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Chuang, C.-H.

Publications and source records attributed to Chuang, C.-H..

14 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Robust stability of second-order systems

It has been shown recently how virtual passive controllers can be designed for second-order dynamic systems to achieve robust stability. The virtual controllers were visualized as systems made up of spring, mass and damping elements. In this paper, a new approach emphasizing on the notion of positive realness to the same second-order dynamic systems is used. Necessary and sufficient conditions for positive realness are presented for scalar spring-mass-dashpot systems. For multi-input multi-output systems, we show how a mass-spring-dashpot system can be made positive real by properly choosing its output variables. In particular, sufficient conditions are shown for the system without output velocity. Furthermore, if velocity cannot be measured then the system parameters must be precise to keep the system positive real. In practice, system parameters are not always constant and cannot be measured precisely. Therefore, in order to be useful positive real systems must be robust to some degrees. This can be achieved with the design presented in this paper.

Chuang, C.-H.↗
NASA NTRS1995

Multiple burn fuel-optimal orbit transfers: Numerical trajectory computation and neighboring optimal feedback guidance

This report describes current work in the numerical computation of multiple burn, fuel-optimal orbit transfers and presents an analysis of the second variation for extremal multiple burn orbital transfers as well as a discussion of a guidance scheme which may be implemented for such transfers. The discussion of numerical computation focuses on the use of multivariate interpolation to aid the computation in the numerical optimization. The second variation analysis includes the development of the conditions for the examination of both fixed and free final time transfers. Evaluations for fixed final time are presented for extremal one, two, and three burn solutions of the first variation. The free final time problem is considered for an extremal two burn solution. In addition, corresponding changes of the second variation formulation over thrust arcs and coast arcs are included. The guidance scheme discussed is an implicit scheme which implements a neighboring optimal feedback guidance strategy to calculate both thrust direction and thrust on-off times.

Chuang, C.-H.↗
NASA NTRS1994

Robust stability of second-order systems

This progress report gives current progress of the research in nonlinear robust control using positive real concept. The progress is documented in a draft paper. In the paper, the manipulator dynamics is reformulated differently from the existing equations of motion for free base robots. This new formulation gives a compact form of the dynamic equations for easy computation. The nonlinear terms are now considered. The results show that for an additional nonlinear friction term, the feedback controller designed using passivity concept works quite well. Although design of such a controller requires simulation of the dynamics for the example shown in the following draft, this design procedure is feasible.

Chuang, C.-H.↗
NASA NTRS1994

Theory and computation of optimal low- and medium-thrust transfers

This report describes the current state of development of methods for calculating optimal orbital transfers with large numbers of burns. Reported on first is the homotopy-motivated and so-called direction correction method. So far this method has been partially tested with one solver; the final step has yet to be implemented. Second is the patched transfer method. This method is rooted in some simplifying approximations made on the original optimal control problem. The transfer is broken up into single-burn segments, each single-burn solved as a predictor step and the whole problem then solved with a corrector step.

Chuang, C.-H.↗
NASA NTRS1994

Robust stability of second-order systems

Nonlinear control using feedback linearization or inverse dynamics for robotic manipulators yields good results in the absence of modeling uncertainty. However, modeling uncertainties due to unknown joint friction coefficients and payload variations can give rise to undesirable characteristics when these control systems are implemented. It is shown how passivity concepts can be used to supplement the feedback linearization control design technique, in order to make it robust with respect to the uncertain effects mentioned above. Results are obtained for space manipulators with freely floating base; however, they are applicable to fixed base manipulators as well. The controller guarantees asymptotic tracking of the joint variables. Closed-loop simulation results are illustrated for planar space manipulators for cases where uncertainty exists in friction modeling and payload inertial parameters.

Chuang, C.-H.↗
NASA NTRS1994

Theory and computation of optimal low- and medium-thrust transfers

This report presents two numerical methods considered for the computation of fuel-optimal, low-thrust orbit transfers in large numbers of burns. The origins of these methods are observations made with the extremal solutions of transfers in small numbers of burns; there seems to exist a trend such that the longer the time allowed to perform an optimal transfer the less fuel that is used. These longer transfers are obviously of interest since they require a motor of low thrust; however, we also find a trend that the longer the time allowed to perform the optimal transfer the more burns are required to satisfy optimality. Unfortunately, this usually increases the difficulty of computation. Both of the methods described use small-numbered burn solutions to determine solutions in large numbers of burns. One method is a homotopy method that corrects for problems that arise when a solution requires a new burn or coast arc for optimality. The other method is to simply patch together long transfers from smaller ones. An orbit correction problem is solved to develop this method. This method may also lead to a good guidance law for transfer orbits with long transfer times.

Chuang, C.-H.↗
NASA NTRS1993

Robust stability of second-order systems

A feedback linearization technique is used in conjunction with passivity concepts to design robust controllers for space robots. It is assumed that bounded modeling uncertainties exist in the inertia matrix and the vector representing the coriolis, centripetal, and friction forces. Under these assumptions, the controller guarantees asymptotic tracking of the joint variables. A Lagrangian approach is used to develop a dynamic model for space robots. Closed-loop simulation results are illustrated for a simple case of a single link planar manipulator with freely floating base.

