Gerhard Kreisselmeier

Robust model reference adaptive control

We propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed-loop adaptive control system with respect to unmodeled plant uncertainties. The robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law. The extra a priori information needed to design the adaptive law, are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function.

Stable model reference adaptive control in the presence of bounded disturbances

The adaptive control of a linear time-invariant plant in the presence of bounded disturbances is considered. In addition to the usual assumptions made regarding the plant transfer function, it is also assumed that the high-frequency gain k p of the plant and an upper bound on the magnitude of the controller parameters are known. Under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system.

Application of vector performance optimization to a robust control loop design for a fighter aircraft

Abstract For a McDonnell-Douglas F-4C aircraft a robust, fixed gain controller is designed, which provides satisfying handling qualities of the longitudinal motion or the aircraft over the complete flight range without gain scheduling. Robustness is achieved in the sense of covering largo paramoter variations and providing good gain and phase margins, Only low control rates and low feedback gains are involved, The results are obtained by application of a performance vector optimization design method which accounts for a great many different design objectives simultaneously in a highly systematic fashion. Two different designs are presented placing emphasis on pitch rate control (pointing) and normal acceleration control (manoeuvring) respectively.

A continuous-time observer which converges in finite time

It is shown that a continuous-time observer, which comprises two standard nth order observers and a delay D, can observe the state of an nth order linear system in finite time D exactly. In particular, (almost) any convergence time D can be assigned, independent of the observer eigenvalues.

Stable adaptive regulation of arbitrary nth-order plants

This paper presents an algorithm for adaptively stabilizing and asymptotically regulating an arbitrary single-input single-output linear time-invariant plant, which is controllable and observable, of known order n , and has unknown parameters. No further assumptions are made. No external probing signal is required.

Nonlinear observers for autonomous Lipschitz continuous systems

This paper considers the state observation problem for autonomous nonlinear systems. An observation mapping is introduced, which is defined by applying a linear integral operator (rather than a differential operator) to the output of the system. It is shown that this observation mapping is well suited to capture the observability nature of smooth as well as nonsmooth systems, and to construct observers of a remarkably simple structure: A linear state variable filter followed by a nonlinearity. The observer is established by showing that observability and finite complexity of the system are sufficient conditions for the observer to exist, and by giving an explicit expression for its nonlinearity. It is demonstrated that the existence conditions are satisfied, and hence our results include a new observer which is not high-gain, for the wide class of smooth systems. It is shown that the observer can as well be designed to realize an arbitrary, finite accuracy rather than ultimate exactness. On a compact region of the state space, this requires only observability of the system. A corresponding numerical design procedure is described, which is easy to implement and computationally feasible for low order systems.

A Robust Indirect Adaptive Control Approach

This paper considers the robust design of an indirect adaptive control approach, which is applicable when the unknown parameters of a linear, time invariant plant lie in a known convex set throughout which no unstable pole-zero cancellation occurs. In order to achieve the robustness, the use of a relative dead zone in the adaptive law is proposed. It is shown that, with a suitably designed relative dead zone, the adaptive control system is (globally) stable, even in the presence of small, unmodeled plant uncertainties.

Stabilization of linear systems in the presence of output measurement saturation

This note considers siso nonlinear systems, which have a linear controllable and observable part followed by a measurement saturation nonlinearity. A controller is presented, which feeds back only the saturating output measurements and nevertheless globally asymptotically stabilizes the system. The equilibrium is actually reached in finite time, i.e. the controller is dead beat.

Numerical nonlinear regulator design

This paper considers the state regulation problem for nonlinear plants P with initial conditions in a prespecified region G. A computer implementable algorithm is presented, which is theoretically ensured to yield a practically asymptotically stabilizing feedback controller from G, if one exists. Since the plant P is represented by a discrete time mapping, which is only assumed to be continuous, the approach is of wide applicability for plants of moderate order. >

Adaptive control via adaptive observation and asymptotic feedback matrix synthesis

For unknown linear, time invariant systems an adaptive feedback control scheme is established. It is composed of a stable adaptive state and parameter observation part, and a stable asymptotic synthesis of an adaptive feedback matrix part, the latter based on the current parameter estimates. Both adaptive state feedback control and adaptive feedback control, using the adaptively observed state instead of the true state, are shown to result in closed loop control systems, which behave globally asymptotically stable in the sense of Lyapunov with respect to the initial uncertainty, provided only that the input of the unknown system is sufficiently excited by means of an external command signal. Thereby an algebraic separation property for adaptive state feedback control is also established, extending an earlier nonadaptive result. In particular, no assumptions on the parameters of the unknown system nor on the speed of the adaptive observer and the adaptive feedback matrix generator are made.