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NASA NTRS1984

Analytical redundancy and the design of robust failure detection systems

The Failure Detection and Identification (FDI) process is viewed as consisting of two stages: residual generation and decision making. It is argued that a robust FDI system can be achieved by designing a robust residual generation process. Analytical redundancy, the basis for residual generation, is characterized in terms of a parity space. Using the concept of parity relations, residuals can be generated in a number of ways and the design of a robust residual generation process can be formulated as a minimax optimization problem. An example is included to illustrate this design methodology. Previously announcedd in STAR as N83-20653

Chow, E. Y.↗

NASA NTRS1985

Robust Adaptive Control

Several concepts and results in robust adaptive control are are discussed and is organized in three parts. The first part surveys existing algorithms. Different formulations of the problem and theoretical solutions that have been suggested are reviewed here. The second part contains new results related to the role of persistent excitation in robust adaptive systems and the use of hybrid control to improve robustness. In the third part promising new areas for future research are suggested which combine different approaches currently known.

Narendra, K. S.↗

NASA NTRS1985

Robust failure detection filters

The robustness of detection filters applied to the detection of actuator failures on a free-free beam is analyzed. This analysis is based on computer simulation tests of the detection filters in the presence of different types of model mismatch, and on frequency response functions of the transfers corresponding to the model mismatch. The robustness of detection filters based on a model of the beam containing a large number of structural modes varied dramatically with the placement of some of the filter poles. The dynamics of these filters were very hard to analyze. The design of detection filters with a number of modes equal to the number of sensors was trivial. They can be configured to detect any number of actuator failure events. The dynamics of these filters were very easy to analyze and their robustness properties were much improved. A change of the output transformation allowed the filter to perform satisfactorily with realistic levels of model mismatch.

Sanmartin, A. M.↗

NASA NTRS1986

Control design for robust stability in linear regulators: Application to aerospace flight control

Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.

Yedavalli, R. K.↗

NASA NTRS1986

Robust multivariable controller design for flexible spacecraft

Large, flexible spacecraft are typically characterized by a large number of significant elastic modes with very small inherent damping, low, closely spaced natural frequencies, and the lack of accurate knowledge of the structural parameters. Summarized here is some recent research on the design of robust controllers for such spacecraft, which will maintain stability, and possible performance, despite these problems. Two types of controllers are considered, the first being the linear-quadratic-Gaussian-(LQG)-type. The second type utilizes output feedback using collocated sensors and actuators. The problem of designing robust LQG-type controllers using the frequency domain loop transfer recovery (LTR) method is considered, and the method is applied to a large antenna model. Analytical results regarding the regions of stability for LQG-type controllers in the presence of actuator nonlinearities are also presented. The results obtained for the large antenna indicate that the LQG/LTR method is a promising approach for control system design for flexible spacecraft. For the second type of controllers (collocated controllers), it is proved that the stability is maintained in the presence of certain commonly encountered nonlinearities and first-order actuator dynamics. These results indicate that collocated controllers are good candidates for robust control in situations where model errors are large.

Joshi, Suresh M.↗

NASA NTRS1988

A method for designing robust multivariable feedback systems

A new methodology is developed for the synthesis of linear, time-invariant (LTI) controllers for multivariable LTI systems. The aim is to achieve stability and performance robustness of the feedback system in the presence of multiple unstructured uncertainty blocks; i.e., to satisfy a frequency-domain inequality in terms of the structured singular value. The design technique is referred to as the Causality Recovery Methodology (CRM). Starting with an initial (nominally) stabilizing compensator, the CRM produces a closed-loop system whose performance-robustness is at least as good as, and hopefully superior to, that of the original design. The robustness improvement is obtained by solving an infinite-dimensional, convex optimization program. A finite-dimensional implementation of the CRM was developed, and it was applied to a multivariate design example.

Milich, David Albert↗

NASA NTRS1988

Robustness with real parametric and structured complex uncertainty

The problem of robust stability and performance in feedback control systems with n real (possibly related) uncertain parameters and structured unmodeled dynamics (the latter taking the form of m complex blocks dynamic uncertainties) is considered. A robustness margin rm is defined with respect to such model uncertainty structure and an algorithm is developed to compute it. Robust stability and performance are characterized in terms of r sub m or the structured singular value mu. An iterative procedure using the above algorithm is given to compute tight bounds on k sub m and mu. These bounds are exact for the case m = 3 or less.

