Fixed-order Dynamic Compensation Research Articles

Fixed-order dynamic compensation for axial flow compression systems

We develop linear fixed-order (i.e., full and reduced order) pressure rise feedback dynamic compensators for axial flow compressors with throttle valve actuation. Unlike the nonlinear static controllers proposed in the literature possessing gain at all frequencies, the proposed dynamic compensators explicitly account for compressor performance versus sensor accuracy, compressor performance versus processor throughput, and compressor performance versus disturbance rejection. Furthermore, the proposed controller is predicated on only pressure rise measurements, providing a considerable simplification in the sensing architecture over the bifurcation-based and backstepping controllers proposed in the literature.

Fixed-structure controller design for systems with actuator amplitude and rate non-linearities

In this paper we develop output feedback controllers and fixed-order (i.e., full- and reduced-order) dynamic compensators for systems with actuator amplitude and rate saturation constraints. The proposed design methodology employs a rate limiter as part of the controller architecture. The problem of simultaneous control amplitude and rate saturation is embedded within an optimization problem by constructing a Riccati equation whose solution guarantees closed-loop global/local asymptotic stability in the face of sector bounded actuator amplitude and rate non-linearities. Application of the proposed framework is demonstrated via a flight control example involving actuator amplitude and rate saturation constraints.

Fixed-order dynamic compensation for linear systems with actuator amplitude and rate saturation constraints

In this paper we develop fixed-order (i.e. full- and reduced-order) controllers for continuous-time and discrete-time linear systems with actuator amplitude and rate saturation constraints. The problem is formulated as a multiobjective problem involving a convex combination of an L1 norm and the H2 norm to capture actuator saturation constraints and closedloop system performance in the face of exogenous white noise disturbances. The L1

Stochastic stabilizability of a class of discrete-time non-linear systems

This paper presents a characterization of all state covariances assignable by a linear static output feedback controller to a class of discrete-time non-linear stochastic systems and a parametrization of all such controllers that will achieve a desired covariance. These results indirectly provide similar results for fixed-order dynamic feedback compensators. This characterization enables one to test the stochastic stabilizability of such systems by output feedback. An alternative formulation of stochastic stabilizability by output feedback is also included. Then, these results are specialized to the state feedback case and presented together with the previous results of the authors' to form a more complete and unified picture of stochastic stabilizability conditions.

Mixed H 2/L 1 fixed-architecture controller design for multi-input/single-output systems

In this paper we develop a mixed-norm H 2/L 1 controller synthesis framework via fixed-order dynamic compensation for multi-input/single-output systems. For flexibility in controller synthesis, we adopt the approach of fixed-structure controller design which allows consideration of arbitrary controller structures, including order, internal structure, and decentralization. Several numerical examples are presented to demonstrate the fixed-structure mixed-norm H 2/L 1 controller synthesis approach.

Stabilization of linear systems with simultaneous state, actuation, and measurement delays

This paper considers the problem of stabilizing continuous-time linear systems with time delays. Specifically, a fixedorder (i.e. full- and reduced-order) dynamic compensation problem is addressed for systems with simultaneous state, input, and output delays. The principal result involves sufficient conditions for characterizing fixed-order dynamic controllers for delay systems via a system of modified coupled Riccati equations. The controllers obtained are delay independent and hence apply to systems with arbitrary unknown delay.

Nonlinear fixed-order dynamic compensation for passive systems

A method for designing nonlinear fixed-order (i.e. full- and reduced-order) dynamic passive controllers for passive systems is developed using nonlinear dissipation theory. Specifically, by extending linear passive controller synthesis frameworks a family of globally asymptotically stabilizing nonlinear passive controllers is developed that can serve to enhance system performance and energy dissipation. The proposed approach is applied to the rotational/translational proof-mass actuator (RTAC) nonlinear benchmark problem to develop fixed-order dynamic output feedback nonlinear controllers. © 1998 John Wiley & Sons, Ltd.

