Multi-input Multi-output System Identification Research Articles

A new structure for non-linear black-box system identification using the extended Kalman filter

A new tool for black-box non-linear system identification of multi-input multi-output systems is presented in this paper. The new structure extends the conventional linear state-space model into a non-linear framework, where each parameter is a non-linear function of the inputs or the states. The method works iteratively in the time domain using an extended Kalman filter. The model retains a state-space structure in modal canonical form, which ensures that a minimal number of parameters need to be identified and also produces additional information in terms of the system eigenvalues and the dominant modes. This structure is a completely black-box system, which requires no physical understanding of the process for successful identification, and it is possible to expand easily the order and the complexity of non-linearities, while ensuring good parameter conditioning. A simple non-linear example illustrates the method, and identification of a highly non-linear brake model is also presented. These examples show that the method can be applied as a mechanism for model order reduction; it is equally very suitable as a tool for non-linear plant system identification. In both capacities this new method is valuable, particularly as the generation of simplified models for the whole vehicle and its subsystems is an increasingly important aspect of modern vehicle design.

Estimation of Human Hip and Knee Multi-Joint Dynamics Using the LOPES Gait Trainer

In this study, we present and evaluate a novel method to estimate multi-joint leg impedance, using a robotic gait training device. The method is based on multi-input–multi-output system identification techniques and is designed for continuous torque perturbations at the hip and knee joint simultaneously. Eight elderly subjects (age 67–82) performed relax and position tasks in three different leg orientations. Multi-joint impedance was estimated nonparametrically and was subsequently modeled in terms of inertia and (inter)joint stiffness and damping. The results indicate that all stiffness and damping parameters were significantly higher during the position task compared to the relax task. The majority of the stiffness and damping parameters were not significantly affected by leg orientation. The results also emphasize the importance of considering the visco-elastic coupling between joints when modeling multi-joint dynamics. Measuring joint stiffness with the same device that is used for robotic gait training allows convenient testing of joint properties in conjunction with the robotic gait training protocol. These measures might serve as a good basis for quantitative assessment and follow up of patients with abnormal joint stiffness due to neurological disorders, and may reveal how changes in these joint properties affect their gait function.

Piezoelectric Beam for Intrabody Propulsion Controlled by Embedded Sensing

The body is a very challenging environment for locomotion. The mechanical properties of intrabody fluids and tissues vary by location and time. In order to move an embedded biomedical device such as a deep brain stimulation electrode, one has to identify the properties of the environment and set the propulsive actuator's input accordingly. We developed a piezoelectric actuator for propelling a microrobot in cerebro spinal fluid or burrowing in the brain tissue parenchyma. The propulsion is created by the vibration of the beam at the resonance frequencies. The driving of the actuators is controlled by in situ multi-input multi-output system identification (SI) using part of the beam as sensor and part as actuator. In this study, we model the sensing of the device, present the SI method, the calculation of the input signals to achieve maximal propulsion, and we test the driving method experimentally. The microactuator is examined in 500-cP silicon oil and a 20-mm-long actuator can achieve 3-μN propulsive force.

Identification of Multi-Input Multi-Output Systems Using Combined Direct and Indirect Methods

Successful deployment of cooperative decentralized model predicative control needs reasonably accurate subsystem interactions models. Processes in which open-loop tests are not permitted, closed-loop identification of subsystems interactions is crucial. An approach that combines the direct and indirect methods of closed-loop identification is proposed in this paper. It is shown that full dynamics of MIMO systems can be determined following a two-steps identification procedure. A representative case study is used to demonstrate the efficacy of the proposed approach.

System stability improvement through optimal control allocation in voltage source converter-based high-voltage direct current links

Control of both active and reactive power in voltage source converter (VSC)-based high-voltage direct current (HVDC) links could be very effective for system stability improvement. The challenge, however, is to properly allocate the overall control duty among the available control variables in order to minimise the total control effort and hence allow use of less expensive converters (actuators). Here relative gain array and residue analysis are used to identify the most appropriate control loops avoiding possible interactions. Optimal allocation of the secondary control duty between the two ends of the VSC HVDC link is demonstrated. Active and reactive power modulation at the rectifier end, in a certain proportion, turns out to be most effective. Two scenarios, with normal and heavy loading conditions, are considered to justify the generality of the conclusions. Subspace-based multi-input–multi-output system identification is used to estimate and validate linearised state-space models through pseudo random binary sequence probing. Linear analysis is substantiated with non-linear simulations in DIgSILENT PowerFactory with detailed representation of HVDC links.

