Engineering topics

Saberi, Ali

Publications and source records attributed to Saberi, Ali.

15 records

NASA NTRS1993

Necessary and sufficient conditions under which an H2 optimal control problem has a unique solution

A set of necessary and sufficient conditions under which a general H2-optimal control problem has a unique solution is derived. It is shown that the solution for an H2-optimal control problem, if it exists, is unique if and only if (1) the transfer function from the control input to the controlled output is left invertible, and (2) the transfer function from the disturbance to the measurement output is right invertible.

Chen, Ben M.↗

NASA NTRS1993

Discrete-time H(infinity) control problem with strictly proper measurement feedback

The paper is concerned with the discrete-time H(sub infinity) control problem with strictly proper measurement feedback. The authors derive necessary and sufficient conditions for the existence of a strictly proper compensator which achieves a given H(sub infinity) norm bound. Note that contrary to the continuous time, in discrete time there might exist a suitable proper compensator but no suitable strictly proper compensator. Finally, they give an explicit formula for one controller which achieves this bound.

Stoorvogel, Anton A.↗

NASA NTRS1993

Construction and parameterization of all static and dynamic H2-optimal state feedback solutions, optimal fixed modes, and fixed decoupling zeros

This paper considers an H2 optimization problem via state feedback. The class of problems dealt with here are general singular type which have a left invertible transfer matrix function from the control input to the controlled output. This class subsumes the regular H2 optimization problems. The paper constructs and parameterizes all the static and dynamic H2 optimal state feedback solutions. Moreover, all the eigenvalues of an optimal closed-loop system are characterized. All optimal closed-loop systems share a set of eigenvalues which are termed here as the optimal fixed modes. Every H2 optimal controller must assign among the closed-loop eigenvalues the set of optimal fixed modes. This set of optimal fixed modes includes a set of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and locations of pole-zero cancellations present in any H2 optimal design. It is shown that both the sets of optimal fixed modes and optimal fixed decoupling zeros do not vary depending upon whether the static or the dynamic controllers are used.

Chen, Ben M.↗

NASA NTRS1992

A non-iterative method for computing the infimum in H(infinity)-optimization

This paper presents a simple and non-iterative procedure for the computation of the exact value of the infimum in the singular H(infinity)-optimization problem, and is an extension of our earlier work. The problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H(infinity)-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the j-omega axis and also satisfy certain geometric conditions. The computation of the infimum in our method involves solving two well-defined Riccati and two Liapunov equations.

Chen, Ben M.↗

NASA NTRS1992

Simultaneous H2/H-infinity optimal control - The state feedback case

A simultaneous H2/H-infinity control problem is considered. This problem seeks to minimize the H2 norm of a closed-loop transfer matrix while simultaneously satisfying a prescribed H-infinity norm bound on some other closed-loop transfer matrix by utilizing dynamic state feedback controllers. Such a problem was formulated earlier by Rotea and Khargonekar (1991) who considered only so called regular problems. Here, for a class of singular problems, necessary and sufficient conditions are established so that the posed simultaneous H2/H-infinity problem is solvable by using state feedback controllers. The class of singular problems considered have a left invertible transfer function matrix from the control input to the controlled output which is used for the H2 norm performance measure. This class of problems subsumes the class of regular problems.

Saberi, Ali↗

NASA NTRS1992

Full and reduced order observer based controller design for H2-optimization

The most general H2 control problem is considered. The authors derive necessary and sufficient conditions when the infimum is attained by state feedback. They do the same for the measurement feedback case where necessary and sufficient conditions are derived when the infimum is attained by proper dynamic compensator. Reduced-order compensators are investigated if some states are observable without noise. For all of these cases the freedom that the non-uniqueness of optimal compensators gives in assigning the closed-loop eigenvalues is discussed. The case when the infimum cannot be attained is investigated. A constructive algorithm is presented to find a minimizing sequence of stabilizing controllers and the freedom in the asymptotic locations of the closed-loop eigenvalues is discussed. This procedure is repeated for three different cases: static state feedback, full-order measurement feedback, and reduced-order measurement feedback.

Stoorvogel, Anton A.↗

NASA NTRS1992

Non-iterative computation of the infimum in H-infinity-optimization for plants with invariant zeros on the j-omega axis

A simple and noniterative procedure for the computation of the exact value of the infimum in the singular H-infinity optimization problem is presented. The problem formulation is general, and no restrictions are placed on the finite and infinite zero structures of the system and on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables. The method is applicable to a class of singular H-infinity optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output satisfy certain geometric conditions. In particular, the authors extend the result of B. M. Chen et al. (1991) by allowing these two transfer functions to have invariant zeros on the j-omega axis.

Chen, Ben M.↗

NASA NTRS1992

Loop transfer recovery for general nonminimum phase discrete time systems. I - Analysis

A complete analysis of loop transfer recovery (LTR) for general nonstrictly proper, not necessarily minimum phase discrete time systems is presented. Three different observer-based controllers, namely, `prediction estimator' and full or reduced-order type `current estimator' based controllers, are used. The analysis corresponding to all these three controllers is unified into a single mathematical framework. The LTR analysis given here focuses on three fundamental issues: (1) the recoverability of a target loop when it is arbitrarily given, (2) the recoverability of a target loop while taking into account its specific characteristics, and (3) the establishment of necessary and sufficient conditions on the given system so that it has at least one recoverable target loop transfer function or sensitivity function. Various differences that arise in LTR analysis of continuous and discrete systems are pointed out.