Mixed-norm H2/L1 controller synthesis via fixed-order dynamic compensation: A Riccati equation approach

One of the fundamental problems in feedback control design is the ability of the control system to reject uncertain exogenous disturbances. Since a single performance objective is seldom adequate to capture multiple and often conflicting system disturbances, in this paper we develop a Riccati equation approach for mixed H2/L1 controller synthesis via fixed-order dynamic compensation. This multiobjec2 tive problem is treated by forming a convex combination of both the H2 (quadratic) and L1 bound (worst-case peak amplitude response) performance measures. For flexibility in controller synthesis, we adopt the approach of fixed-structure controller design which allows consideration of arbitrary controller structures, including order, internal structure, and decentralization. Finally, using a quasi-Newton continuation algorithm, we demonstrate the effectiveness of the proposed mixed-norm H2/L1 Riccati equation approach via several design examples.

A periodic fixed-structure approach to multirate control

We develop an approach to designing reduced-order multirate controllers. A discrete-time model that accounts for the multirate timing sequence of measurements is presented and is shown to have periodically time-varying dynamics. Using discrete-time stability theory, the optimal projection approach to fixed-order (i.e. full- and reduced-order) dynamic compensation is generalized to obtain reduced-order periodic controllers that account for the multirate architecture. It is shown that the optimal reduced-order controller is characterized by means of a periodically time-varying system of equations consisting of coupled Riccati and Lyapunov equations. In addition, the multirate static output-feedback control problem is considered. For both problems, the design equations are presented in a concise, unified manner to facilitate their accessibility for developing numerical algorithms for practical applications. >

Approximate recovery of H-infinity loop shapes using fixed-order dynamic compensation

This paper presents a method for designing fixed-order dynamic compensators that approximate the Hm full state feedback, closed-loop transfer function properties from disturbance inputs to controlled outputs. This formulation uses an observer canonical form to represent the dynamic compensator which allows the design to be treated as a modified constant gain output feedback problem. The approximate recovery is accomplished through a unique selection of the quadratic performance index weighting matrices. This design procedure is demonstrated by two design examples. The first example is a simple fourth-order model used to demonstrate the procedure. The second example is a longitudinal flight controller for the F-18/HARV Supermaneuverable aircraft. This flight controller is compared to both a full- and reduced-order H^ compensator.

Further development of an approximate loop transfer recovery methodology for fixed order dynamic compensator design

AbstractThis paper further develops a methodology for designing fixed order compensators. The formulation uses an approximate loop transfer recovery (LTR) method to achieve performance and stability subject to a disturbance and unstructured uncertainty at either the plant input or the plant output. The approximate LTR methodology has the advantage that the quadratic performance index weighting matrices are uniquely defined. To reduce sensitivity to real parameter uncertainty, the performance index is modified to include a penalty on the closed‐loop sensitivity dynamics. The formulation avoids the explicit introduction of sensitivity states into the performance index and thus does not increase the overall dimension of the problem. An example design for the coupled mass benchmark control problem is provided to demonstrate this methodology.

Optimal dynamic output feedback for nonzero set point regulation: the discrete-time case

Standard discrete-time LQG theory is generalized to a regulation problem involving a priori specified nonzero set points for the state and control variables and nonzero-mean disturbances. The optimal control law consists of a closed loop component feeding back measurements and a constant open-loop component which accounts for the nonzero set point and the nonzero mean disturbance. For generality, the results are obtained for the problem of fixed-order (i.e., full- and reduced-order) dynamic compensation. It is shown that the closed-loop controller can be designed independently of the open-loop control.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust stability and performance via fixed-order dynamic compensation: the discrete-time case

A discrete-time feedback-control-design problem involving parametric uncertainty is considered. A quadratic bound suggested by recent work on discrete-time state-space H/sub infinity / theory is utilized in conjunction with the guaranteed cost approach to guarantee robust stability with a robust performance bound. The principal result involves sufficient conditions for characterizing robust full- and reduced-order controllers with a worst case H/sub 1/ performance bound. >

A riccati equation approach to the singular LQG problem

The problem of optimal fixed-order dynamic compensation for the singular LQG problem is considered. Necessary conditions characterizing the optimal compensator for the case involving both singular measurement noise and singular control weighting are given. The solution consists of a set of two algebraic Riccati equations and two Lyapunov equations coupled by three projection matrices. One projection is the standard order reduction projection while the other two projections reflect the two types of singularity that exist in the system. The three projections are shown to satisfy disjointness conditions. In addition to order reduction, an advantage of the fixed-structure approach is that differentiation, which is often undersirable from a practical point of view and which may exist in the unconstrained optimal control, can be avoided. It is shown that the fixed-order compensator agrees with the unconstrained solution when the latter possesses the same number of differentiations as are included in the prespecified controller structure and when the order is selected appropriately.

