Disturbance Model Identification and Model Free Synthesis of Controllers for Multivariable Systems

In this work, two different problems are addressed. In the first part, the problem of synthesizing a set of stabilizing controllers for unknown multivariable systems using direct data is analyzed. This is a model free approach to control design and uses only the frequency domain data of the system. It is a perfect complement to modern and post modern methods that begin the control design with a system model. A three step method, involving sequential design, search for stability boundaries and stability check is proposed. It is shown through examples that a complete set of stabilizing controllers of the chosen form can be obtained for the class of linear stable multivariable systems. The complexity of the proposed method is invariant with respect to the order of the system and increases with the increase in the number of input channels of the given multivariable system. The second part of the work deals with the problem of identification of model uncertainties and the effect of unwanted exogenous inputs acting on a discrete time multivariable system using its output information. A disturbance model is introduced which accounts for the system model uncertainties and the effect of unwanted exogenous inputs acting on the system. The frequency content of the exogenous signals is assumed to be known. A linear dynamical model of the disturbance is assumed with an input that has the same frequency content as that of the exogenous input signal. The extended model of the system is then subjected to Kalman filtering and the disturbance states estimates are used to obtain a least squares estimate of the disturbance model parameters. The proposed approach is applied to a linear multivariable system perturbed by an exogenous signal of known frequency content and the results obtained depict the efficacy of the proposed approach

Data compression for estimation of the physical parameters of stable and unstable linear systems

A two-stage method for the identification of physical system parameters from experimental data is presented. The first stage compresses the data as an empirical model which encapsulates the data content at frequencies of interest. The second stage then uses data extracted from the empirical model of the first stage within a nonlinear estimation scheme to estimate the unknown physical parameters. Furthermore, the paper proposes use of exponential data weighting in the identification of partially unknown, unstable systems so that they can be treated in the same framework as stable systems. Experimental data are used to demonstrate the efficacy of the proposed approach

A Robust Approach to Optimal Matched Filter Design in Ultrasonic Non-Destructive Evaluation (NDE)

The matched filter was demonstrated to be a powerful yet efficient technique to enhance defect detection and imaging in ultrasonic non-destructive evaluation (NDE) of coarse grain materials, provided that the filter was properly designed and optimized. In the literature, in order to accurately approximate the defect echoes, the design utilized the real excitation signals, which made it time consuming and less straightforward to implement in practice. In this paper, we present a more robust and flexible approach to optimal matched filter design using the simulated excitation signals, and the control parameters are chosen and optimized based on the real scenario of array transducer, transmitter-receiver system response, and the test sample, as a result, the filter response is optimized and depends on the material characteristics. Experiments on industrial samples are conducted and the results confirm the great benefits of the method

Estimation of generalised frequency response functions

Volterra series theory has a wide application in the representation, analysis, design and control of nonlinear systems. A new method of estimating the Volterra kernels in the frequency domain is introduced based on a non-parametric algorithm. Unlike the traditional non-parametric methods using the DFT transformed input-output data, this new approach uses the time domain measurements directly to estimate the frequency domain response functions

Piecewise Volterra modelling of the Duffing oscillator in the frequency domain

When analysing the nonlinear Duffing oscillator, the weak nonlinearity is basically dependent on the amplitude range of the input excitation. The nonlinear differential equation models of such nonlinear oscillators, which can be transformed into the frequency domain, can generally only provide Volterra modelling and analysis in the frequency-domain over a fraction of the entire framework of weak nonlinearity. This paper discusses the problem of using a new non-parametric routine to extend the capability of Volterra analysis, in the frequency domain, to weakly nonlinear Duffing systems at a wider range of excitation amplitude range which the current underlying nonlinear differential equation models fail to address

Estimation of the parameters of continuous-time systems using data compression

This chapter provides a unified introductory account of the estimation of the parameters of continuous-time systems using data compression based on a number of previous publication

A Data-driven Approach to Robust Control of Multivariable Systems by Convex Optimization

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of matrix polynomial functions and can be formulated as a centralized, decentralized or distributed controller. All standard performance specifications like $H_2$, $H_\infty$ and loop shaping are considered in a unified framework for continuous- and discrete-time systems. The control problem is formulated as a convex-concave optimization problem and then convexified by linearization of the concave part around an initial controller. The performance criterion converges monotonically to a local optimal solution in an iterative algorithm. The effectiveness of the method is compared with fixed-structure controllers using non-smooth optimization and with full-order optimal controllers via simulation examples. Finally, the experimental data of a gyroscope is used to design a data-driven controller that is successfully applied on the real system