simulations are carried out on a standard big sedan CarSim vehicle model to explore the robustness with respect to unmodelled effects such as combined latera land longitudinal tire forces, pitch and roll and parameters variations. The simulations show reduced path following errors and new stable manoeuvres in comparison with the model predictive steering controller implemented by CarSim in both cases of autonomous and non autonomous control.

Piecewise affine control for lane departure avoidance

This article presents the design of a lane departure avoidance system which is conceived to operate even in demanding manoeuvres with respect to the lateral vehicle dynamics. Piecewise affine state feedback and output feedback controllers are used to handle the nonlinear behaviour of the lateral tyre forces. The controllers are designed based on the search of a piecewise quadratic Lyapunov function casted as a bilinear matrix inequalities problem. Experimental tests demonstrate the performance of the controller in degraded road conditions.

Active steering control based on piecewise affine regions

This paper shows that an active front steering control can be designed taking into account the nonlinear behaviour of the tire-road forces considering the vehicle dynamics with respect to the tire sideslip angle and by approximating the tire force characteristics by piecewise affine functions. The proposed control strategy involves the design of two control loops: the first one is a state feedback and it is designed to improve the vehicle dynamics using the pole placement techniques while the second control loop uses a PI control to ensure the tracking of constant yaw rate reference signal on the basis of the yaw rate tracking error despite constant disturbances and parameters uncertainties. Several simulations, including disturbances rejections and step references, are carried out on a standard CarSim D-Class vehicle model to explore the robustness with respect to unmodelled effects such as combined lateral and longitudinal tire forces, pitch, roll and driver dynamics. The simulations confirm that the proposed PWL control can greatly improve the vehicle stability and may be advantageous in very demanding manoeuvres in comparison with the use of the proposed controller designed for the linear region only.