State-space formulas for gain-scheduled l/sub 1/-optimal controllers

This paper presents a rational /spl Lscr//sub 1/ and mixed /spl Lscr//sub 1///spl Hscr//sub /spl infin// compensator design methodology for continuous time systems. The problem formulation involves finding a finite dimensional stabilizing feedback controller that minimizes the /spl Lscr/1 norm of a closed-loop transfer matrix subject to a frequency domain /spl Hscr//sub /spl infin// norm constraint on another closed-loop transfer matrix. It is shown that for a one-block problem the optimal solution can be approximated arbitrarily closely in terms of the closed-loop /spl Lscr//sub 1/ norm, by solving a sequence of convex optimization problems over linear matrix inequalities. Numerical example is provided to demonstrate the effectiveness of this approach.

We propose a design method for active seismic isolation control taking account of actuator saturation. By using a hyperbolic tangential function that is differentiable to controller output, we formulate the linear parameter varying system according to the controller output and design a gain-scheduled controller. By carrying out simulations and experiments of seismic excitation, our proposed gain-scheduled controller is compared with an H/sub /spl infin// fixed controller or a sliding mode controller. It is verified that the proposed controller maintains performance of isolation even if a large earthquake with which the actuator saturation occurs comes, although the other controllers lower the performance than uncontrolled case.

Multiobjective frequency domain design aims to find a controller that gives desirable properties to several closed loop frequency responses simultaneously. This problem may be cast as a problem of finding a controller such that the worst-case /spl Hscr//sub /spl infin// norm, i.e. the largest among several /spl Hscr//sub /spl infin// norms, satisfies a prespecified bound. The authors define an upper bound, the /spl rho/ measure, for the worst-case /spl Hscr//sub /spl infin//, norm in terms of a scaled /spl Hscr//sub /spl infin// cost function. The authors show that the problem of finding a controller that minimizes /spl rho/ can be reduced to a finite dimensional convex program for the unknown scales and a standard /spl Hscr//sub /spl infin// problem. The authors give affine matrix inequalities for controller synthesis when the scales are restricted to constant matrices. A numerical example is used to illustrate the advantages of the authors' formulation, over the single objective /spl Hscr//sub /spl infin//, formulation, for solving multiobjective /spl Hscr//sub /spl infin// problems.

One of the fundamental problems in feedback control design is the ability of the control system to maintain stability and performance in the face of system uncertainties. To this end, elegant multivariable robust control design frameworks such as /spl Hscr//sub /spl infin// control, /spl Lscr//sub 1/ control, and /spl mu/ synthesis have been developed to address the robust stability and performance control problem. An implicit assumption inherent in these design frameworks is that the controller will be implemented exactly. In a paper by Keel and Bhattacharyya (1996) it was shown that even though such frameworks are robust with respect to system uncertainty, they are extremely fragile with respect to errors in the controller coefficients. In this paper, we extend the fixed-structure controller synthesis approach to develop non-fragile or resilient controllers to controller gain variations.

This paper deals with the linear /spl Hscr//sub /spl infin// filtering problem for a class of regionally stable uncertain nonlinear systems subject to bounded disturbances and measurement noises. The nonlinear systems is represented by differential-algebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters. For this class of systems, LMI conditions are proposed for ensuring a prescribed upper-bound on the /spl Lscr//sub 2/-gain of the input-to-estimation error operator for a given linear asymptotically stable filter. The result is based on polynomial Lyapunov functions. Then, using an appropriate parameterization of the Lyapunov function we extend the analysis result for designing linear filters in a /spl Hscr//sub /spl infin// sense via a convex optimization problem.

A fault detection filter is designed by minimising the response to confounding noises whilst keeping the fault response constant. A linear quadratic optimisation problem, related to /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// optimal control is used. The Q matrix of the associated Riccati equation is indefinite in contrast to the indefinite R matrix of /spl Hscr//sub /spl infin// control. We extend linear optimal control theory to solve the fault detection problem in this framework.

The standard state space solutions to the /spl Hscr//sub /spl infin// control problem for linear time-invariant systems are generalized to nonlinear time-invariant systems. A class of local nonlinear (output feedback) /spl Hscr//sub /spl infin//-controllers are parameterized as nonlinear fractional transformations on contractive, stable nonlinear parameters. As in the linear case, the /spl Hscr//sub /spl infin// control problem is solved by its reduction to state feedback and output estimation problems, together with a separation argument. Sufficient conditions for /spl Hscr//sub /spl infin//-control problem to be locally solved are also derived with this machinery. >

Recent theoretical developments have improved the understanding of gain scheduled control and suggested new methods for design, analysis and implementation of such nonlinear control systems. An integrated software environment for gain scheduled local controller network design and analysis, including computer-aided modelling and system identification, is described. Some background theory is included, and a speed control design problem for an experimental vehicle illustrates the application of the approach.