Pena, Ricardo S. Sanchez↗

NASA NTRS1988

A method for designing robust multivariable feedback systems

A new methodology is developed for the synthesis of linear, time-invariant (LTI) controllers for multivariable LTI systems. The aim is to achieve stability and performance robustness of the feedback system in the presence of multiple unstructured uncertainty blocks; i.e., to satisfy a frequency-domain inequality in terms of the structured singular value. The design technique is referred to as the causality recovery methodology (CRM). Starting with an initial (nominally) stabilizing compensator, the CRM produces a closed-loop system whose performance-robustness is at least as good as, and hopefully superior to, that of the original design. The robustness improvement is obtained by solving an infinite-dimensional, convex optimization program. A finite-dimensional implementation of the CRM was developed, and it was applied to a multivariate design example.

Milich, David A.↗

NASA NTRS1989

On the control of elastic vehicles - Model simplification and stability robustness

Quantitative criteria are presented for model simplification, or order reduction, such that the reduced order model may be used to synthesize and evaluate a control law, and the stability and stability robustness obtained using the reduced-order model will be preserved when controlling the full-order system. The error introduced due to model simplification is treated as modeling uncertainty, and some of the results from multivariable robustness theory are brought to bear on the model simplification problem. A numerical procedure developed previously is shown to lead to results that meet the necessary criteria. The procedure is applied to reduce the model of a flexible aircraft. Also, the importance of the control law itself, in meeting the modeling criteria, is underscored. An example is included that demonstrates that an apparently robust control law actually amplifies modest modeling errors in the critical frequency region, and leads to undesirable results. The cause of this problem is identified to be associated with the canceling of lightly-damped transmission zeroes in the plant.

Schmidt, David K.↗

NASA NTRS1989

Robustness analysis for real parametric uncertainty

Some key results in the literature in the area of robustness analysis for linear feedback systems with structured model uncertainty are reviewed. Some new results are given. Model uncertainty is described as a combination of real uncertain parameters and norm bounded unmodeled dynamics. Here the focus is on the case of parametric uncertainty. An elementary and unified derivation of the celebrated theorem of Kharitonov and the Edge Theorem is presented. Next, an algorithmic approach for robustness analysis in the cases of multilinear and polynomic parametric uncertainty (i.e., the closed loop characteristic polynomial depends multilinearly and polynomially respectively on the parameters) is given. The latter cases are most important from practical considerations. Some novel modifications in this algorithm which result in a procedure of polynomial time behavior in the number of uncertain parameters is outlined. Finally, it is shown how the more general problem of robustness analysis for combined parametric and dynamic (i.e., unmodeled dynamics) uncertainty can be reduced to the case of polynomic parametric uncertainty, and thus be solved by means of the algorithm.

Sideris, Athanasios↗

NASA NTRS1990

Multivariable flight control synthesis and literal robustness analysis for an aeroelastic vehicle

An integrated flight/aeroelastic control law is developed analytically for a hypothetical large supersonic transport aircraft in which the first aeroelastic mode frequency of the fuselage (6 rad/sec) is near the short-period mode (2 rad/sec). The approach employed is based on a linear-quadratic-regulator (LQR) formulation (yielding model-following state-feedback gains), followed by asymptotic loop-transfer recovery of LQR robustness (to produce an output-feedback control law). The derivation is outlined, and numerical results comparing the performance and multivariate stability robustness of the present controller with those of a classical controller are presented in graphs. The two controllers are shown to have similar characteristics, even with respect to the sources of limitations on robustness.

Schmidt, David K.↗

NASA NTRS1990

Experimental study of robustness in adaptive control for large flexible structures

An experimental study is performed to investigate the robustness of model reference adaptive control for the large flexible structures control application. The main nonidealities of concern are unmodeled dynamics, input saturation, and time delay effects (here, actuator and sensor dynamics are lumped into the last item for convenience). This study focuses on the robustness with respect to input saturation and time delay effects, since robustness to unmodeled dynamics is inherent to the basic algorithm and has been demonstrated experimentally elsewhere.

