Slew Maneuver Research Articles

Design of stabilizing control laws for mechanical systems based on Lyapunov's method

Design methods of stabilizing control laws are discussed for general mechanical systems. Hamiltonians of the mechanical systems are assumed not to depend on time explicitly, but the mechanical systems may embody elastic bodies and nonlinear motions. The methods are based on Lyapunov's second method for stability analysis, and the equations of motion of the controlled systems are not necessary for control design. A candidate for the Lyapunov function is the composition of the Hamiltonians of the subsystems in a given system. A sufficient condition of stabilizing control laws is derived and is extended so as to allow a class of frequency-dep endent control laws with positive real filters, observers, or prefilters. The multiplier method (augmented Lagrangian method) is also introduced to attain desirable equilibrium in the closed-loop systems and results in integral control action. Slew maneuver of a flexible beam is employed as a design example to demonstrate the closed-loop characteristics of several control laws based on the present method. YAPUNOV S second method is a powerful tool for the stability analysis of dynamical systems. One of the preferable features of the method is that it is not necessary to obtain the explicit solutions of the differential equations governing the dynamical systems and, therefore, it can often be applied successfully to nonlinear systems and distributed parameter systems. The method is suitable especially for stability analysis of mechanical systems, since the Hamiltonians of mechanical systems are natural candidates of the Lyapunov function. Lyapunov's method is employed in Ref. 1 for designing control laws for rigid manipulators that are nonlinear systems. The Lyapunov function consists of the Hamiltonian of the whole system and a potential function introduced to achieve the desirable configuration of the manipulators. Lyapunov's method is utilized in Ref. 2 to analyze the stability of direct velocity feedback for active vibration suppression of flexible space structures, where the system energy is chosen as a candidate of the Lyapunov function. In Ref. 3, flexible multilink manipulators are treated, and the closedloop stability of proportional- derivative (PD) and strain feedback is analyzed applying Lyapunov's method to an ordinary differential equation obtained through modal expansion. It is shown in Ref. 4 that Lyapunov's method is directly applicable without modal expansion to coupled partial and ordinary differential equations that describe the slew maneuver of a flexible beam, and the PD control law for the attitude angle is shown to be stable by employing the Lyapunov function that consists of the Hamiltonian of the whole system and a potential function to attain a desirable attitude angle. In Refs. 5 and 6, which consider a problem similar to Ref. 4, the Lyapunov function consists of a weighted sum of Hamiltonians of the rigid hub and the flexible beam, not simply the Hamiltonian of the whole system, and a potential function to attain desirable equilibrium. The coupled partial and ordinary differential equations are treated directly without modal expansion in the analysis, and the resultant control law feeds back the attitude angle, the angular rate, the shear force, and the bending moment at the root of the beam. It is shown that the feedback law with a constant gain results in satisfactory

Robust closed-loop control design for spacecraft slew maneuver using thrusters

In this paper, a closed-loop switching function for on-off thruster firings is proposed to provide good attitude control performance in the presence of modeling errors for single-axis slew maneuver of a rigid spacecraft and to eliminate double-sided thruster firings. The size of a single-sided deadband in the switching function provides the capability of a tradeoff between maneuver time and fuel expenditure. The application of this switching function for the single-axis slew maneuvers of flexible spacecraft is also analyzed. The analytical simulations and experimental results demonstrate that the proposed switching function provides significant improvement in the slew maneuver performance.

An application of fuzzy logic control to a gimballed payload on a space platform

This paper will present results of applying two autonomous fuzzy controllers to a dynamically coupled system. The system consists of a space platform and a gimballed payload. The controllers are developed with the systems decoupled. Parametric studies are performed on the support limits for the error, change-in-error, and control. These parametric variations provide insight into satisfactorily tuning the controllers. The controllers were compared to controllers developed using Linear Quadratic Regulator (LQR) control design. The controllers are used to perform slew maneuvers and disturbance rejection. A design procedure using constraints due to hardware or software specification is also examined. When error and control support limits are specified, tuning the fuzzy controller is made relatively easy. The systems were coupled and the response of the payload and platform were examined for commanded payload trajectories and impulses applied to the platform. The fuzzy controllers performed very well in all cases.

