Optimal discrete-time dynamic output-feedback design - A w-domain approach
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Ha, Cheolkeun↗
Engineering topics
Ly, Uy-Loi
Publications and source records attributed to Ly, Uy-Loi.
A new approach to mixed H2/H infinity controller synthesis using gradient-based parameter optimization methods
In the past few years, the mixed H(sub 2)/H-infinity control problem has been the object of much research interest since it allows the incorporation of robust stability into the LQG framework. The general mixed H(sub 2)/H-infinity design problem has yet to be solved analytically. Numerous schemes have considered upper bounds for the H(sub 2)-performance criterion and/or imposed restrictive constraints on the class of systems under investigation. Furthermore, many modern control applications rely on dynamic models obtained from finite-element analysis and thus involve high-order plant models. Hence the capability to design low-order (fixed-order) controllers is of great importance. In this research a new design method was developed that optimizes the exact H(sub 2)-norm of a certain subsystem subject to robust stability in terms of H-infinity constraints and a minimal number of system assumptions. The derived algorithm is based on a differentiable scalar time-domain penalty function to represent the H-infinity constraints in the overall optimization. The scheme is capable of handling multiple plant conditions and hence multiple performance criteria and H-infinity constraints and incorporates additional constraints such as fixed-order and/or fixed structure controllers. The defined penalty function is applicable to any constraint that is expressible in form of a real symmetric matrix-inequity.
Ly, Uy-Loi↗
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.↗
Mixed H(2)/H(sub infinity): Control with output feedback compensators using parameter optimization
Among the many possible norm-based optimization methods, the concept of H-infinity optimal control has gained enormous attention in the past few years. Here the H-infinity framework, based on the Small Gain Theorem and the Youla Parameterization, effectively treats system uncertainties in the control law synthesis. A design approach involving a mixed H(sub 2)/H-infinity norm strives to combine the advantages of both methods. This advantage motivates researchers toward finding solutions to the mixed H(sub 2)/H-infinity control problem. The approach developed in this research is based on a finite time cost functional that depicts an H-infinity bound control problem in a H(sub 2)-optimization setting. The goal is to define a time-domain cost function that optimizes the H(sub 2)-norm of a system with an H-infinity-constraint function.
Schoemig, Ewald↗
Control design of a UH-60 rotorcraft via CLTR and direct optimization
High-performance rotorcraft controller design is characterized by the need to compensate for both the longitudinal and lateral dynamics simultaneously. Rather than leaving these modes largely decoupled, one often needs for performance consideration to incorporate direct mode decoupling as a part of the controller design, especially when the system model includes high-frequency dynamics from the rotor and lag states. In addition to the usual design considerations of stability augmentation, a high-performance rotorcraft such as the UH-60 would also require a good command bandwidth and decoupling in the heave, yaw, pitch and roll command responses. In this paper, the method of closed-loop transfer recovery (CLTR) and direct optimization are applied to the control design of a UH-60 rotorcraft.
Vansteenwyk, Brett↗
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↗
Mixed H2/H(infinity)-Control with an output-feedback compensator using parameter optimization
Among the many possible norm-based optimization methods, the concept of H-infinity optimal control has gained enormous attention in the past few years. Here the H-infinity framework, based on the Small Gain Theorem and the Youla Parameterization, effectively treats system uncertainties in the control law synthesis. A design approach involving a mixed H(sub 2)/H-infinity norm strives to combine the advantages of both methods. This advantage motivates researchers toward finding solutions to the mixed H(sub 2)/H-infinity control problem. The approach developed in this research is based on a finite time cost functional that depicts an H-infinity bound control problem in a H(sub 2)-optimization setting. The goal is to define a time-domain cost function that optimizes the H(sub 2)-norm of a system with an H-infinity-constraint function.
Schoemig, Ewald↗
A reliable algorithm for optimal control synthesis
In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.
Vansteenwyk, Brett↗
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.↗
Design of a total energy control autopilot using constrained parameter optimization
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Voth, Christopher↗
Reliable numerical computation in an optimal output-feedback design
A reliable algorithm is presented for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is a part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. This approach through the use of an accurate Pade series approximation does not require the closed-loop system matrix to be diagonalizable. The algorithm was included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm was demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.
Vansteenwyk, Brett↗
Reliable numerical computation in an optimal output-feedback design
This paper presents a reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. The algorithm has been included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.
Vansteenwyk, Brett↗
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.↗
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.↗
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.↗
Optimal discrete-time dynamic output-feedback design - A w-domain approach
An alternative method for optimal digital control design is described in this paper. The method is based on the usage of the w-transform and has many attractive design features. One of these is its immediate connection with frequency loop-shaping techniques that are now popular and effective for multivariable control synthesis in continuous-time domain. Furthermore, any design algorithms originally developed for continuous-time systems can now be immediately extended to the discrete-time domain. The main results presented in this paper are the exact problem formulation and solution of an optimal discrete-time dynamic output-feedback design in the w-domain involving a quadratic performance index to random disturbances. In addition, necessary conditions for optimality are obtained for the numerical solution of the optimal output-feedback compensator design. A numerical example is presented illustrating its application to the design of a low-order dynamic compensator in a stability augmentation system of a commercial transport.
Ha, Cheolkeun↗
Advanced rotorcraft control using parameter optimization
A reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters is presented. The algorithm is part of a design algorithm for an optimal linear dynamic output feedback controller that minimizes a finite time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed loop eigensystem. This approach through the use of a accurate Pade series approximation does not require the closed loop system matrix to be diagonalizable. The algorithm has been included in a control design package for optimal robust low order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed loop system under an arbitrary controller design initialization and during the numerical search.
Vansteenwyk, Brett↗
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.↗