Decentralized robust control-system for a non-square MIMO system, the air-path of a turbocharged Diesel engine

The targeted purpose here is the control of a nonlinear and non-square system with three inputs and two outputs in order to reduce soot and greenhouse gas pollutants. In this paper, a non-square multivariable controller for the air-path system of a turbocharged Diesel engine is proposed. The controller is designed using the CRONE (Commande Robuste d'Ordre Non Entier) Control-System-Design approach to maintain performance and robust stability for a wide set of operating points. In this research, we focused on the multi-input multi-output system identification problem, and test-bench data were processed to find a nominal linear model. The controller was then designed via an open-loop transfer function optimization. Finally, simulation results from a simulation model show the performance of the proposed control-system.

Integration of support vector regression and annealing dynamical learning algorithm for MIMO system identification

This paper presents a robust approach to identify multi-input multi-output (MIMO) systems. Integrating support vector regression (SVR) and annealing dynamical learning algorithm (ADLA), the proposed method is adopted to optimize a radial basis function network (RBFN) for identification of MIMO systems. In the system identification, first, SVR is adopted to determine the number of hidden layer nodes, the initial structure of the RBFN. After initialization, ADLA with nonlinear time-varying learning rate is then applied to train the RBFN. In the ADLA, the determination of the learning rate would be an important work for the trade-off between stability and speed of convergence. A computationally efficient optimization method, particle swarm optimization (PSO) method, is adopted to simultaneously find optimal learning rates. Due to the advantages of SVR and ADLA (SVR-ADLA), the proposed RBFN (SVR-ADLA-RBFN) has good performance for MIMO system identification. Two examples are illustrated to show the feasibility and superiority of the proposed SVR-ADLA-RBFNs for identification of MIMO systems. Simulation results are provided to demonstrate the effectiveness of the proposed algorithm.

Identification and Control of MIMO Systems with State Time Delay (Short Communication)

Time-delay identification is one of the most important parameters in designing controllers. In the cases where the number of inputs and outputs in a system are more than one, this identification is of great concern. In this paper, a novel autocorrelation-based scheme for the state variable time-delay identification for multi-input multi-output (MIMO) system has been presented. This method is based on the stochastic phenomena which are capable of identifying each state variable independent of other variables, a control strategy for controlling such systems; and furthermore confirming the stability criteria. The results demonstrate the effectiveness of the proposed control strategy which has the advantage of confirming the stability, simple implementation and analysis.

Closed-Loop Identification of MIMO Systems: A New Look at Identifiability and Experiment Design

This paper addresses a question that has been posed to us: Is it necessary to excite all reference signals for the identification of a multivariable system operating in closed loop with a linear lime-invariant controller? In this paper, we follow a careful re-examination of the notions of identifiability and informative experiments for multi-input multi-output (MIMO) closed-loop systems, which provides a negative answer to this question. Our analysis also allows to establish conditions on the controller complexity that guarantee existence of a unique global minimum of the identification criterion in the absence of external excitation; these conditions extend to the MIMO case conditions that were known for the SISO case. We illustrate our results for 2-input 2-output systems by presenting various possible experiment designs that produce a unique global minimum for the identification criterion.

Design of Ternary Signals for MIMO Identification in the Presence of Noise and Nonlinear Distortion

A new approach to designing sets of ternary periodic signals with different periods for multi-input multi-output system identification is described. The signals are pseudo-random signals with uniform nonzero harmonics, generated from Galois field GF(q), where q is a prime or a power of a prime. The signals are designed to be uncorrelated, so that effects of different inputs can be easily decoupled. However, correlated harmonics can be included if necessary, for applications in the identification of ill-conditioned processes. A design table is given for q les 31. An example is presented for the design of five uncorrelated signals with a common period N = 168 . Three of these signals are applied to identify the transfer function matrix as well as the singular values of a simulated distillation column. Results obtained are compared with those achieved using two alternative methods.

Identification of MIMO systems using radial basis function networks with hybrid learning algorithm

When a radial basis function network (RBFN) is used for identification of a nonlinear multi-input multi-output (MIMO) system, the number of hidden layer nodes, the initial parameters of the kernel, and the initial weights of the network must be determined first. For this purpose, a systematic way that integrates the support vector regression (SVR) and the least squares regression (LSR) is proposed to construct the initial structure of the RBFN. The first step of the proposed method is to determine the number of hidden layer nodes and the initial parameters of the kernel by the SVR method. Then the weights of the RBFN are determined by solving a simple minimization problem based on the concept of LSR. After initialization, an annealing robust learning algorithm (ARLA) is then applied to train the RBFN. With the proposed initialization approach, one can find that the designed RBFN has few hidden layer nodes while maintaining good performance. To show the feasibility and superiority of the annealing robust radial basis function networks (ARRBFNs) for identification of MIMO systems, several illustrative examples are included.

Subspace method for continuous-time fractional system identification

The aim of this paper is to develop a subspace method for state-space identification of continuous-time systems using fractional commensurate models. As compared to the classical state-space representation, the commensurate differentiation order must be estimated besides the state-space matrices. The latter are estimated with conventional subspace-based techniques using QR and singular value decompositions, whereas the commensurate order is estimated using nonlinear programming. This is the first method developed for multi-input multi-output system identification of fractional models. The performances are demonstrated by simulations at various signal-to-noise ratios assuming a known then an unknown commensurate order.

