Multiple-output Dynamic Systems Research Articles

Statistical inference of multivariable modal stability margins of time-delay perturbed power systems

This paper proposes a modal statistical inference algorithm to define multivariable operational stability limits of time-delay perturbed dynamic systems by employing remote sensor signals. Our proposal overcomes the drawbacks of linear independence and inter-area geometry of time-delays to analyze multiple-input, multiple-output dynamic systems. The manuscript contributes with: (a) the study of stability margins under distributed uncertainty and time-delays for large power systems, (b) the determination of stability conditions of inter-area oscillations through a new probabilistic modeling approach under the influence of intermissions, and (c) the usage of the proposed methodology to derive controlled stability limits and assess the modal resilience of perturbed power systems. Studies on the multi-scale signals sensitivity and multivariable polynomial intersection from empirical perspectives in modal stability analysis are also explored. Results on an IEEE 16-generator 68-bus system are presented to illustrate the effectiveness of the proposed algorithm. The estimation of multivariable operational stability limits and time-delays of inter-area oscillation modes are verified with the vector fitting procedure and first-order Padé approximation.

On the Output of Nonlinear Systems Excited by Discrete Prolate Spheroidal Sequences

The discrete prolate spheroidal sequences (DPSSs)—a set of optimally bandlimited sequences with unique properties—are important to applications in both science and engineering. In this work, properties of nonlinear system response due to DPSS excitation are reported. In particular, the sequences are shown to be approximately orthogonal after passing through a nonlinear, multiple-input multiple-output dynamical system under quite general conditions. This work quantifies these conditions in terms of constraints upon the higher-order generalized transfer functions characterizing the Volterra expansion of a MIMO system, the Volterra order of the system, and the DPSS bandwidth parameter $W$ and time-bandwidth parameter $NW$ . The approximate system output orthogonality allows multiple-input, multiple-output characterization of the linear narrowband response of a nonlinear system using simultaneous, DPSS excitation.

Generalized spline nonlinear adaptive filters

A new spline based generalized non-linear filter.Adaptive spline function is used as basis function.Provides improved classification accuracy.Successfully applied in dynamic system identification. A new nonlinear filter, which employs an adaptive spline function as the basis function is designed in this paper. The input signal to this filter is used to generate suitable parameters to update the control points in a spline function. The update rule for updating the control points have been derived and a mean square analysis has been carried out. The output of the spline functions are suitably combined together to obtain the filter response. This filter is called the generalized spline nonlinear adaptive filter (GSNAF). The proposed GSNAF is similar to a functional link artificial neural network (FLANN), considering a functional expansion using spline basis functions. GSNAF has been shown to offer improved accuracy in benchmark classification scenarios and provide enhanced modeling accuracy in single input single output as well as in multiple input multiple output dynamic system identification cases.

D-RM Builder: A software tool for generating fast and accurate nonlinear dynamic reduced models from high-fidelity models

Abstract Dynamic reduced models (D-RMs) derived from rigorous models are highly desired for speeding up dynamic simulations. A useful software tool named D-RM Builder was developed to automatically generate data-driven D-RMs from high-fidelity dynamic models. It allows a user to configure input/output variables, sample input space and generate sequences of step changes, launch high-fidelity model simulations, fit simulation results to a D-RM, and finally visualize and validate the D-RM. The Decoupled A-B Net (DABNet) nonlinear system identification model was used as the main D-RM type and was enhanced to model nonlinear multiple input and multiple output dynamic systems with options for double-pole formulation to handle fast/slow time scales and pole value optimization. The D-RM Builder tool has been successfully used to generate D-RMs for a highly nonlinear pH neutralization reactor system and a two-time-scale bubbling fluidized bed adsorber-reactor for CO2 capture.

Analytical synthesis of functional low-order observers

Simultaneous estimation of several linear combinations of the state variables of a multiple input---multiple output dynamical system is considered. A method for decomposing the state vector into several components is proposed such that only some of these components are needed to reconstruct the desired vector function. An algorithm for the analytical synthesis is described that yields a functional observer of the minimum possible order. The procedure for computing the observer coefficients is reduced to a modal control problem. The proposed method is based on the matrix canonization technique.

