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

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

Robust integrated autopilot/autothrottle design using constrained parameter optimization

A multivariable control design method based on constrained parameter optimization was applied to the design of a multiloop aircraft flight control system. Specifically, the design method is applied to the following: (1) direct synthesis of a multivariable 'inner-loop' feedback control system based on total energy control principles; (2) synthesis of speed/altitude-hold designs as 'outer-loop' feedback/feedforward control systems around the above inner loop; and (3) direct synthesis of a combined 'inner-loop' and 'outer-loop' multivariable control system. The design procedure offers a direct and structured approach for the determination of a set of controller gains that meet design specifications in closed-loop stability, command tracking performance, disturbance rejection, and limits on control activities. The presented approach may be applied to a broader class of multiloop flight control systems. Direct tradeoffs between many real design goals are rendered systematic by this method following careful problem formulation of the design objectives and constraints. Performance characteristics of the optimization design were improved over the current autopilot design on the B737-100 Transport Research Vehicle (TSRV) at the landing approach and cruise flight conditions; particularly in the areas of closed-loop damping, command responses, and control activity in the presence of turbulence

A direct method for designing optimal control systems that are insensitive to arbitrarily large changes in physical parameters

A new concept has been developed for designing optimal feedback controllers that will be insensitive to given, arbitrarily large variations in physical parameters. The method uses as a single figure of merit the expected value of a quadratic performance index, the minimization of which determines directly (without trial and error) the desired set of feedback gains. These values of the feedback gains (where such exist) guarantee at the outset closed-loop stability for all possible values of physical parameters in the prescribed domain of uncertainty. The new method extends the well known method for the optimal regulator design where physical parameters have single, precisely known values, to the case where they may have a range of values. In addition, it encompasses (as a special case) the Minimax design developed also for handling systems whose physical parameters may have a range of values (which the Minimax explores by trial and error while the new method accounts automatically for the entire range). An essential feature of the new procedure is that it includes exactly in its cost criterion whatever effects accompany large departures in the plant parameters from their nominal values. This is why the new method is able to guarantee stability over the whole range of parameter values, where perturbation techniques are not. The feasibility and usefulness of the new design technique are illustrated by numerical examples in which control systems are designed for second-order plants each of whose parameters may have a given range of values. Comparisons which results using standard optimal design and the Minimax technique are given. Application to high-order systems will need to be accompanied by further development of appropriate computational procedures

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 H²-1ike 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 contro

A Time-Domain Penalty Function Approach to Mixed HZ/H,-Control Using Parameter Optimization Methods

In this paper we consider the problem of minimum nominal Hz-norm with H,-constraints for systems with multiple operating points. The performance measure is defined as a weighted sum of the corresponding nominal H2norms while robust stability of the individual closed-loop systems is defined in terms of a H,-bound for each plant condition. In this paper we define a new time-domain scalar cost function J, (t,) representing the H,-bounds in an overall cost function for the mixed H’/H,-design. J,(tj) is, for finite time tf, a penalty function and, for tj + 00, a barrier function. Using Jm(tj), the mixed Hz/H,-design problem results in an unconstrained op timization problem, that, for I!-, 00, recovers the original objective of minimizing the performance measure sub ject to the Hm-bounds. The resulting optimization problem is smooth and hence standard gradient-based software can be applied. The class of controllers considered includes proper and strictly proper LTI controllers with fixed structure and/or fixed order. 1

Experimental Robust Reduced-Order Hybrid Position/Force Control for Two- Link Flexible Manipulators

This paper reports on experimental evaluation of different hybrid position and force controllers during a surface-following task using a two-link flexible manipulator. Standard full-order and reduced-order Linear-Quadratic-Gauss-ian (LQG) controllers are compared to robust reduced-order controllers obtained from direct optimization. Experimental results show that the reduced-order controllers provide comparable performance to the full-order con-trollers. Thus, by use of direct optimization, the benefits of reduced-order controllers (smaller memory requirements and faster sampling rates) can be achieved while accounting for varying plant conditions in terms of robustness. Ad-ditionally, hybrid optimization schemes are compared for designing each position and force controller separately and combining them (superposition) versus designing all the controllers at the same time (simultaneous optimization). Ex-perimental results show that simultaneous optimization can provide better results than designing the force and position controllers separately.

Minimum Control Effort State Feedback 7-,2-Control

Optimal 4.-controllers may exhibit lage gains, resulting in large control efforts. In this papar we consider the problem of desgning a minimum gain static ful statefeedback controller such that the dosed-loop transfer function satisfies a 4.-constramlt. The main result of the paper shows that, by minimizing an upper bound for the Frobenius-norm of the feedback-gain matrix mad parametrization as in [6], using a the problem can be cast into a fi.nite-dimensional, convex optimization problem. Scalar cost-function-s for the 74.-bound and various other constraints allow the application of gradient-based software packages to these problems. Finaly, we illustrate how to apply this theory to the mixed 7z/`4.-control problem with minimum control effort. 1