Showing papers by "Richard M. Murray published in 1997"

Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

Abstract: This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers.

Configuration Controllability of Simple Mechanical Control Systems

Abstract: In this paper we present a definition of "configuration controllability" for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this new version of controllability is derived. This condition involves an object which we call the symmetric product. Of particular interest is a definition of "equilibrium controllability" for which we are able to derive computable sufficient conditions. Examples illustrate the theory.

Stabilization of integrator chains in the presence of magnitude and rate saturations: a gain scheduling approach

Abstract: We present a gain scheduling technique for stabilizing integrator chains in the presence of magnitude and rate limitations on the input. The controller was first presented by Lauvdal et al. (1997), where they showed excellent experimental results on a pitch axis flight control experiment at Caltech in the case of input rate limits only. The controller has several interesting features: it is easy to tune and it gives a minimal loss in performance. These properties are illustrated in a simulation study.

Rotating stall control of an axial flow compressor using pulsed air injection

Abstract: This paper presents the use of pulsed air injection to control rotating stall in a low-speed, axial flow compressor. In the first part of the paper, the injection of air is modeled as an unsteady shift of the compressor characteristic, and incorporated into a low dimensional model of the compressor. By observing the change in the bifurcation behavior of this model subject to nonlinear feedback, the viability of various air injection orientations is established. An orientation consistent with this analysis is then used for feedback control. By measuring the unsteady pressures near the rotor face, a control algorithm determines the magnitude and phase of the first mode of rotating stall and controls the injection of air in the front of the rotor face. Experimental results show that this technique eliminates the hysteresis loop normally associated with rotating stall. A parametric study is used to determine the optimal control parameters for suppression of stall. The resulting control strategy is also shown to suppress surge when a plenum is present. Using a high-fidelity model, the main features of the experimental results are duplicated via simulations.

Numerically Efficient Robustness Analysis of Trajectory Tracking for Nonlinear Systems

Abstract: A numerical algorithm for computing necessary conditions for performance specifications is developed for nonlinear uncertain systems following a prescribed trajectory. This algorithm provides a computational efficient means of evaluating the performance of a nonlinear system in the presence of noise, real parametric uncertainty, and unmodeled dynamics. The algorithm is similar in nature and behavior to the power algorithm for the mu lower bound, and does not rely on a descent method. The algorithm is applied to two flight control examples.

Uniting local and global controllers for the Caltech ducted fan

Abstract: Caltech's ducted fan experiment is used as a case study to investigate the properties of an algorithm for uniting local and global controllers proposed by Teel et al. (1997). To simplify the control design process and to illustrate robustness, the ducted fan is modeled as a linear system with input rate limits. The local controller is an (fairly aggressive) LQR state feedback while the (semi-) global controller is a much less aggressive LQR state feedback. Closed-loop simulation results are provided using a fully nonlinear model of the ducted fan derived from wind tunnel data. Experimental results are also provided using the actual Caltech ducted fan.

Reduction of bleed valve rate requirements for control of rotating stall using continuous air injection

Abstract: Actuation of the compressor characteristic, via the use of continuous air injection, has been experimentally verified on a single-stage, low-speed axial compressor, to provide a method of reducing the rate requirement of bleed valve control of rotating stall. The experiments show that the bleed valve rate requirement is reduced from approximately 145 Hz to below 10 Hz when the amount of compressor characteristic actuation is increased. Theoretical tools based on a low order model (1-3 states) and simulations based on a reduced order distributed model (37 states) have been developed to estimate the gain and rate requirements of the bleed controller. All of the analytical formulas and simulations share the same qualitative trends with respect to the experiments. This qualitative agreement indicates that bleed valve control of rotating stall depends crucially on the rate limit of the bleed valve, and the theoretical tools indicate that the rate limit requirement depends on both the stable and the unstable part of the compressor characteristic. By combining compressor characteristic identification tools and the analytic relations, insights for designing a compressor-bleed pair are provided.

