Slow peaking and low-gain designs for global stabilization of nonlinear systems

This paper presents an analysis of the slow-peaking phenomenon, a pitfall of low-gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems. The phenomenon is best understood on a chain of integrators perturbed by a vector field up(x, u) that satisfies p(x, 0) = 0. Because small controls (or low-gain designs) are sufficient to stabilize the unperturbed chain of integrators, it may seem that smaller controls, which attenuate the perturbation up(x, u) in a large compact set, can be employed to achieve larger regions of attraction. This intuition is false, however, and peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p(x, u). These growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system. When this higher order condition is satisfied, an explicit control law is derived that achieves global asymptotic stability of x = 0. This stabilization result is extended to more general cascade nonlinear systems in which the perturbation p(x, v) v, v = (ξ, u) T, contains the state ξ and the control u of a stabilizable subsystem ξ = a(ξ, u). As an illustration, a control law is derived that achieves global stabilization of the frictionless ball-and-beam model.

Path-following steering control for articulated vehicles

Passive steering systems have been used for some years to control the steering of trailer axles on articulated vehicles. These normally use a 'command steer' control strategy, which is designed to work well in steady-state circles at low speeds, but which generates inappropriate steer angles during transient low-speed maneuvers and at high speeds. In this paper, 'active' steering control strategies are developed for articulated heavy goods vehicles. These aim to achieve accurate path following for tractor and trailer, for all paths and all normal vehicle speeds, in the presence of external disturbances. Controllers are designed to implement the path-following strategies at low and high speeds, whilst taking into account the complexities and practicalities of articulated vehicles. At low speeds, the articulation and steer angles on articulated heavy goods vehicles are large and small-angle approximations are not appropriate. Hence, nonlinear controllers based on kinematics are required. But at high-speeds, the dynamic stability of control system is compromised if the kinematics-based controllers remain active. This is because a key state of the system, the side-slip characteristics of the trailer, exhibits a sign-change with increasing speeds. The low and high speed controllers are blended together using a speed-dependent gain, in the intermediate speed range. Simulations are conducted to compare the performance of the new steering controllers with conventional vehicles (with unsteered drive and trailer axles) and with vehicles with command steer controllers on their trailer axles. The simulations show that active steering has the potential to improve significantly the directional performance of articulated vehicles for a wide range of conditions, throughout the speed range. © VC 2013 by ASME.

Assessing boost-assist options for turbocharged engines using 1-D engine simulation and model predictive control

Delivering acceptable low end torque and good transient response is a significant challenge for all turbocharged engines. As downsized gasoline engines and Diesel engines make up a larger and larger proportion of the light-duty engines entering the market, the issue takes on greater significance. Several schemes have been proposed to improve torque response in highly boosted engines, including the use of electrical assist turbochargers and compressed air assist. In this paper we examine these methods with respect to their effectiveness in improving transient response and their relative performance along with some of the practical considerations for real world application. Results shown in this paper are from 1-D simulations using the Ricardo WAVE software package. The simulation model is based on a production light-duty Diesel engine modified to allow the introduction of compressed air at various points in the air-path as well as direct torque application to the turbocharger shaft (such as might be available from an electrical assist turbocharger). Whilst the 1-D simulation software provides a suitable environment for investigating the various boost assistance options, the overall air path performance also depends upon the control system. The introduction of boost assistance complicates the control in two significant ways: the system may run into constraints (such as compressor surge) that are not encountered in normal operation and the assistance introduces an additional control input. Production engine controllers are usually based on gain-scheduled PID control and extensive calibration. For this study, the non-linear nature of the engine together with the multiple configurations considered and the slower than real-time execution of 1-D models makes such an approach time consuming. Moreover, an ad-hoc approach would leave some doubt as to the fairness of comparisons between the different boost-assist options. Model Predictive Control has been shown to offer a convenient approach to controlling the 1-D simulations in a close to optimal manner for a typical Diesel VGT-EGR air path configuration. We show that the same technique can be applied to all the considered assistance methods with only modest calibration effort required. Copyright © 2012 SAE International.

Reference frame re-alignment for vector control of the brushless doubly-fed machine

Vector control provides stability and performance when applied to the brushless doubly-fed machine, however cross-coupling effects can arise between inputs and outputs. To address these effects, a procedure is proposed to both visualize and minimize the cross-coupling by means of steady-state mapping and a re-alignment of the dq reference frame. With this method implemented, gain-response tests show improved decoupling across the operating region. © 2013 EUCA.