Chuang, C.-H.↗
NASA NTRS1993

Theory and computation of optimal low- and medium-thrust transfers

This report presents the formulation of the optimal low- and medium-thrust orbit transfer control problem and methods for numerical solution of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and three-dimensional, non-coplanar, non-aligned elliptic terminal orbits. We setup some examples to demonstrate the ability of two indirect methods to solve the resulting TPBVP's. The methods demonstrated are the multiple-point shooting method as formulated in H. J. Oberle's subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are trade-offs to using either method. BOUNDSCO has very poor convergence for guesses that do not exhibit the correct switching structure. MBCM, however, converges for a wider range of guesses. However, BOUNDSCO's multi-point structure allows more freedom in quesses by increasing the node points as opposed to only quessing the initial state in MBCM. Finally, we note an additional drawback for BOUNDSCO: the routine does not supply information to the users routines for switching function polarity but only the location of a preset number of switching points.

Chuang, C.-H.↗
NASA NTRS1993

A robust controller for second-order systems using acceleration measurements

This paper presents a robust control design using strictly positive realness for second-order dynamic systems. The robust strictly positive real controller allows the system to be stabilized with only acceleration measurements. An important property of this design is that stabilization of the system is independent of the system parameters. The control design connects a virtual system to the given plant. The combined system is positive real regardless of system parameter uncertainty. Then any strictly positive real controllers can be used to achieve robust stability. A spring-mass system example and its computer simulations are presented to demonstrate this controller design. Robust performance property of this design is also demonstrated in a simple example.

Chuang, C.-H.↗
NASA NTRS1993

Computation of optimal low- and medium-thrust orbit transfers

This paper presents the formulation of the optimal low- and medium-thrust orbit transfer control problem, numerical methods for solution, and numerical solutions of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and 3D noncoplanar nonaligned elliptic terminal orbits. We set up examples to demonstrate the ability of two indirect methods to solve the resulting two point boundary value problems (TPBVP). The methods demonstrated are the multiple point shooting method as formulated in Oberle's (1987) subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are tradeoffs to using either method. We present numerical solutions of planar transfers in which both the initial orbit exit and final orbit entry points have been optimized. These solutions include two- and three-burn transfers. The methods used show an ability to handle thrust down to at least T/W(o) = O(10 exp -3). They also show similar convergence abilities with or without the oblateness and drag terms. We discuss the issue of maximizing with respect to the final time and provide evidence that implies a local optimum at a maximum final time for a given number of burns.

Chuang, C.-H.↗
NASA NTRS1993

A passivity based controller for free base manipulators

A feedback linearization technique is used in conjunction with passivity concepts to design robust controllers for free base robots. It is assumed that bounded modeling uncertainties exist in the inertia matrix and the vector representing the coriolis, centripetal, and friction forces. Under these assumptions, the controller guarantees asymptotic tracking of the joint variables. A Lagrangian approach is used to develop a dynamic model for space robots. Closed-loop simulation results are illustrated for a simple case of a single link planar space manipulator with freely floating base.

Chuang, C.-H.↗
NASA NTRS1992

Determination of robust stability margin for second-order systems

Robust stabilization of uncertain systems has been extensively investigated and the stability test for the whole set of uncertain parameters has been reduced to a finite number of test points, four points for the characteristic polynomial with independent coefficients. As a result the robust stability margin can be determined using a reasonable amount of computation. It is impossible to apply the results of the test to a practical system as the coefficients of the characteristic polynomial for a physical system are usually functions of uncertain parameters. However, many physical systems may be represented by a second-order mass-spring-damper system with a special multilinear form in its characteristic polynomial. This paper investigates second-order mass-spring-damper systems and the reduction of the number of test points. It is shown that such a system with arbritrary compensators always has a multilinear characteristic polynomial. It is also shown that a line in the two-dimensional parameter space forms the boundary after the mapping of a multilinear characteristic polynomial and this interior extreme line forms a conic curve in the complex plane. The boundary of uncertain domain for a multilinear polynomial with two uncertainty parameters can be determined analytically using this curve, and the four sides image of a square of the uncertain parameter. Therefore, the stability margin may be determined by checking the intersections of the boundary with the zero point. A similar procedure can be used for second-order systems with more than two uncertainty parameters when parameter optimization is used in determining the boundary.

Chuang, C.-H.↗
NASA NTRS1989

Computational analysis of a stability robustness margin for structured real-parameter perturbations

An efficient computational method is presented for stability robustness analysis with structured real-parameter perturbations. A generic model of a class of uncertain dynamical systems is used as an example. The parameter uncertainty is characterized by a real scalar, epsilon. Multilinearity of the closed-loop characteristic polynomial is exploited to permit application of the mapping theorem to calculate the stability robustness margin. It is found that sensitive geometry of the stability boundary in the epsilon, omega-plane renders problematic the calculation of the minimum epsilon as a function of omega. This difficulty is avoided by calculating the minimum distance to the image of the uncertainty domain over omega as a function of epsilon. It is also shown that a certain class of uncertain dynamical systems has the required multilinearity property and are thus amenable to the proposed technique.

Wedell, Evan↗