Outer flatness: Trajectory generation for a model helicopter

Abstract: This paper introduces the concept of outer flatness, a derivative of differential flatness. Outer flatness describes a system that can be split in 2 subsytems, a non-flat inner system and a flat outer system. The outputs of the outer system are the tracking outputs of interest. The inputs of the outer system are the outputs of the inner system, and not subject to our direct control. The inputs of the inner system are the real actuator inputs. This system structure is also present in backstepping and dynamic inversion. We present two theorems on exponential and bounded tracking for outer flat systems, based on Lyapunoff arguments. We validate the approach with simulations and experiments on a model helicopter.

Combined air injection control of rotating stall and bleed valve control of surge

Abstract: A controller for rotating stall in axial flow compressors using pulsed air injection is considered. Theory is developed for the combination of this air injection controller with a bleed valve controller for the system's surge dynamics. The controller analysis is based on the surge dynamics acting on a slow time scale relative to the rotating stall dynamics. Experiments demonstrating this controller design on the Caltech rig are also presented.

Effects of noise, magnitude saturation, and rate limits on rotating stall control

Abstract: Operability enhancement is one of the major goals for active control of rotating stall and surge in axial compression systems. Using a reduced order model derived by Moore and Greitzer (1986), we show that the operability enhancement achieved by bleed valve actuation is seriously limited by fluid noise, and actuator magnitude and rate limits. By approximating the attracting saddle-sink connections, we reduce the 4D model to a 2D system. Algebraic formulas relating the operability enhancement to the actuator limits, the fluid noise, and the shape of the compressor characteristic are obtained by approximating the stable manifold of a saddle fixed point for the reduced system. Finally, the reduction and approximation techniques are shown to be viable by numerical simulations for a model of a low speed rig with a fast valve and a slow valve.

Trajectory tracking for fully actuated mechanical systems

Abstract: We present a general framework for the control of Lagrangian systems with as many inputs as degrees of freedom. Relying on the geometry of mechanical systems on manifolds, we propose a design algorithm for the tracking problem. The notions of error function and transport map lead to a proper definition of configuration and velocity error. These are the crucial ingredients in designing a proportional derivative feedback and feedforward controller. The proposed approach includes as special cases a variety of results on control of manipulators, pointing devices and autonomous vehicles.

Stabilization of a Pitch Axis Flight Control Experiment with Input Rate Saturation

Abstract: Motivated by some specific problems in flight control and roll stabilization of ships, we present a technique for stabilizing a chain of integrators in the presence of rate limitations on the input. Our technique improves on several existing techniques in the literature and has a number of interesting features. The controller is evaluated experimentally on a pitch axis flight control experiment at Caltech. The experimental results show that even in the presence of rate limits that cause a linear controller to go unstable, the time-varying controller stabilizes the system with minimal loss in performance.

Characterizing the Effects of Air Injection on Compressor Performance for Use in Active Control of Rotating Stall

Abstract: Previous work has developed an air injection controller for rotating stall based on the idea of a shifting compressor characteristic and the Moore-Greitzer three state compressor model. In order to demonstrate this form of control experimentally, a series of open loop tests were performed to measure the performance characteristics of a low speed axial flow compression system when air is injected upstream of the rotor face. The position of the air injection port relative to the hub and the rotor face and the angle relative to the mean axial flow were varied. The tests show that the injection of air has drastic effects on the stalling mass flow rate and on the size of the hysteresis loop associated with rotating stall. The stalling mass flow rate was decreased by 10% and the hysteresis loop was completely eliminated under some conditions. The results of the open loop parametric study were then used to implement a closed loop control strategy based on a shifting characteristic.Copyright © 1997 by ASME

Actuator bandwidth and rate limit reduction for control of compressor rotating stall

Abstract: A compressor is disclosed having a characteristic modifier, such as air injection, adapted to modify an operating characteristic of the compressor in order to reduce the bandwidth and rate limit requirements of the compressor. The compressor includes an actuator, such as a bleed valve, whose bandwidth and rate limit parameters meet the corresponding reduced requirements of the compressor. The actuator is adapted to stabilize the compressor with respect to a likely condition in the compressor which would tend to make the compressor operate in a less stable manner. This makes it possible to stabilize the compressor using a more readily available actuator having lower bandwidth and rate limit parameters.