An application of fuzzy logic control to a gimballed payload on a space platform

This paper will present results of applying two autonomous fuzzy controllers to a dynamically coupled system. The system consists of a space platform and a gimballed payload. The controllers are developed with the systems decoupled. Parametric studies are performed on the support limits for the error, change-in-error, and control. These parametric variations provide insight into satisfactorily tuning the controllers. The controllers were compared to controllers developed using Linear Quadratic Regulator (LQR) control design. The controllers are used to perform slew maneuvers and disturbance rejection. A design procedure using constraints due to hardware or software specification is also examined. When error and control support limits are specified, tuning the fuzzy controller is made relatively easy. The systems were coupled and the response of the payload and platform were examined for commanded payload trajectories and impulses applied to the platform. The fuzzy controllers performed very well in all cases.

Path planning with obstacle avoidance as applied to a class of space based flexible manipulators

The present study is a natural extension to the earlier work carried out by the authors in the area of nonlinear control of flexible structures using the Feedback Linearization Technique (FLT). This procedure accounts for the complete nonlinear dynamics of the system. It develops a rather innovative approach to path planning, for a 2-link flexible manipulator, with a specified target and several arbitrarily positioned obstacles. It is important to point out that the presence of link vibrations makes the problem at least an order of magnitude more complicated rendering the conventional algorithms developed for rigid systems virtually of little use. The problem involves generation of regions (contours) representing spheres of influence around the finite size obstacles, with various degrees of permissible penetrations during path planning to the target. To begin with, equations of motion of an orbiting flexible manipulator, undergoing planar slewing maneuvers, are obtained accounting for a shift in the center of mass during maneuvers. Next, a composite control procedure, involving the FLT together with active vibration suppression using piezo-electric actuators, is developed which promises high degree of tracking accuracy. Depending on the performance requirement of the mission, penalty functions are assigned for a given performance index pertaining to the flexible dynamics of the systems. This permits global improvement of the manipulator operation. Finally, effectiveness of the collision avoidance scheme is illustrated through several examples of increasing complexities.

Slewing Maneuvers and Vibration Control of Space Structures by Feedforward/Feedback Moment-Gyro Controls

This paper presents a momentgyro control approach to the maneuver and vibration suppression of a flexible truss arm undergoing a constant slewing motion. The overall slewing motion is triggered by a feedforward input, and a companion feedback controller is employed to augment the feedforward input and subsequently to control vibrations. The feedforward input for the given motion requirement is determined from the combined CMG (Control Momentum Gyro) devices and the desired rigid-body motion. The rigid-body dynamic model has enabled us to identify the attendant CMG momentum saturation constraints. The task for vibration control is carried out in two stages; first in the search of a suitable CMG placement along the beam span for various slewing maneuvers, and subsequently in the development of LQ control algorithms for CMG spin-stabilization. Both analytical and numerical results are presented to show the effectiveness of the present approach.

On the nonlinear slewing dynamics and control of the Space Station based Mobile Servicing System

A relatively general Lagrangian formulation for studying the nonlinear dynamics and control of space-craft with interconnected flexible members in a tree-type topology is developed. Versatility of the formulation is illustrated through a dynamical study of the Space Station based two-link Mobile Servicing System (MSS). The performance of the MSS undergoing inplane and out-of-plane slewing maneuvers is compared. Results indicate that, in absence of control, the maneuvers induce undesirable librational motion of the Space Station as well as vibration of the links. Nonlinear control, based on the Feedback Linearization Technique (FLT), appears promising. Quasi-Closed Loop Control (QCLC), a variation of the FLT, is applied to control the libration of the Space Station. Once the attitude of the Space Station is controlled, the performance of the MSS improves significantly. For a 5-minute maneuver of the MSS, the maximum control torque required is only 34.5 Nm.

Slewing dynamics and control of the Space Station-based mobile servicing system

A relatively general Lagrangian formulation for studying the non-linear dynamics and control of spacecraft with interconnected flexible members in a tree-type topology is developed. Versatility of the formulation is illustrated through a dynamical study of the Space Station-based two-link mobile servicing system (MSS). The performance of the MSS undergoing inplane and out-of-plane slewing maneuvers is compared. Results indicate that, in absence of control, the maneuvers induce undesirable librational motion of the Space Station as well as vibration of the links. Non-linear control based on the feedback linearization technique (FLT), appears promising. Quasi-closed loop control (QCLC), a variation of the FLT, is applied to control the libration of the Space Station. Once the attitude of the Space Station is controlled, the performance of the MSS improves significantly. For a 5-min maneuver of the MSS, the maximum control torque required is only 34.5 Nm.