Fixed-order dynamic compensation for a high-performance fighter aircraft

This paper presents a robust fixed-order dynamic compensator design for a high-performance fighter aircraft. The compensator design methodology is based on an approximate loop transfer recovery technique. Full-state gains are first designed for the dual system, which is the equivalent of designing a full-order observer. Then the loop characteristics at the dual system input are approximated with' a compensator in controller canonical form. Finally, the optimal gains are implemented in the dual compensator to insure robustness and tracking performance at the plant output. The fixed-order dynamic compensator developed here is compared with a previously published full-order observer design.

OptimalH2 andH∞ fixed-order dynamic compensation using canonical forms

This paper presents a technique for designing fixed order dynamic compensators in controller canonical form which are robust to both structured and unstructured uncertainty. The formulation uses an approach which combines an H2 and H∞ optimization process. Specifically, a quadratic performance index is minimized subject to a constraint on the H∞ norm of the closed loop transfer function from disturbances to controlled outputs. This provides robustness to unstructured uncertainty. To provide robustness to structured uncertainty, an upper bound is computed for the worst case parameter variations, and it is then included in the derivation of the optimality conditions. A robust controller for a jetfoil boat is used to demonstrate this design technique. For the specific case of no structured uncertainty, the results of this approach using the canonical form compensator are analytically related to the previously published results for a fixed-order dynamic compensator. It is demonstrated that the use of the canonical form greatly simplifies the system of necessary conditions.

Parameter sensitivity reduction in fixed-order dynamic compensation

This paper presents a simple formulation for designing fixed-order dynamic compensators that are robust to uncertainty at the plant input and have reduced sensitivity to structured uncertainty in the plant dynamics. An approximate loop transfer recovery technique is extended to include a penalty on the trajectory sensitivity dynamics. This approach avoids introducing the sensitivity states, and thus the dimension of the optimization problem is not increased. The usefulness of the technique is illustrated by two compensator designs. The first design considers a case where the uncertain parameters occur in the output matrix. The second design is for a high bandwidth controller for a flexible spacecraft.

Necessary and Sufficient Conditions for Optimal Fixed-Order Dynamic Compensation of Linear Discrete-Time Systems 1

The optimal fixed-order dynamic compensation problem is considered in the case of linear discrete-time systems with quadratic criteria. Necessary and sufficient conditions for the existence of a unique optimal stabilizing compensator of given order are derived. A test, explicit in the system matrices, is provided to determine if a given system satisfies the necessary and sufficient conditions

Active vibration control using fixed order dynamic compensation with frequency shaped cost functionals

An approach for the design of controllers for active suppression of helicopter vibration that combines recent developments in the design of fixed-order dynamic compensators with the frequency-shaped cost functional approach is presented. A robust compensator that provides loop shaping at the plant input is used in conjunction with frequency-shaped cost functionals to arrive at a controller for vibration reduction. The effectiveness of this technique is demonstrated by a detailed case study for the design of an active vibration controller. >

Robust stability and performance via fixed-order dynamic compensation with guaranteed cost bounds

A feedback control-design problem involving structured plant parameter uncertainties is considered. Two robust control-design issues are addressed. The Robust Stability Problem involves deterministic bounded structured parameter variations, while the Robust Performance Problem includes, in addition, a quadratic performance criterion averaged over stochastic disturbances and maximized over the admissible parameter variations. The optimal projection approach to fixed-order, dynamic compensation is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design. The principle result is a sufficient condition for characterizing dynamic controllers of fixed dimension which are guaranteed to provide both robust stability and performance. The sufficient conditions involve a system of modified Riccati and Lyapunov equations coupled by an oblique projection and the uncertainty bounds. The full-order result involves a system of two modified Riccati equations and two modified Lyapunov equations coupled by the uncertainty bounds. The coupling illustrates the breakdown of the separation principle for LQG control with structured plant parameter variations.