Nonlinear control of rotating stall using axisymmetric bleed with continuous air injection on a low-speed, single stage, axial compressor *

Abstract: Active control of rotating stall and surge using bleed valves has been demonstrated on low and high speed compressors using high bandwidth actuators. In this paper we provide a method to reduce the bandwidth and rate requirements for control of rotating stall by combining an axisymmetric bleed valve with continuous air injection. The addition of the continuous air injection is modeled as a shift of both the stable and unstable parts of the compressor characteristic and serves to reduce the requirement of a bleed valve used for rotating stall stabilization purpose. The results are demonstrated using a lowspeed, single stage, axial flow compressor.

An experimental comparison of tradeoffs in using compliant manipulators for robotic grasping tasks

Abstract: Controllers developed for control of flexible-link robots in hybrid force-position control tasks by a new singular perturbation analysis of flexible manipulators are implemented on an experimental two-robot grasping setup. Various performance criteria are set up and experimental results are discussed within that setting to show tradeoffs in using flexible link robots for grasping. We conclude that large flexibility can be controlled without too much additional effort, has performance comparable to rigid robots and possesses enhancing properties which make it attractive for use in certain types of applications.

Simultaneous force-position control for grasping using flexible link manipulators

Abstract: This paper presents a new singular perturbation approach for analyzing flexibility in manipulators. This approach does not treat the flexible manipulator as a perturbation of the rigid manipulator, and therefore, allows for significant amounts of flexibility (beyond the linear range). Analysis based on this approach leads to some provably stable control laws for the position and force control of flexible-link manipulators. Simulation results are presented for a single constrained flexible manipulator.

Robotic manipulation with flexible link fingers

Abstract: A robot manipulator is a spatial mechanism consisting essentially of a series of bodies, called "links", connected to each other at "joints". The joints can be of various types: revolute, rotary, planar, prismatic, telescopic or combinations of these. A serial connection of the links results in an open-chain manipulator. Closed-chain manipulators result from non-serial (or parallel) connections between links. Actuators at the joints of the manipulator provide power for motion. A robot is usually not designed for a very specific or repetitive task which can be done equally well by task-specific machines. Its strength lies in its ability to handle a range of tasks by virtue of being "re-programmable". Therefore, in addition to the mechanical hardware two other elements are integral to the description of a robot: sensors and control. With the advent of micro-electronics and digital computers the availability of sensors is ever increasing and the control is usually done by software executed by computers which also collect the sensory data. It is possible to model quite accurately, the dynamics of robot manipulators for purposes of control. However, for most practical robots the models are complex and numerically intensive to calculate in real-time. Traditional analyses of robot manipulators consider the whole mechanism to be rigid. Relaxation of the assumption of rigidity leads to further complication of the dynamics of the manipulator, leading to more difficulties in control. The overall motion of the manipulator is augmented by additional motion due to the dynamics of flexibility which must be considered. Sensing is also made more difficult. However, the ability to control robots with significant structural flexibilities, referred to as flexible robots in the rest of this thesis, influences robotics in many ways. It allows for consideration of new applications, observance of less conservative structural design and performance enhancements in certain classes of robotic tasks, which will be addressed in greater detail in the sections which follow.

Differential flatness of two one-forms in arbitrary number of variables

Abstract: Given a differentially flat system of ODEs. flat outputs that depend only on original variables but not on their derivatives are called zero-flat outputs and systems possessing such outputs are called zero-flat. In this paper we present a theory of zero-flatness for a system of two one-forms in arbitrary number of variables (t, x1. …. χN). Our approach splits the task of finding zero-flat outputs into two parts. First part involves solving for distributions that satisfy a set of algebraic conditions. The second part involves finding an integrable distribution from the solution set of the first part. Typically this part involves solving PDEs. Our results are also applicable in determining if a control alfine system in n states and n−2 controls has flat outputs that depend only on states. We illustrate our method by examples.