Loop Transfer Recovery Design Research Articles

Loop transfer recovery design for synchronization of homogeneous linear multi-agent systems

In this paper we propose the use of loop transfer recovery procedure in the context of cooperative control to aid the design of output feedback synchronization controllers with desirable performance characteristics. It is shown that, for a certain class of linear multi-agent systems, an upper bound on the singular values of the sensitivity matrix for the global networked system can be related to the dynamics of a classical single-system Kalman filter. A numerical example is presented to illustrate the main conclusions of this paper.

Reduced‐order LQG/LTR procedure for the plant output side

SummaryIt is commonly believed that reduced‐order observers, including reduced‐order Kalman filters, cannot be used in the loop transfer recovery (LTR) design of the plant output side. In contrast to common understanding, we show that, at least for nonminimum‐phase plants, the reduced‐order Kalman filter can be used in the linear‐quadratic‐Gaussian (LQG)/LTR design of the plant output side with clear meaning in systems theory. The key concept is to regard a reduced‐order Kalman filter as a high‐gain full‐order Kalman filter. For the reduced‐order LQG controller, we examine the asymptotic property achieved by applying the recovery procedure used in the full‐order LQG/LTR design. Using the equivalent full‐order Kalman filter, we find that the sensitivity property of the reduced‐order LQG controller is asymptotically equivalent to that of a high‐gain partial output injection system. Motivated by this result, we propose the reduced‐order LQG/LTR procedure taking the high‐gain partial output injection system as a target. Some target properties are discussed to clarify the difference from the full‐order design. A multivariable design example is presented to show that the procedure provides a systematic design of a reduced‐order controller with optimality consideration.

Design of optimal disturbance cancellation controllers via modified loop transfer recovery

The authors proposed a modified loop transfer recovery (LTR) method for designing the disturbance cancellation controllers where the disturbances were assumed to be step functions and the optimality of the controllers was not considered. This paper discusses the extension of their work to a more general class of disturbances with optimality consideration. It is assumed that the plant is minimum phase and the disturbances entering the plant input side are generated by function generators with unknown initial conditions. A quadratic performance index explicitly representing the disturbance cancellation requirement is introduced. The optimal disturbance cancellation controller minimizing the performance index is constructed by the separation principle. As a target for the LTR design, the optimal disturbance cancellation controller based on the measurement of the plant state is chosen. It is shown that the target feedback property can be recovered in the output feedback controller by a simple modification of the standard LTR procedure. A numerical example is presented to illustrate the effectiveness of the proposed optimal design.

Design of optimal output disturbance cancellation controllers via loop transfer recovery

The authors have introduced optimal disturbance cancellation controllers as a class of controllers minimizing a non-standard quadratic performance index explicitly including disturbances. This paper discusses the application of the classical loop transfer recovery (LTR) technique to the optimal disturbance cancellation controller for step disturbances entering the plant output. The estimation error dynamics of the Kalman filter jointly estimating the plant states and the disturbances is chosen as a target of the LTR design. The weighting coefficient of the performance index is used to recover the target which has guaranteed stability margins as in the standard LTR design. It is shown by a numerical example that the proposed design provides flexible tuning of the disturbance rejection capability with sufficient stability margins.

Study of autonomous underwater vehicle wave disturbance rejection in the diving plane

Autonomous underwater vehicles operating near the sea surface are subject to wave disturbances in their motion, which can affect severely the data acquisition during the vehicle motion. Bathymetric maps, for example, may suffer a big loss in quality due to such kind of disturbances that can impose oscillations in the vehicle depth and attitude. This article describes a controller structure for compensating the wave disturbances in the vertical plane for a torpedo-like autonomous underwater vehicle, based on a modified version of the linear quadratic Gaussian with loop transfer recovery control combined with a wave filter. The proposed methodology uses additional to the classic linear quadratic Gaussian with loop transfer recovery design the measurement of non-controlled states, such as the pitch rate and heave velocity, in the control action. The wave disturbances were filtered away by a shaping filter fitted to the sea spectrum, and the sensor signals were integrated by an extended Kalman filter. The proposed control methodology was tested against the classical linear quadratic Gaussian with loop transfer recovery controller in a 6-degree-of-freedom non-linear autonomous underwater vehicle simulator, producing a better performance in most demanding conditions such high wave crests. The tests also revealed the impact of the hydroplane geometry on the controller performance, which should not be underestimated by the autopilot designer.

