J. Karl Hedrick

Observer design for a class of nonlinear systems

A viable design methodology to construct observers for a class of nonlinear systems is developed. The proposed technique is based on the off-line solution of a Riccati equation, and can be solved using commercially available software packages. For globally valid results, the class of systems considered is characterized by globally Lipschitz nonlinearities. Local results relax this assumption to only a local requirement. For a more general description of nonlinear systems, the methodology yields approximate observers, locally. The proposed theory is used to design an observer for a single-link flexible joint robot. This observer estimates the robot link variables based on the joint measurements.

Adaptive dynamic surface control : a simplified algorithm for adaptive backstepping control of nonlinear systems

In this paper, we propose a new algorithm for adaptive backstepping control of non-linear uncertain systems. Current backstepping algorithms require repeated differentiations of the modelled non-linearities. The addition of n first order low pass filters allows the algorithms to be implemented without differentiating any model non-linearities. The uncertainties are assumed to be linear in the unknown constant parameters. The combined adaptive backstepping/first order filter system is proven to be semi-globally stable for sufficiently fast filters by a singular perturbation approach.

Disturbance propagation in vehicle strings

This note focuses on disturbance propagation in vehicle strings. It is known that using only relative spacing information to follow a constant distance behind the preceding vehicle leads to string instability. Specifically, small disturbances acting on one vehicle can propagate and have a large effect on another vehicle. We show that this limitation is due to a complementary sensitivity integral constraint. We also examine how the disturbance to error gain for an entire platoon scales with the number of vehicles. This analysis is done for the predecessor following strategy as well as a control structure where each vehicle looks at both neighbors.

Tracking nonlinear non-minimum phase systems using sliding control

Nonlinear systems affine in the input, and having a well-defined (vector) relative degree are considered. The invertibility of the input output dynamics can be used to achieve tracking of smooth desired trajectories if the associated ‘zero-dynamics’ are stable. We consider tracking in nonlinear systems with unacceptable zero-dynamics (i.e. non-minimum phase systems). The desired trajectories are assumed to be generated by some exosystem. We use sliding control to achieve tracking independent of disturbances entering in the channels of the input. The main idea is (i) to do an output-redefinition such that the zero-dynamics with respect to this new output are acceptable; (ii) to define a modified desired trajectory for the new output to track such that in the process, the original output tracks the original desired trajectory asymptotically.

Modified Skyhook Control of Semi-Active Suspensions: A New Model, Gain Scheduling, and Hardware-in-the-Loop Tuning

In this paper, a road adaptive modified skyhook control for the semi-active Macpherson strut suspension system of hydraulic type is investigated. A new control-oriented model, which incorporates the rotational motion of the unsprung mass, is introduced. The control law extends the conventional skyhook-groundhook control scheme and schedules its gains for various road conditions. Using the vertical acceleration data measured, the road conditions are estimated by using the linearized new model developed. Two filters for estimating the absolute velocity of the sprung mass and the relative velocity in the rattle space are also designed. The hydraulic semi-active actuator dynamics are incorporated in the hardware-in-the-loop tuning stage of the control algorithm developed. The optimal gains for the ISO road classes are discussed. Experimental results are included. @DOI: 10.1115/1.1434265#

Control of multivariable non-linear systems by the sliding mode method

Sliding mode control is a technique that has been successfully used for SISO nonlinear systems in controllable canonical form and for some particular multivariable system structures. It is the purpose of this paper to generalize the sliding mode approach to a larger class of multivariable systems and to illustrate the relationship between I/O linearization and the sliding mode approach when the error dynamics on the sliding surfaces are chosen to be linear and time-invariant. The developed technique is applied to a multivariable non-linear example.

Development of a Collision Avoidance System

The analysis of a rear-end collision warning/ avoidance (CW/CA) system algorithm will be presented. The system is designed to meet several criteria: 1. System warnings should result in a minimum load on driver attention. 2. Automatic control of the brakes should not interfere with normal driving operation.

Robust input-output feedback linearization

To make input-output feedback linearization a practical and systematic design methodology for single-input nonlinear systems, two problems need to be addressed. One is to handle systematically the difficulties associated with the internal dynamics or zero-dynamics when the relative degree is less than the system order. The other is to account for the effect of model uncertainties in the successive differentiations of the output of interest. While the first problem has recently received considerable attention, the second has been largely unexplored. This paper represents a preliminary study of a systematic methodology to account robustly for parametric uncertainties in the original system model. The approach is based on combining sliding control ideas with the recursive construction of a closed-loop Lyapunov function, and is illustrated with a simple example.

Optimal path planning in a constant wind with a bounded turning rate

In this paper, we explore the problem of generating the optimal time path from an initial position and orientation to a flnal position and orientation in the two-dimensional plane for an aircraft with a bounded turning radius in the presence of a constant wind. Following the work of Boissonnat, we show using the Minimum Principle that the optimal path consists of periods of maximum turn rate or straight lines. We demonstrate, however, that unlike the no wind case, the optimal path can consist of three arcs where the length of the second arc is less than …. A method for generating the optimal path is also presented which iteratively solves the no wind case to intercept a moving virtual target. I. Introduction Optimal path planning is an important problem for robotics and unmanned vehicles. In this paper, we explore a method for flnding the shortest path from an initial position and orientation to a flnal position and and orientation in the two-dimensional plane for an aircraft with a bounded turning radius in the presence of a constant wind. This work was motivated by our group’s work with our ∞eet of small autonomous aircraft. Each modifled Sig Rascal aircraft ∞ies under the combined control of an ofi-the-shelf Piccolo avionics package for low level control and an onboard PC104 computer for higher level tasks. These aircraft ∞y at a nominal speed of 20 m/s, and wind speeds of over 5 m/s have been encountered during ∞ight testing. The problem described above was flrst solved in the case of no wind by Dubins using geometric arguments 8

Multiple-surface sliding control of a class of uncertain nonlinear systemsm

We develop a ‘multiple-surface’ sliding control for a class of single-input single-output nonlinear systems whose uncertainties do not satisfy the standard matching condition. A coordinate dependence condition on the uncertainty bound is assumed. A ‘computed normal form’ is defined to handle such uncertainties instead of the normal form used in conventional input-output linearization. A control algorithm which can be applied to global tracking problems has been developed and evaluated for a benchmark example.