Nonlinear predictive control for Hammerstein–Wiener systems

This paper discusses a nonlinear Model Predictive Control (MPC) algorithm for multiple-input multiple-output dynamic systems represented by cascade Hammerstein–Wiener models. The block-oriented Hammerstein–Wiener model, which consists of a linear dynamic block embedded between two nonlinear steady-state blocks, may be successfully used to describe numerous processes. A direct application of such a model for prediction in MPC results in a nonlinear optimisation problem which must be solved at each sampling instant on-line. To reduce the computational burden, a linear approximation of the predicted system trajectory linearised along the future control scenario is successively found on-line and used for prediction. Thanks to linearisation, the presented algorithm needs only quadratic optimisation, time-consuming and difficult on-line nonlinear optimisation is not necessary. In contrast to some control approaches for cascade models, the presented algorithm does not need inverse of the steady-state blocks of the model. For two benchmark systems, it is demonstrated that the algorithm gives control accuracy very similar to that obtained in the MPC approach with nonlinear optimisation while performance of linear MPC and MPC with simplified linearisation is much worse.

Model Independent Numerical Procedure for the Diagonalization of a Multiple Input Multiple Output Dynamic System

Seismic noise limits Earth based gravitational wave interferometric detectors at low frequencies. The detection threshold can be lowered down to a few Hz using a seismic attenuation system based on Inverted Pendulum (IP) which sustains interferometer optical components by means of a chain of pendulums. The IP, acting as a mechanical low pass filter, is able to filter out seismic noise in the horizontal plane and at the same time it provides a quasi-inertial stage where the suspension point of the chain of pendulums lies. The main degrees of freedom of an IP are three: two translational modes and one rotational mode. Therefore, to fully determinate its position, three independent sensors are mounted at the periphery of the IP top table. For the same reason, three independent actuators are used to move the IP. The geometrical position of the sensors is different from actuator positions, in addition, both of them are not connected to the normal modes of the IP. Each sensor will be sensitive in all the three IP normal modes and each actuator will generate movements which are a mix of the three modes. To take advantage of controlling a Single Input Single Output (SISO) system instead of a Multiple Input Multiple Output (MIMO) system, a diagonalization of the actuation and detection system is needed. An original and model independent experimental procedure for determining the system dynamics, giving an effective diagonalization has been developed and tested.

Tracking in linear MIMO systems under external perturbations

Consideration was given to tracking the given trajectories of the output variables of the linear multiple-input multiple-output dynamic systems under uncontrollable external perturbations. A procedure to rearrange the mathematical model of a control plant in a consistent block form of controllability and observability of the output (measurable) variables with regard for the external perturbations was developed within the framework of the block approach. This form underlies the decomposition procedures of feedback design enabling one to track the given trajectories invariantly to the external perturbations.

To Drop or Not to Drop: Design Principles for Kalman Filtering Over Wireless Fading Channels

It is the general assumption that in estimation and control over wireless links, the receiver should drop any erroneous packets. While this approach is appropriate for non real-time data-network applications, it can result in instability and loss of performance in networked control systems. In this technical note we consider estimation of a multiple-input multiple-output dynamical system over a mobile fading communication channel using a Kalman filter. We show that the communication protocols suitable for other already-existing applications like data networks may not be entirely applicable for estimation and control of a rapidly changing dynamical system. We then develop new design paradigms in terms of handling noisy packets for such delay-sensitive applications. We reformulate the estimation problem to include the impact of stochastic communication noise in the erroneous packets. We prove that, in the absence of a permanent cross-layer information path, packet drop should be designed to balance information loss and communication noise in order to optimize the performance.

Studies on On-line State and Parameter Estimation through a Real-time Process Simulator

A PC-based simulator of non-linear multiple-input multiple-output dynamic systems was employed for studies concerning the on-line estimation of both ‘non-measured’ state variables and multiple specific growth rates of a virtual baker’s yeast fed-batch fermentation. The identification algorithms were implemented in an ‘Observer Computer’ which received, optionally in ‘real-time’, in ‘scaled time’ or in ‘simulation time’, the ‘measured’ state variables generated by the process simulator in the ‘Process Computer’. The state observer showed a robust behaviour under different situations where process parameters, operating variables and measuring characteristics (noise and delays) were changed in the process computer. The simulation package was seen to be an efficient and cheap tool for the simulation of non-linear processes with time varying parameters, providing a realistic environment for tests of identification, estimation and control strategies.