Concurrent Mechanism and Control Design for the Slewing of Flexible Space Structures

An integrated single-step design approach to the synthesis of a mechanical device and an active controller is presented for slew maneuvers of flexible space structures. A mechanical device consists of a noncircular gear pair that acts as a varying gear ratio transmission between an electro-mechanical actuator and a flexible structure. Such a system has been introduced as an analytical application in minimizing flexural vibrations in the slewing maneuver of flexible space structures such as large solar panels and satellites in space. Only a simple regulator-type feedback controller is called for to control this complex electro-mechanical-and-structural system and the purpose is to design this complex system in an integrated procedure to achieve low flexural vibrations of the structure. Numerical simulations of the slewing control tasks for a planar articulated double-beam structure are presented.

Analytical solution of attitude motion for spacecraft with a slewing appendage

This paper investigates pitch motion and in orbital plane elastic vibration of a spacecraft with a flexible beam type appendage undergoing prescribed slew maneuver. The governing equations are transformed into a standard quasi-linear form, and then solved by Butenin's variation of parameters approach. Validity of the analytical solutions is assessed over a range of system parameters and initial conditions by comparing them with the results of numerical integration. The results show that they are very good approximations and provide extensive insight into the dynamical response of the system.

Large angle slew maneuvers with autonomous sun vector avoidance

References 1 Jamark, B., Turn of an Theory and Applications of Nonlinear Control Systems, North-Holland, New York, 1986, pp. 53-64. 2 Clements, J. C, Minimum-Time Turn Trajectories to Fly-toPoints, Optimal Control Applications & Methods, Vol. 11, No. 1, 1990, pp. 39-50. 3 Hedrick, and Bryson, A. E., Minimum Time Turns for a Supersonic Airplane at Constant Altitude, Journal of Aircraft, 1971, pp. 182-187. 4 Clements, J. C., Real-Time Optimal Control of Aircraft Turn Trajectories, Journal of Guidance, Control, and Dynamics, Vol. 16, No. 2, 1993, pp. 385-387. 5 Bryson, A. E., and Ho, Y.-C., Applied Optimal Control, Hemisphere, Washington, DC, 1975.

On the elastic mode estimation aspect of a class of multibody flexible systems

An investigation pertaining to estimation of the elastic generalized coordinates for a given class of flexible structures is presented. To begin with, a model for studying nonlinear dynamics of the structure is described. The governing equations of motion are obtained using the Lagrangian procedure with modal discretization. Next, deformations caused by rapid slewing maneuvers are estimated using the least square estimation approach. As an alternative, a procedure based on the operator spline technique is proposed and its potential assessed. It is motivated by the need for achieving an on-line estimation procedure permitting real time control. Finally, a comparative performance study of the two procedures is undertaken using a simplified model of the flexible system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonlinear rotational maneuver and vibration damping of NASA SCOLE system

We treat the question of large rotational maneuver and vibration stabilization of NASA Spacecraft Control Laboratory Experiment (SCOLE) system. The mathematical model of SCOLE system includes the dynamical equations for rigid body slew maneuver and three-dimensional vibration of the flexible beam and the reflector with an offset mass. The design approach taken here is to decompose the rigid mode control from vibration stabilization. Feedback input (Shuttle torque)-output (attitude angles) map linearization technique is used for designing attitude control system for large-angle slewing. Linearization of the input-output (i-o) map is accomplished by nonlinear inversion theory. It is shown that attitude control system asymptotically decouples the flexible dynamics and a linear feedback law is easily designed for vibration suppression. For the synthesis of the control law an observer is designed. Simulation results are presented to show that in the closed-loop system large angle maneuvers can be accomplished using only the measured state variables.

Sensor-based proximity operation of an astronaut reference flying robot

Proximity operation of an astronaut reference flying robot (ARFR) performing in-orbit servicing in the manner of an astronaut mounted on a propulsion unit is studied by developing a ground experiment model. The ARFR is a sensor-based autonomous robot with triple arms and flying mobility. This paper deals with sensor-based flying maneuvers and manipulation for floating target retrieval. A control system architecture is constructed according to the principle of 'high-level coordination, low-level local action'. A strategy in proximity operation constituting body motion adjustment, arm slew and hand motion adjustment to capture the target is proposed. A simplified arm slew maneuver using a command modifier with inertial sensor feedback is applied to compensate for the disturbance of the robot body. Active limp control is also introduced for capturing with low impact. The effectiveness of the proposed method is shown in a simulation experiment of a satellite retrieval mission on an air-bearing testbed using t...

Optimal control of a flexible manipulator

Manipulators handling payload masses several times larger than their own weight are considered. The optimal control rule, based on rigid body dynamics, is used to minimize the time of a slewing maneuver of a single link. The performance of such control is simulated using ADINA. The influence of various flexibility parameters on the performance of the optimal control is discussed.