In this paper, a behavioral version of the /spl Hscr//sub /spl infin// problem for continuous time, linear time invariant systems is formulated and solved. This general formulation, of which standard /spl Hscr//sub /spl infin// is a special case, provides added freedom in the design of optimal controllers, and can in fact be viewed as a means of designing optimal systems. In particular, the formulation presented allows for singular interconnections, which naturally occur when interconnecting systems. >

In this paper we present the L1 adaptive controller for time-varying reference systems. This extension is motivated by the need for augmentation of baseline gain-scheduled controller, which naturally leads to a time-varying reference system. Keeping this in mind, the synthesis of L1 adaptive controller in this paper pursues two objectives. First, the adaptive augmentation must recover the nominal performance of the gainscheduled controlled system at different operating points, without overruling the performance of the baseline controller. Second, the design of the adaptive augmentation should be pursued in a way so that in the absence of uncertainties the output of it is zero. Thus, the adaptive augmentation must include the dynamics of the closedloop system, controlled by the baseline gain-scheduled controller, as a part of its feedback. The dynamics of the gain-scheduled controller change dependent upon the scheduling variables, resulting in a time-varying closed-loop reference system with a “slow rate” of variation. In this paper, we analyze the stability and the performance of the L1 adaptive controller for a time-varying reference system. We show that the L1 adaptive augmentation of the baseline gain-scheduled controller does not require a “slower rate” of variation for the scheduling variables, used in the design of baseline gain-scheduled controller. The performance of the gainscheduled controller can be retained by uniformly increasing the rate of adaptation. We further illustrate how the theory can be used for adaptive augmentation of a baseline gain-scheduled controller by simulating racetrack maneuver of autonomous aerial refueling.

A flow controller design approach based on the /spl mu/-synthesis is proposed. Performances of the resulting controllers and the /spl Hscr//sup /spl infin// controllers designed based on the approach we proposed earlier (2000), are compared.

For variable speed wind turbines (WT) operating in the full load range, a collective pitch control is used to limit the speed to its nominal value. The concept of a nonlinear PI gain scheduling controller is particularly suitable for compensating the nonlinear rotor behavior and is widely used in the wind industry. However, a simple calculation method to calculate its controller parameters while considering the full dynamics of the control loop is not available yet. In this paper the linearization process as well as a simple calculation method to find suitable controller parameters based on methods of classical control engineering is introduced. In contrast to previous methods the full dynamics of the open loop system, in particular the dynamics of the controlled pitch servomotors and the dynamics of the drive train with its first eigenfrequency, can be considered within the controller design. This is done by analyzing the behavior of the gain scheduling control and deriving a simplified linearized model of the open loop system. In this way it is possible to optimize the controller parameters by using the bode diagram. The usability of the simple design method is shown on the basis of simulation results considering the influence of wind fluctuations as well as wind gusts.

Attempts to solve the state-feedback H/sub 2//H/sub /spl infin// control problem by a LMI technique that allows for uncommon LMI solutions. In order to obtain a common controller ensuring the two performance criteria while allowing uncommon LMI solutions, we figure out what portion of the LMI solution should be constrained. Then, utilizing the freedom of the unconstrained portion, we propose an iterative method to obtain an updated controller gain which further improves the H/sub 2/ performance under the /spl Hscr//sub /spl infin// constraint. An illustrated example is included.

A state feedback /spl Hscr//sub /spl infin//-suboptimal control problem on TSO(3) for a rigid spacecraft with three control torques and disturbances is addressed, the Hamilton-Jacobi inequality associated with a corresponding state feedback /spl Hscr//sub /spl infin//-suboptimal control problem on TS/sup 3/ is solved globally. The /spl Hscr//sub /spl infin//-suboptimal state feedback on TS/sup 3/ involves the Euler parameters and solves the original problem on TSO(3) when the initial values of the Euler parameters are appropriately chosen.

Deals with the direct design of state feedback mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin//, control for sampled-data systems. In particular, a state feedback control design method is proposed to achieve the performance tradeoff between /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// objectives characterized by the Nash game approach in a continuous time domain.