Chen, Ben M.↗

NASA NTRS1992

Loop transfer recovery for general nonminimum phase discrete time systems. II - Design

The authors consider the design of controllers for the recovery of target loop transfer function or sensitivity and complementary sensitivity functions for general nonminimum phase discrete time systems. The necessary design constraints and the available design freedom are reviewed. In view of the available freedom, possible specifications on the eigenstructure of the observer dynamic matrix are formulated. Three different types of controllers which are respectively based on prediction, current, and reduced-order estimators are considered. For each one of those controllers, three different design techniques are developed. The first one is an eigenstructure assignment scheme, while the other two are optimization-based designs. The eigenstructure assignment method yields a controller design which achieves any chosen recovery error matrix among a set of admissible recovery error matrices. On the other hand, one of the optimization-based design methods leads to a controller that achieves a recovery error matrix having the infimum H-infinity norm, while the other does the same except it achieves a recovery error matrix having the infimum H2 norm.

Chen, Ben M.↗

NASA NTRS1992

Closed-loop transfer recovery with observer-based controllers. I - Analysis. II - Design

A detailed study is presented of three fundamental issues related to the problem of closed-loop transfer (CLT) recovery. The first issues concerns what can and cannot be achieved for a given system and for an arbitrary target CLT function (TCLTF). The second issue involves developing necessary and/or sufficient conditions for a TCLTF to be recoverable either exactly or approximately. The third issue involves the necessary and/or sufficient conditions on a given system such that it has at least one recoverable TCLTF. The results of the analysis identify some fundamental limitations of the given system as a consequence of its structural properties which enables designers to appreciate at the outset different design limitations incurred in the synthesis of output-feedback controllers. Then, the actual design of full-order or reduced-order observer-based controllers is addressed which will achieve as close as possibly the desired TCLTF. Three design methods are considered: (1) the ATEA method, (2) a method that minimizes the H2-norm of a recovery matrix, and (3) a method that minimizes the respective H(infinity) norm. The relative merits of the methods are discussed.

Chen, Ben M.↗

NASA NTRS1991

A reduced order observer based controller design for H-infinity optimization

In this paper the H-infinity control problem is investigated. It is well-known that for this problem, in general, controllers of the same dynamic order as the given system are needed. However, in the case that the standard assumptions on two direct feedthrough matrices are not satisfied, it is here shown that dynamic compensators of a lower dynamical order can be found. This result can be derived by using the standard reduced order observer based controllers in the case that one or more states are measured without noise.

Stoorvogel, Anton A.↗

NASA NTRS1991

An exact algebraic solution of the infimum in H-infinity optimization with output feedback

This paper presents a simple and noniterative procedure for the computation of the exact value of the infimum in the standard H-infinity-optimal control with output feedback. The problem formulation is general and does not place any restrictions on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. The method is applicable to systems that satisfy (1) the transfer function from the control input to the controlled output is right-invertible and has no invariant zeros on the j(w) axis and, (2) the transfer function from the disturbance to the measurement output is left-invertible and has no invariant zeros on the j(w) axis. A set of necessary and sufficient conditions for the solvability of H-infinity-almost disturbance decoupling problem via measurement feedback with internal stability is also given.

Chen, Ben M.↗

NASA NTRS1991

Closed-loop transfer recovery with observer-based controllers. I - Analysis

The description of a novel problem in loop transfer recovery is presented. The problem of closed-loop recovery (CLTR) is examined using a measurement feedback-control law where the closed-loop transfer function from the external signal to the controlled output can be made either exactly equal or approximately close to the so-called target closed-loop transfer function achieved under full-state feedback. The analysis of CLTR applies specifically to the general class of observer-based controllers and focuses on three fundamental issues. The first issue is concerned with what can and cannot be achieved for a given system and for an arbitrary target closed-loop transfer function. The second issue is to develop necessary and/or sufficient conditions for a target closed-loop transfer function to be recoverable either exactly or approximately. The third issue deals with the necessary and/or sufficient conditions on a given system such that it has at least one recoverable target closed-loop transfer function. The result is applied to the lateral autopilot design for a commercial transport airplane.

Chen, Ben M.↗

NASA NTRS1991

Closed-loop transfer recovery with observer-based controllers. II - Design

The paper focuses on the design problem related to the recovery of a target closed-loop transfer function using both full-order and reduced-order observer-based controllers. Design schemes for the reduced-order observer-based controllers are similar to those of full-order controllers; hence, for simplicity, only the case for full-order observer-based controller designs is given. Three types of design schemes are discussed in detail. The first one is an asymptotic time-scale eigenstructure assignment method, and the other two are optimization-based methods where a certain norm of the recovery matrix is minimized. Asymptotic behavior associated with each design method is highlighted. Relative advantages and disadvantages of both the ATEA and optimization-based schemes are discussed. A numerical example is used to illustrate the design possibilities from each of these methods, the available design freedom, and the significance of selecting the limit of the recovery matrix, especially in the case of a nonrecoverable design.

Chen, Ben M.↗

NASA NTRS1991

A non-iterative method for computing the infimum in H(infinity)-optimization

The authors, as an extension of their earlier work, present a simple noniterative procedure for the computation of the exact value of the infimum in the singular H(infinity)-optimization problem and is an extension of their earlier work. The problem formulation is general and does not place any restrictions on the direct feedthrough terms between the disturbance input and the measurement output variables. The method is applicable to a class of singular H(infinity)-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the j-omega axis and also satisfy certain geometric conditions.

Chen, Ben M.↗