Ih, Che-Hang Charles↗

NASA NTRS1991

Control of a small working robot on a large flexible manipulator for suppressing vibrations: Development of a robust control law for flexible robot and it's stability analysis

Researchers developed a robust control law for slow motions for the accurate trajectory control of a flexible robot. The control law does not need larger velocity gains than position gains, which some researchers need to ensure the stability of a rigid robot. Initial experimentation for the Small Articulated Manipulator (SAM) shows that control laws that use smaller velocity gains are more robust to signal noise than the control laws that use larger velocity gains. Researchers analyzed the stability of the composite control law, the robust control for the slow motion, and the strain rate feedback for the fast control. The stability analysis was done by using a quadratic Liapunov function. Researchers found that the flexible motion of links could be controlled by relating the input force to the flexible signals which are sensed at the near tip of each link. The signals are contaminated by the time delayed input force. However, the effect of the time delayed input force can be reduced by giving a certain configuration to the SAM.

Soo, Han Lee↗

NASA NTRS1991

Synthesis of structural/control systems robust with respect to design variable tolerances

A methodology is presented for the synthesis of control augmented structures which can be modeled as an assemblage of beam, truss, and nonstructural mass elements augmented by a robust noncollocated direct output feedback control system. The control system is robust in the sense that it can tolerate manufacturing and realization errors. The robust control system is synthesized using a constraint buffering technique in conjunction with the approximation concepts approach to system synthesis. All of the design constraints on the system, including the dynamic stability, are buffered by a nonlinear quantity that is a function of acceptable tolerances on the design variables and the sensitivity of the constraints to changes in these design variables. Numerical results which illustrate the effectiveness of the method presented are given.

Thomas, H. L.↗

NASA NTRS1991

A sequential approach to multivariable stability robustness analysis

In sequential loop closure, the importance of evaluating the stability and stability robustness at the intermediate loop closures is well known, yet how the stability and stability robustness evaluated at the intermediate steps contribute to the stability and stability robustness of the overall feedback system must be developed. An analysis of the complete feedback system reveals the multivariable Nyquist contributions from the intermediate loop closures. It is also shown that the results greatly simplify if frequency separation exists between the intermediate loops. The analysis is presented with a two-step loop closure procedure using 'inner' and 'outer' loops which can be generalized to multi-step situations. The control of the longitudinal dynamics of an aircraft is addressed to further clarify and demonstrate the results.

Newman, Brett↗

NASA NTRS1991

Robust Kalman filter design for predictive wind shear detection

Severe, low-altitude wind shear is a threat to aviation safety. Airborne sensors under development measure the radial component of wind along a line directly in front of an aircraft. In this paper, optimal estimation theory is used to define a detection algorithm to warn of hazardous wind shear from these sensors. To achieve robustness, a wind shear detection algorithm must distinguish threatening wind shear from less hazardous gustiness, despite variations in wind shear structure. This paper presents statistical analysis methods to refine wind shear detection algorithm robustness. Computational methods predict the ability to warn of severe wind shear and avoid false warning. Comparative capability of the detection algorithm as a function of its design parameters is determined, identifying designs that provide robust detection of severe wind shear.

Stratton, Alexander D.↗

NASA NTRS1991

Robustness analysis of multirate and periodically time varying systems

A new method for analyzing the stability and robustness of multirate and periodically time varying systems is presented. It is shown that a multirate or periodically time varying system can be transformed into an equivalent time invariant system. For a SISO system, traditional gain and phase margins can be found by direct application of the Nyquist criterion to this equivalent time invariant system. For a MIMO system, structured and unstructured singular values can be used to determine the system's robustness. The limitations and implications of utilizing this equivalent time invariant system for calculating gain and phase margins, and for estimating robustness via singular value analysis are discussed.

Berg, Martin C.↗

NASA NTRS1991

Robustness of solutions to a benchmark control problem

The stochastic robustness of solutions to a benchmark control design problem has been analyzed. The analysis quantifies the controllers' stability and performance robustness with structured uncertainties in up to six system parameters. The analysis provides insights about system response that are not readily derived from other robustness criteria, providing a common ground for judging controllers produced by alternative methods.

Stengel, Robert F.↗