Multivariable Feedback Systems Research Articles

Tradeoffs in Networked Feedback Systems: From Information-Theoretic Measures to Bode-Type Integrals

This paper investigates performance limitation issues of multivariable networked feedback systems with multiport communication channels. We develop a general information-theoretic paradigm for analyzing the limitations and tradeoffs imposed by communication channels, which is enabled by the development of new information measures and Bode-type integral inequalities. The integral inequalities quantify the tradeoffs in disturbance attenuation for broad classes of systems consisting of linear time-invariant plants and causal, possibly nonlinear, time-varying stabilizing controllers communicating over general noisy channels with causal encoders and decoders. The channel blurredness, a newly developed information measure for the quality of multiport communication channels, is used to characterize the effect of communication channel constraints on the integrals and henceforth the tradeoff in disturbance attenuation. For several canonical channels with power constraints, such as additive white Gaussian noise channels, additive colored Gaussian noise channels, and fading channels, we derive explicit forms for the channel blurredness, which, together with the Bode-type integral inequalities, show that to mitigate the noise effect on performance tradeoff, the power of the communication channels must be distributed in ways fundamentally different from the Shannon’s classical “water-filling” power allocation policy.

Subsystem identification of multivariable feedback and feedforward systems

We present a frequency-domain technique for identifying multivariable feedback and feedforward subsystems that are interconnected with a known subsystem. This subsystem identification algorithm uses closed-loop input–output data, but no other system signals are assumed to be measured. In particular, neither the feedback signal nor the outputs of the unknown subsystems are assumed to be measured. We use a candidate-pool approach to identify the feedback and feedforward transfer function matrices, while guaranteeing asymptotic stability of the identified closed-loop transfer function matrix. The main analytic result shows that if the data noise is sufficiently small and the candidate pool is sufficiently dense, then the parameters of the identified feedback and feedforward transfer function matrices are arbitrarily close to the true parameters.

The design and evaluation of a multi-sensory vibrotactile feedback system for a myoelectric prosthetic hand

Upper-limb amputees have reported that one of their main dissatisfactions with current commercialised prosthetic arms is a lack of sensory feedback. The current study investigates the feasibility of providing feedback of grip force, slippage, and finger position through vibrotactile stimulators to the prosthetic users. Tests are performed to determine subject’s spatial sensitivity as well as their abilities to differentiate discrete vibration intensity levels. We find that human subjects can correctly identify discrete sensory levels (with 90% accuracy) from 62 Hz to 250 Hz for tactors placed at least 3 cm apart. The accuracy of the EMG classifier system would decrease if all three tactors are activated. Even though a multivariable vibrotactile feedback system may not be feasible initially due to information overload, the user performance may improve with training. Multi-tactor system can be implemented with a slight decrease in electromyographic signal classification for the control of a neuroprosthetic hand.

Exact computation of loop gain margins of multivariable feedback systems

This paper addresses the problem of loop gain margins of multivariable feedback system. A frequency domain approach is proposed to accurately computing loop gain margins for multivariable feedback systems. With the help of vector mapping method, the loop gain margins problem is converted to some constrained optimization, which is solved numerically by the Lagrange multiplier and Newton–Raphson iteration algorithm. The proposed approach can determine all the stabilizing boundaries and provide exact gain margins in comparison with conservativeness of the linear matrix inequalities (LMI) results reported before.

Robust control for a two-axis gimbaled sensor system with multivariable feedback systems

A dynamic model for the stabilisation loop of a two-axis gimbaled sensor system is formulated and system parameters have been identified by practical experiments. The validity of the dynamic model is illustrated by the experimental and simulation result. The Lead-proportional-integral (PI) controller design using a loop-shaping method based on the frequency response for the stabilisation loop of the sensor system is realised. This practical design approach has been proven to be simple and robust in actual application. The robust H∞ controller design approach combining model matching and mixed sensitivity problem to improve the command following and disturbance rejection performance in the presence of external disturbances and model uncertainties is implemented, which is designed within the framework of the standard H∞ optimisation problem by combining a conventional mixed sensitivity and model matching problem with robust stability. The experimental and simulation results show that the both two proposed controllers satisfy all desired requirements for the stabilisation loop associated with the gain crossover frequency, the gain and phase margin and the body-motion decoupling performance. It is shown through performance comparison and analysis that the proposed H∞ controller is preferable to the proposed Lead-PI controller in terms of system stability, the disturbance rejection rate and because of its fast time response characteristics. However, it is clear that the two proposed controller design procedures for the robust control of the stabilisation loop of a two-axis gimbaled sensor system can be very effective in practical applications in terms of both stability and disturbance rejection.

Active Optics of Large Segmented Mirrors: Dynamics and Control

This paper examines the active optics of future large segmented telescopes from the point of view of dynamic simulation and control. The first part of the paper is devoted to the modeling of the mirror. The model has a moderated size and separates the quasi-static behavior of the mirror (primary response) from the dynamic response (secondary or residual response). The second part of the paper is devoted to control. The control strategy considers explicitly the primary response ofthe telescope through a singular value controller. The control-structure interaction is addressed with the general robustness theory of multivariable feedback systems, where the secondary response is considered as uncertainty. This approach is very fast and allows extensive parametric studies. The study is illustrated with an example involving 90 segments, 270 inputs, and 654 outputs.

