James S. Freudenberg

Right half plane poles and zeros and design tradeoffs in feedback systems

This paper expresses limitations imposed by right half plane poles and zeros of the open-loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed-loop system. The limitations are determined by integral relationships which must be satisfied by these functions. The integral relationships are interpreted in the context of feedback design.

Feedback Stabilization Over Signal-to-Noise Ratio Constrained Channels

There has recently been significant interest in feedback stabilization problems over communication channels, including several with bit rate limited feedback. Motivated by considering one source of such bit rate limits, we study the problem of stabilization over a signal-to-noise ratio (SNR) constrained channel. We discuss both continuous and discrete time cases, and show that for either state feedback, or for output feedback delay-free, minimum phase plants, there are limitations on the ability to stabilize an unstable plant over an SNR constrained channel. These limitations in fact match precisely those that might have been inferred by considering the associated ideal Shannon capacity bit rate over the same channel.

Control of variable geometry turbocharged diesel engines for reduced emissions

The emission control problem for an automotive direct injected compression ignition (diesel) engine equipped with exhaust gas recirculation (EGR) and a variable geometry turbocharger (VGT) is considered. The objective is to operate the engine to meet drivers torque demand and minimize NO/sub x/ emissions while at the same time avoiding visible smoke generation. It is demonstrated that the steady-state optimization of engine emissions results in operating points where EGR and VGT actuators are in effect redundant in their effect on the variables that most directly affect the emissions. A multivariable feedback controller is proposed which accounts for this actuator redundancy. Furthermore, it coordinates the two actuators to fully utilize their joint effect on engine emission performance. Experimental results confirm good response properties of the proposed controller.

A relationship between sensitivity and stability of multivariable feedback systems

Both comparison sensitivity and robust stability analysis attempt to extend concepts which are well understood in scalar feedback systems to multivariable control system design. Although the two bodies of work have developed about a decade apart, the basic philosophies are similar. Both attempt to maintain a system property (sensitivity reduction versus stability) in the presence of plant modeling errors. This paper demonstrates how the similarity in philosophy translates into a similarity in results and interpretations.

Nodal dynamics, not degree distributions, determine the structural controllability of complex networks.

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167–173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set, is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.

Power Flow Characterization of a Bidirectional Galvanically Isolated High-Power DC/DC Converter Over a Wide Operating Range

This paper studies the power flow characterization of a bidirectional galvanically isolated high-power dual active bridge DC/DC converter. In experimental tests at the University of Michigan, we have observed three phenomena, which we term as internal power transfer, phase drift, and low system efficiency, that are present under certain operating conditions. These phenomena cannot be explained by conventional power transfer analysis. The authors develop a new model, based on a detailed analysis over a short time scale, that incorporates additional parameters, including the power semiconductor voltage loss and dead time. The new power flow model may be used to explain the observed phenomena and to characterize the power flow of the converter. The model may also be used to perform accurate power flow computations over a wide operating range, thereby supporting optimal hardware design, operating range selection, and power management strategy development. Experimental results are presented to illustrate the validity of the new model.

Loop transfer recovery for nonminimum phase plants

A study of what happens when the loop transfer recovery (LTS) procedure is applied to nonminimum-phase (NMP) plants, how design limitations due to right-half-plane zeros manifest themselves in the LTR procedure, and how this knowledge can be incorporated into design is presented. Explicit expressions are given for the asymptotic behavior of the loop transfer and sensitivity functions resulting from application of the LTR procedure to nonminimum-phase plants. It is shown that there exists a tradeoff between the feedback properties of the state feedback loop and the ability to recover those properties using the LTR procedure. >

Control of semiconductor manufacturing equipment: real-time feedback control of a reactive ion etcher

This paper describes the development of real-time control technology for the improvement of manufacturing characteristics of reactive ion etchers. A general control strategy is presented. The principal ideas are to sense key plasma parameters, develop a dynamic input-output model for the subsystem connecting the equipment inputs to the key plasma variables, and design and implement a multivariable control system to control these variables. Experimental results show that this approach to closed-loop control leads to a much more stable etch rate in the presence of a variety of disturbances as compared to current industrial practice. >

Stabilization and Disturbance Attenuation Over a Gaussian Communication Channel

We consider the problem of stabilizing an unstable system driven by a Gaussian disturbance using a feedback signal transmitted over a memoryless Gaussian communication channel. By applying the concept of entropy power, we show that the mean square norm of the state vector must satisfy a lower bound that holds for any causal, measurable communication and control strategies that result in signals having well defined differential entropy. In addition, we show that use of nonlinear, time varying strategies does not allow stabilization over a channel with a lower signal-to-noise ratio than that achievable with linear time invariant state feedback. Finally, we show that for scalar systems the lower bound on the mean square norm of the state is tight, and achievable using linear time invariant communication and control.

A sensitivity tradeoff for plants with time delay

In this paper we show that the sensitivity function of a scalar feedback system must satisfy an integral constraint when the open-loop transfer function is strictly proper and contains a time delay. The integral constraint is identical to the classical Bode sensitivity integral, which holds provided the open-loop gain has greater than a one-pole rolloff. The design implications of the two constraints are somewhat different, however, and this difference is discussed. The relation between open-loop phase and a conflict between bandwidth and sensitivity properties is explored.