LTR design of disturbance cancellation integral controllers for time-delay plants

For time-delay plants, the loop transfer recovery (LTR) technique for the integral controller design based on disturbance cancellation is discussed. Since the design requires an unstabilizable extended plant, the standard LTR method cannot be applied. The new LTR method proposed by the authors for lumped plants is extended to time-delay plants by introducing appropriate predictors. A simple design example is presented to illustrate the proposed design method.

An application of LTR design in fault detection

The fault detection and isolation (FDI) problem is considered in this paper. The FDI problem is formulated as a filter design problem, where the faults in the system is estimated and the disturbance acting on the system is rejected. It turns out that the filter design problem can be considered as a standard Loop Transfer Recovery (LTR) design problem. As a consequence of the connection between LTR and FDI design, it is shown in an example how the LQG/LTR design method for a full order and a proportional-integral observer can be applied with advantages in connection with FDI.

LTR design of discrete-time proportional-integral observers

Applies the proportional-integral (PI) observer in connection with loop-transfer recovery (LTR) design for discrete-time systems. Both the prediction and the filtering versions of the PI observer are considered. We show that a PI observer makes it possible to obtain time recovery, i.e., exact recovery for t/spl rarr//spl infin/, under mild conditions. Two systematic LTR design methods, one based on an extension of the linear quadratic Gaussian loop-transfer recovery (LQG/LTR) and the other based on linear matrix inequality (LMI), are derived for the discrete-time PI observer case, Explicit expressions for the recovery error when exact recovery is not achievable for all frequencies are also given.

Loop Transfer Recovery for Sampled-Data Systems

This paper considers the design of loop transfer recovery (LTR) controller for sampled-data systems. The LTR design problem is formulated by using the 2 x 2 setup formulation. Following the standard LTR theory, the difference between the target loop and the full-loop is defined as the recovery error, which is equal to the target loop multiplied by the recovery matrix. The minimization of the recovery error is derived by using H2 and H∞ designs.

Loop transfer recovery design via new observer‐based and css architecture‐based controllers

AbstractTwo new controller structures, namely the continuous‐time current‐type observer and current‐type CSS (Chen‐Saberi‐Sannuti) architecture‐based controllers, are considered in this paper for loop transfer recovery design for general non‐strictly proper non‐minimum phase systems. The proposed observer is structurally analogous to the current estimator of discrete‐time systems, while the proposed CSS architecture falls into the category of the controller structures developed recently by Chen, Saberi and Sannuti. The properties of these new structures are characterized. In particular, sets of necessary and sufficient conditions under which a target loop transfer function can be either exactly and/or asymptotically recovered by the abovementioned controllers are obtained. More importantly, the new current‐type observer balances the observer structures for continuous‐time and discrete‐time linear systems.

LTR design of proportional‐integral observers

AbstractThis paper applies the proportional‐integral (PI) observer in connection with loop transfer recovery (LTR) design for continuous‐time systems. We show that a PI observer makes it possible to obtain time recovery, i.e., exact recovery for t →∞, under mild conditions. Based on an extension of the LQG/LTR method of proportional (P) observers, a systematic LTR design method is derived for the PI observer. Our recovery design method allows time recovery and frequency (normal) recovery to be done independently. Furthermore, we give explicit expressions for the recovery error when asymptotic recovery cannot be obtained. A design example demonstrates the advantages of time recovery in the non‐minimum phase case.