Small-signal model and dynamic analysis of variable speed induction machine wind farms

A unified, modular, small-signal dynamic model for an induction machine-based wind farm is presented. The proposed model can represent an arbitrary number of fixed-speed, partially variable-speed (doubly fed) and variable-speed induction machine-based wind units in a wind farm. The model represents the dynamics of (i) each wind turbine-generator electromechanical system, (ii) each converter system and the corresponding controls and (iii) the host electrical grid, within the subsynchronous frequency range (0.1–60 Hz). In contrast to the widely used state-space formulation, the proposed approach is based on developing electrical and mechanical transfer-function matrices to formulate the overall system as a multivariable feedback system. Thus, it provides significant flexibility to represent a large number of wind units and their controllers, identical or non-identical, within a wind farm.Based on the developed model, a frequency response-based method is also introduced, as an alternative to the eigen analysis approach, for small-signal subsynchronous dynamic analysis of the wind farm and its host electrical grid. The proposed method provides a new performance robustness criterion for performance evaluation and also a design tool based on the ‘size’ of the system transfer-function matrix. The concept of induced norm is adopted here as a measure of matrix size. As an example, applications of the model and the analysis approach to a two-unit wind farm is presented and the results are validated based on time-domain simulation studies in the PSCAD/EMTDC environment.

Model of the RFX-mod poloidal field circuit

Aiming at predictive simulation of the plasma magnetic parameters during the RFX-mod discharges, a model was designed to simulate the poloidal field power supply system, detailing each individual switching unit and the single ac–dc converter with its local control circuit, together with the magnet system and the complete multi-variable feedback system devoted to the plasma shape and position control. The model was realized by coupling a linear model of the axi-symmetric evolution of the plasma with a detailed implementation of the RFX-mod circuit developed by means of the SimPowerSystem Toolbox in the framework of the Matlab-Simulink™ package. In order to evolve the plasma current, a Bessel Function Model (BFM) is adopted to implement the energy transfer from the toroidal to the poloidal field. The axi-symmetric controller is implemented to close the loop and is the same running on the VME nodes of the real control system. The model was successfully tested against experimental data, showing good agreement between measured and calculated waveforms.

Plenary Session II: Neurophysiological Monitoring of the Critically Ill 8:15 a.m.–10:15 a.m.

1 Ronald Emerson ( 1 Neurology, Columbia University, New York, NY )Until recently, functional neurological assessment of neurologically critically ill patients has been limited largely to periodic physical examinations, often compromised by medication effects, along with occasional, brief EEG's. This is changing with the availability of continuous/EEG monitoring, made practical by recent advances in computer and network technology. Indeed, in some centers, continuous EEG monitoring, with or without concurrent video, has become part of routine neuro‐critical care. Its greatest initial impact has been on the recognition and management of non‐convulsive seizures. The use of EEG monitoring for real‐time detection of cerebral ischemia will likely become compelling as effective treatments for acute stroke emerge. Practical implementation of EEG‐based cerebral ischemia detection in the ICU, however, awaits development of reliable, robust automated detection algorithms capable of triggering bedside alarms. Concurrent monitoring of other physiological parameters, including blood pressures, intracranial pressure and brain tissue oxygenation along with EEG‐derived parameters may provide the basis for development of better treatment models incorporating multivariable feedback systems. Evoked potentials can provide useful prognostic information, with long latency evoked potentials attracting recent attention as possible predictors of recovery of consciousness in comatose patients.

Optimal control of multirate sampled-data feedback systems via a polynomial approach

The linear quadratic Gaussian design of multirate-sampled multivariable feedback systems using input-output models is described. The theoretical emphasis is placed upon the formulation of augmented representations in which each variable is specified at its associated sample instants throughout one cycle of the sequence of sampling operations. The structures of the polynomial matrices utilised illuminate the causality issues involved and facilitate the acquisition of the optimal control solution from coupled diophantine equations.

New approach to milling circuit control—robust inverse Nyquist array design

The aim of this paper is to present an application of robust inverse Nyquist array control design method to a milling circuit in Majdanpek Copper Mine. An existent model of a milling circuit was adopted to respond to robust inverse Nyquist array methodology demand by introducing model uncertainty, and optimal robust controller of milling circuit is designed. The proposed controller is robust for reference signals. The robustness of multivariable feedback systems with designed controller is tested and compared with different, previously designed multivariable controllers. Simulation results, in time domain, demonstrate the preferable performance of the designed robust controller in setpoint tracking. Implementation of the new controller without any investments in new equipment significantly improves performance of the milling process.

