Stable Dynamic Inversion Research Articles

A KALMAN FILTER-BASED STABLE DYNAMIC INVERSION FOR DISCRETE-TIME, LINEAR, TIME-VARYING SYSTEMS

In this paper the problem of estimating an unknown input for discrete-time, non-minimum phase, multivariable, linear time-varying systems (LTV) is considered. The initial condition of the plant may be unknown and stochastic process and measurement noise are included. The input signal is modelled as a random walk with drifts. Then it is estimated using a Kalman filter for a uniformly detectable augmented system. A necessary and sufficient condition for the detectability of the augmented system is provided. A Kalman filter-based stable dynamic inversion (SDI) for LTV systems is obtained as a consequence of our solution to the proposed problem. The inversion technique can be applied to achieve output tracking for LTV systems in the presence of non-minimum phase zeros and measurement and/or system noise. We are mainly motivated by typical need to replicate time signals in the automobile industry. Similar problems appear also in other fields as machine tool applications, aeronautic industry a.o.

STABLE DYNAMIC INVERSION OF NONMINIMUM-PHASE SCALAR LINEAR SYSTEMS

The paper presents a transfer function approach to the stable dynamic inversion of nonminimum-phase scalar linear systems. The technique is based on the study of the structure of the causal unstable input obtained with the standard inversion technique. It is shown that the unbounded term of this input can be decomposed as the sum of a linear combination of unstable zero modes for which new formulae are provided. Then, a closed-form expression of the bounded noncausal solution of the input-output inversion problem is proposed. An automatic inversion scheme built by exploiting the new inversion formula is also presented.

State Space Modeling and Stable Dynamic Inversion for Trajectory Tracking on an Industrial Seat Test Rig

This paper introduces a novel approach for trajectory tracking on seat test rigs. Seat test rigs are used in the automotive industry to test prototypes of new seats with respect to their comfort and vibration characteristics. Classically, a digital Fourier transform (DFT) approach, based on a Frequency Response Function (FRF) model, is used in this domain and different software packages exist that are based on this approach. The novel approach proposes state space models to identify the test rig and uses the recently developed Stable Dynamic Inversion (SDI) to invert the obtained state space models. The approach is validated on an industrial seat test rig and it is shown that the new approach is a competitive alternative to the existing DFT based methods. A closed loop experiment is also performed; this shows that the feedback controller allows one to reduce the state space model order without loss of accuracy.

ROBUST MULTIVARIABLE SET-POINT REGULATION VIA STABLE DYNAMIC INVERSION

In this paper we propose a design methodology for the robust regulation of uncertain nonminimum-phase multivariable linear systems. The method basically consists of defining a suitable vector of parameterized desired output functions and of designing a parameterized decoupling controller of the nominal plant. Then, a parameterized command function for each input is determined by means of a stable dynamic inversion procedure. Eventually, solving an optimization problem permits to minimize the worst-case settling time, subject to amplitude limits on the control variables and constraints on the overshoots and undershoots of the outputs. A worked example based on a three-inputs three-outputs plant shows the effectiveness of the methodology.

Optimal inversion-based control for the set-point regulation of nonminimum-phase uncertain scalar systems

We propose an optimal inversion-based control for the set-point constrained regulation of nonminimum-phase uncertain scalar systems. This approach is based on a new control architecture where the main purpose of the feedback is to reduce the sensitivity to parametric plant uncertainties permitting in such a way the effective use of a feedforward action determined via a stable dynamic inversion. Essential constituents of the architecture are a parameterized family of "transition" polynomials to shape ideal output transfers and a parameterized controller ensuring the internal model principle. The methodology is then centered on the optimal combined design of the feedback controller and of the inversion-based command signal in order to minimize the worst-case settling time subject to an amplitude constraint on the control variable and to arbitrarily assigned overshoot and undershoot bounds. Finally, an approximate or suboptimal solution to the resulting nonlinear optimization problem can be obtained by genetic algorithms. A worked example highlights the effectiveness of the overall methodology.

Motion perception in schizophrenic patients

In this paper we propose a design methodology for the robust regulation of uncertain nonminimum-phase multivariable linear systems. The method basically consists of defining a suitable vector of parameterized desired output functions and of designing a parameterized decoupling controller of the nominal plant. Then, a parameterized command function for each input is determined by means of a stable dynamic inversion procedure. Eventually, solving an optimization problem permits to minimize the worst-case settling time, subject to amplitude limits on the control variables and constraints on the overshoots and undershoots of the outputs. A worked example based on a three-inputs three-outputs plant shows the effectiveness of the methodology.