Discrete-time compensators with loop transfer recovery

Loop transfer recovery (LTR) has gained some prominence over the last years. In this paper, the authors briefly overview the main design features of the LQG/LTR controller both at the input and at the output of the plant, using the delta operator formulation developed in Middleton and Goodwin (1990). Two discrete-time compensators with LTR capability are then derived following the LTR design approach proposed in Chen, Saberi, and Sannuti (1991) for the continuous-time case. These compensators are shown to outperform their underlying LQG/LTR controllers from the perspective of recovery error. Of particular importance, they share the same degree of recovery as the continuous time compensators of the above papers when the sampling period goes to zero. >

Loop transfer recovery design using biased and unbiased controllers

Loop transfer recovery is considered to be a special form of loop sensitivity shaping in this paper. This viewpoint suggests a design strategy which relaxes the requirement that the estimator or controller be unbiased. This strategy is illustrated using a stable, SISO example with a nonminimum phase zero. The approach still faces the design tradeoffs and limitations inherent in all feedback systems including those which apply to nonminimum phase plants. The formulation used here, however, suggests a different approach for dealing with these issues.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the Solution to Matrix Equation $TA - FT = LC$ and Its Applications

Equation $TA - FT = LC$ is fundamental to state space control system design. However, the existing solution to this equation cannot satisfy the necessary requirements that F be in Jordan form and that all rows of T be explicitly expressed in terms of their respective basis vectors. These two requirements are imposed by some basic and practical design problems such as eigenvector assignment and minimal function observer design. This paper shows that a new solution to this matrix equation can truly satisfy those requirements. Consequently, this solution can be applied directly to explicitly solve the above two design problems. Based on this solution, precise loop transfer recovery (LTR ), approximate LTR, and output feedback design are unified and much more easily achieved for all systems with more outputs than inputs. This paper also shows the superior efficiency and stability of the computation of this solution.

Loop transfer recovery for general observer architectures

A general and concise formulation is given of the loop transfer recovery (LTR) design problem based on recovery errors. Three types of recovery errors are treated, open loop recovery, sensitivity recovery and input-output recovery errors. The three corresponding versions of the asymptotic recovery problem turn out to be equivalent, since the minimization of the recovery errors all amount to the minimization of a certain matrix, the recovery matrix. Using the recovery error definitions, simple necessary and sufficient conditions for the controllers are derived both for the exact and asymptotic recovery cases. This general recovery formulation covers all known observer based compensator types as special cases. The conditions given in this setting are effectively the aim of all known LTR design methods. The recovery formulation is interpreted in terms of a model-matching problem as well, which is examined by means of the Q-parametrization. It is shown how the general controller obtained by the Q-parametrization can be written as a Luenberger observer based controller. In all cases, n controller states suffice to achieve recovery. The compensators are characterized for errors both on the input- and on the output-node (dual case).

指定した回復度を満たすLoop Transfer Recovery設計法による最小次元オブザーバの設計

指定した回復度を満たすLoop Transfer Recovery設計法による最小次元オブザーバの設計

Observer design for loop transfer recovery and for uncertain dynamical systems

A theory of observer design for exact and approximate loop-transfer recovery (LTR) and for uncertain dynamical systems is given. The method decomposes a given multivariable nominal system into several single-input, single-output subsystems, each of which can be designed separately. Both full-order and reduced-order observer designs can be derived. The design addresses the case when uncertainties are modeled as blocks exterior to the given plant and the case when uncertainties are prescribed structurally in terms of a state-space description. When the uncertainties in a given plant are modeled external to it, the observer design corresponds to a traditional LTR design, When uncertainties are given in terms of a state-space description, observer design can take into account uncertain elements of both linear and nonlinear type. This analysis can be viewed as a contribution to the development of a separation principle under which control system design for an uncertain dynamic system can be decomposed into designing a state feedback law and an observer for implementing the state feedback design. >