Structure/Control Synthesis with Nonnegligible Actuator Mass

Simultaneous design of a structure/active control system in which the mass of the actuators required to implement the active control is considered is addressed. The inclusion of required actuator mass essentially tightens the coupling between structure and control dynamics and introduces an inner iteration loop in the overall design process. Because this inner iteration loop significantly increases the computational burden, an algorithm for estimating the required actuator mass, given the control law and the desired maneuver, is presented. Additionally, a secant‐based actuator mass update algorithm is investigated in order to improve convergence characteristics of the inner iteration loop. A nonlinear optimization algorithm is used to direct the design process. The methodology is demonstrated on the design of a large two‐dimensional L‐shaped structure in which it is desired to minimize the line‐of‐sight‐pointing error between the two ends of the L after a worst‐case slew maneuver.

On the control of a class of flexible manipulators using feedback linearization approach

The paper studies nonlinear dynamics and control of the Space Station based mobile, flexible, two-link manipulators accounting for elastic character of the joints. The governing highly nonlinear, nonautonomous and coupled equations of motion are described first followed by the modal discretization procedure. A parametric response study suggests situations with unacceptable levels of deflections and accelerations for certain proposed missions, as well as station libration and payload positioning errors. An inverse control technique is suggested to achieve high tracking accuracy of the MSS in presence of maneuver induced as well as other external and internal disturbances. The control strategy is so designed as to regulate the libration of the Space Station and to insure joints tracking of prescribed trajectories, while limiting the effect of the structural vibration during large slewing maneuvers of the MSS. Two different control schemes, both based on the feedback linearization technique, are developed and their relative merit assessed.

Dynamics and control of the Shuttle based large antenna system during slewing maneuvers

A relatively general formulation for studying dynamics of a large class of interconnected flexible and/or rigid bodies forming a chain type topology is developed. The problem is approached using the Lagrangian procedure with the generalized forces accounting for the environmental effects, damping and control. The flexible members are taken to be the Euler-Bernoulli beams with their bending and torsional deformations discretized using a series of admissible functions. As a particular case, the general formulation is applied to study complex dynamics of the SCOLE (Spacecraft COntrol Laboratory Experiment) system as proposed in the NASA's design challenge. The classical infinite time linear state feedback regulator utilizing the Shuttle's primary and vernier thrusters is designed to suppress the vibrations as well as control the Shuttle attitude motion. The results suggest that flexibility of the mast during the prescribed slewing maneuver substantially induces the line-of-sight error if the Shuttle is uncontrolled. However, the proposed control strategy can damp both the vibrational motion of the mast and librational motion of the Shuttle to the specified acceptable limit within 5 s of the completion of the maneuver.

Nonlinear strain-displacement relations and flexible multibody dynamics

This paper considers dynamics of chains of flexible bodies undergoing large rigid body motions but small elastic deflections. The role of nonlinear strain-displacement relations in the development of the motion equations correct to first order in elastic deflections is investigated. The general form of these equations linearized only in the small elastic deflections is presented, and the relative significance of various nonlinear terms is studied both analytically and through the use of numerical simulations. Numerical simulations are performed for a two-link chain constrained to move in the plane, subject to hinge torques. Each link is modeled as a thin beam. Slew maneuver simulation results are compared for models with and without properly modeled kinematics of deformation. The goal of this case study is to quantify the importance of the terms in the equations of motion that arise from the inclusion of nonlinear strain-displacement relations. It is concluded that unless the consistently linearized equations in elastic deflections and their time rates of change are available and necessary, the inconsistently (prematurely) linearized equations should be replaced in all cases by ruthlessly linearized equations, equations in which all nonlinear terms involving the elastic deflections and their time rates of change are ignored.

Performance of an Orbiting Flexible Mobile Manipulator

This paper presents a Lagrangian formulation for studying the dynamics and control of the Space Station based Mobile Servicing System (MSS) for a particular case of in-plane libration and maneuvers. The simplified case is purposely considered to focus on the effects of structural and joint flexibilities of the MSS on the complex interactions between the station and manipulator dynamics during slewing and translational maneuvers. The response results suggest that under critical combinations of parameters, the system can become unstable. During maneuvers, the deflection of the MSS can become excessive, leading to payload positioning error and the librational disturbance can also be significant. A linear quadratic regular is designed to simultaneously control the deflection of the manipulator and maintain the station at its operating configuration.