Predictive control of fast output—sampled digital feedback systems via a polynomial approach

This paper describes the synthesis of model-based predictive controllers for multivariable digital feedback systems in which the plant output signals are measured at a faster rate than the controls are applied. In contrast with the recent literature devoted to multirate sampled-data system theory, where state-variable system representations are used exclusively, a polynomial modelling approach that exploits the frequency and switch decomposition techniques established in the 1950s is adopted. It is demonstrated that the principal advantage of fast output signal-sampled predictive control algorithms lies in their potential to suppress process and, particularly, measurement noise disturbances.

Achievable performance of multivariable systems with unstable zeros and poles

This paper examines the fundamental limitations imposed by unstable (right half plane; RHP) zeros and poles in multivariable feedback systems. We generalize previously known controller-independent lower bounds on the H

Multivariable model state feedback: Computationally simple, easy-to-tune alternative to MPC

Methods for the design and tuning of multivariable model state feedback (MMSF) systems for complete and triangular output decoupling of inherently stable processes are presented. MMSF is a method of implementing multivariable IMC controllers that substantially reduces the complexity of the implementation and compensates for control effort saturation. Complexity is reduced because the controls are formed as a linear combination of past and current model states. Saturation-induced directionality problems are avoided by temporarily increasing filter time constants to bring the control vector into the constraint set. The possibility that needed future controls will be inadequate to compensate for past control actions is avoided by setting minimum values for the controller filter time constants. The feedback structure of MMSF facilitates on-line tuning, one process variable at a time. Also, because MMSF is a form of IMC, it can be tuned off-line to accommodate process uncertainty using H∞ methods.

Logarithmic integrals, interpolation bounds, and performance limitations in MIMO feedback systems

We study performance limitation issues found in linear multivariable feedback systems. Our main contributions include Bode and Poisson type integral inequalities and performance limits for the sensitivity and complementary sensitivity functions. These results characterize and quantify explicitly how open-loop unstable poles and nonminimum phase zeros may impose inherent limitations on feedback design and fundamental limits on the best achievable performance. The role of time delay is also studied in this context. Most notably, we show that the performance and design limitations in multivariable systems intrinsically depend on the locations as well as directions of unstable poles and nonminimum phase zeros, and in particular, on how pole and zero directions are aligned. The latter is characterized by angles measuring the mutual orientation between zero and pole directions, and it is shown to play a crucial role in multivariable system design.

The loop shaping design procedure for parallel operating dc/dc converters

Simple and straightforward three-stage design procedure for multivariable feedback systems is presented. Developed controller for parallel operating dc/dc converters is compared to μ-optimal Internal Model Control and decentralized controllers, both in frequency and time domain. The Loop Shaping Design Procedure shows flexibility when limits on control variables are placed. Considerable advantages come from the separate performance and stability considerations and the open-loop shaping approach. The procedure has the ability to “account for plant characteristics” and to dampen lightly damped plant modes using the feedback effect, rather than to cancel them with controller zeros. Cancelation of these modes by some less flexible robust optimization techniques can lead to poor robust stability and robust performance properties.

Integral constraints and performance limits on complementary sensitivity: discrete-time systems

We study performance limitation issues for multivariable discrete-time feedback systems. The complementary sensitivity function is employed as a performance measure, and Bode and Poisson-type integral inequalities and H ∞ -type performance limits are derived. The results exhibit frequency-dependent constraints as well as best achievable limits on the complementary sensitivity function, which are shown to be determined by nonminimum phase zeros, unstable poles, and time delays. In particular, the directions of such zeros and poles are seen to play a central role to this effect.

Robust Decoupled System Design of Uncertain Multivariable Feedback Systems

This paper presents a design algorithm of involving robust decoupled control of uncertain multivariable feedback systems. Two-degree-of-freedom system structure is adopted to handle the quantitative robustness and decoupled performance requirements. Quantitative feedback theory is applied for loop compensator design to achieve quantitative robustness. A decoupled model matching approach is employed for prefilter design to achieve input-output decoupling performance. Thus, the design method of two-degree-of-freedom compensators is proposed to achieve decoupled system control with quantitative robust performance. Since internal stability is satisfied, this design method performs appropriately for any stable or unstable, minimum or non-minimum phase system. The AFTI/F-16 flight control system is considered as the design example to illustrate the design algorithm.

Achievable H ∞ -performance of multivariable systems with unstable zeros and poles

Abstract This paper examines the limitations imposed by Right Half Plane (RHP) zeros and poles in multivariable feedback systems. The main result is to provide lower bounds on ‖WXV(s)‖∞ where X is S, SI, T or TI (sensitivity and complementary sensitivity). Previously derived lower bounds on the H∞-norm of S and T are thus generalized to the case with matrix-valued weights, including bounds for reference tracking, disturbance rejection, and input usage.

Integral constraints and performance limits on complementary sensitivity: Discrete-time systems

We study performance limitation issues for multivariable discrete-time feedback systems. The complementary sensitivity function is employed as a performance measure, and Bode and Poisson type integral inequalities and H ∞ type performance limits are derived. The results exhibit frequency-dependent constraints as well as best achievable limits on the complementary sensitivity function, which are shown to be constrained by nonminimum phase zeros and unstable poles. In particular, the directions of such zeros and poles are seen to play a central role to this effect.