Gunter Stein

The LQG/LTR procedure for multivariable feedback control design

This paper provides a tutorial overview of the LQG/LTR design procedure for linear multivariable feedback systems. LQG/LTR is interpreted as the solution of a specific weighted H2-tradeoff between transfer functions in the frequency domain. Properties of this solution are examined for both minimum-phase and nonminimum-phase systems. This leads to a formal weight augmentation procedure for the minimum-phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights. While such arbitrary specifications are not possible for nonminimum-phase problems, a direct relationship between weights and sensitivities is developed for nonminimum-phase SISO and certain nonminimum-phase MIMO cases which guides the weight selection process.

Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics

This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated thai there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implication of the existence of such infinite-gain operators is that 1) sinusoidal reference inputs at specific frequencies and/or 2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.

Performance and robustness analysis for structured uncertainty

This paper introduces a nonconservative measure of performance for linear feedback systems in the face of structured uncertainty. This measure is based on a new matrix function, which we call the Structured Singular Value.

Dynamic inversion: an evolving methodology for flight control design

This paper describes nonlinear dynamic inversion as an alternative design method for flight controls. The method is illustrated with super-manoeuvring control laws for the F-18 high angle-of-attack research vehicle.

Future directions in control in an information-rich world

The Panel on Future Directions in Control, Dynamics, and Systems was formed in April 2000 to provide a renewed vision of future challenges and opportunities in the control field, along with recommendations to government agencies, universities, and research organizations to ensure continued progress in areas of importance to the industrial and defense base. The panel released a report in April 2002, the intent of which is to raise the overall visibility of research in control, highlight its importance in applications of national interest, and indicate some of the key trends that are important for continued vitality of the field. After a brief introduction, we summarize the report, discuss its applications and education and outreach, and conclude with some recommendations.

Robustness of adaptive control algorithms in the presence of unmodeled dynamics

This paper reports the outcome of an exhaustive analytical and numerical investigation of stability and robustness properties of a wide class of adaptive control algorithms in the presence of unmodeled dynamics and output disturbances. The class of adaptive algorithms considered are those commonly referred to as model-reference adaptive control algorithms, self-tuning controllers, and dead-beat adaptive controllers; they have been developed for both continuous-time systems and discrete-time systems. The existing adaptive control algorithms have been proven to be globally assymptotically stable under certain assumptions, the key ones being (a) that the number of poles and zeroes of the unknown plant are known, and (b) that the primary performance criterion is related to good command following. These theoretical assumptions are too restrictive from an engineering point of view. Real plants always contain unmodeled high-frequency dynamics and small delays, and hence no upper bound on the number of the plant poles and zeroes exists. Also real plants are always subject to unmeasurable output additive disturbances, although these may be quite small. Hence, it is important to critically examine the stability robustness properties of the existing adaptive algorithms when some of the theoretical assumptions are removed; in particular, their stability and performance properties in the presence of unmodeled dynamics and output disturbances. A unified analytical approach has been developed and documented in the recently completed Ph.D. thesis by Rohrs [15] that can be used to examine the class of existing adaptive algorithms. It was discovered that all existing algorithms contain an infinite-gain operator in the dynamic system that defines command reference errors and parameter errors; it is argued that such an infinite gain operator appears to be generic to all adaptive algorithms, whether they exhibit explicit or implicit parameter identification. The practical engineering consequences of the existence of the infinite-gain operator are disastrous. Analytical and simulation results demonstrate that sinusoidal reference inputs at specific frequencies and/or sinusoidal output disturbances at any frequency (including d.c.) cause the loop gain of the adaptive control system to increase without bound, thereby exciting the (unmodeled) plant dynamics, and yielding an unstable control system. Hence, it is concluded that none of the adaptive algorithms considered can be used with confidence in a practical control system design, because instability will set in with a high probability.

Respect the unstable

Control engineers often design feedback control systems for inherently unstable systems, to keep them operating safely. In such cases, there are fundamental limitations on the achievable sensitivity function. The article discusses the potentially serious consequences of sensitivity constraints, input saturation, and instability. Inadequacies of control systems in such cases have led to deaths.

Beyond singular values and loop shapes

This paper provides a tutorial look at the status of singular value loop shaping as a paradigm for multivariable feedback design. It shows that this paradigm is effective whenever a design problems specifications are spatially round, but that it can be arbitrarily conservative otherwise. This happens because singular value conditions for robust performance are not tight (sufficient but not necessary) and can severely overstate actual requirements. An alternate paradigm is discussed that promises to overcome these limitations. This alternative includes a more general problem formulation, a new matrix function mu, and tight conditions for both robust stability and robust performance. The current state of development of this paradigm supports analysis and comparisons of existing feedback designs. To a limited extent, it also supports formal mathematical synthesis of new optimal designs, although much research remains to be done in the synthesis area.

A Frequency-Domain Estimator for Use in Adaptive Control Systems

The paper presents a frequency-domain estimator which can identify both a nominal model of a plant as well as a frequency-domain bounding function on the modeling error associated with this nominal model. This estimator, which we call a robust estimator, can be used in conjunction with a robust control-law redesign algorithm to form a robust adaptive controller.

Integrated system identification and PID controller tuning by frequency loop-shaping

A systematic design methodology for proportional-integral-derivative (PID) controllers is presented. Starting from data sets, a model of the system and its uncertainty bounds are obtained. The parameters of the controller are tuned by a convex optimization algorithm, minimizing a weighted difference between the actual loop transfer function and a target in an /spl Lscr//sub 2///spl Lscr//sub /spl infin// sense. The target selection is guided by the identified model and its uncertainty. The problem of disjoint data sets and/or different models for the same system is also addressed. The method has proved successful in numerous practical cases showing both expediency in controller design and implementation and improved performance over existing controllers.