STATE-SPACE MODEL IDENTIFICATION USING INPUT AND OUTPUT DATA WITH STEADY STATE VALUES

In this paper, we propose a new deterministic off-line identification method that obtains a state-space model by using input and output data with steady state values. This method is composed of the method, M. Kosaka, K. Koizumi and H. Shibata Transactions of the Society of Instrument and Control Engineers 36(4), 2000, 319-327. zeroing the 0 ∼ N-tuple integral values of output error of single-input single-output transfer function model and Ho-Kalman's method, H.P. Zeiger and A.J. Mc Ewen, IEEE Transactions on Automatic Control, AC 19-2, 1974, 153. The feature is that this method can identify by using step responses and, consequently, this is suitable for mechanical system identification in which noise and vibration are undesirable. Numerical simulations of multi-input multi-output system identification and experimental results are illustrated.

Online neural identification of multi-input multi-output systems

A feedforward neural network tuning algorithm is developed, which is suitable for identification of multi-input multi-output nonlinear functions, by utilising the learning method of a conventional neuro-adaptive control technique. Using Lyapunov functions, it is shown that not only the approximation error converges to values that have arbitrarily reducible upper bounds, but also the weights of the neural network remain bounded. The effectiveness of the identification method and its application in force-control of an uncertain robot interacting with an unknown flexible environment are investigated as an application example.

State-space Model Identification Using Input and Output Data With Steady State Values Zeroing Multiple Integrals of Output Error

This study proposes a new deterministic off-line identification method that obtains a state-space model using input and output data with steady state values. This method comprises of two methods: Zeroing the 0∼N-tuple integral values of the output error of single-input single-output transfer function model (Kosaka et al., 2004) and Ho-Kalman’s method (Zeiger and McEwen, 1974). Herein, we present a new method to derive a matrix similar to the Hankel matrix using multi-input and multi-output data with steady state values. State space matrices A, B, C, and D are derived from the matrix by the method shown in Zeiger and McEwen, 1974 and Longman and Juang, 1989. This method’s utility is that the derived state-space model is emphasized in the low frequency range under certain conditions. Its salient feature is that this method can identify use of step responses; consequently, it is suitable for linear mechanical system identification in which noise and vibration are unacceptable. Numerical simulations of multi-input multi-output system identification are illustrated.

해석적인 정보를 고려한 다중입력을 받는 다자유도계 구조물의 시스템 규명 기법 개발

This paper presents a system identification method for multi-input, multi-output (MIMO) systems, by which a rational polynomial transfer function model is identified from experimentally determined frequency response function data. Analytically determined information is incorporated in this method to obtain a more reliable model, even in the frequency range where the excitation energy is limited. To verify the suggested method, shaking table test for an actively controlled two-story, bench-scale building employing an active mass damper is conducted. The results show that the proposed method is quite effective and robust for system identification of MIMO systems.

定常値をもつ入出力信号を用いた状態空間モデルの同定

In this paper, we propose a new deterministic off-line identification method that delivers a state-space model by using input and output data with steady state values. This method combines the method zeroing the 0N-tuple integral values of output error of single-input single-output transfer function model and Ho-Kalman's method. The feature is that this method can identify by using step responses and, consequently, this is suitable for a mechanical system identification in which persistent fluctuations are unacceptable. Numerical simulations of multi-input multi-output system identification are illustrated and the practicability is verified by application to a pneumatic two link arm system.

Improved State-Space Model Identification Using Input and Output Data with Steady State Values

In this paper, we improve the deterministic off-line identification method (Kosaka et. al., 2002) that obtains a state-space model from input and output data with a constant steady state response. The method is composed of determining the parameters by zeroing the 0 ~ N-tuple integral values of output error between the plant and the model (Kosaka et. al., 2000) and by using Ho-Kalman's method (Zeiger et. al., 1974). The method theoretically has an assumption that plant system matrix A satisfies |A| < 1 because the method utilizes Taylor series expansion. But the method can be applied to plants without the assumption |A| < 1. The feature is that the method is performed by using a step response, which is suitable to a mechnical system where noise and vibration are undesirable, and that the identification result is accurate at low frequency range. Numerical simulations of multi-input multi-output system identification are illustrated.

Identification of discrete-time MIMO systems using a class of observable canonical-form

The paper presents an identification algorithm for a discrete-time (D-T) multiinput multioutput (MIMO) deterministic system. The proposed identification algorithm which is based on calculating a matrix fraction description (MFD) from available input-output data can be considered as a version of the recently developed subspace model identification (SMI) schemes. The system to be identified is represented using a special class of observable canonical-forms which have the property that all its observability indices are equal. The used observable canonical-form is convenient in the sense that it makes the identification problem of the MIMO systems very similar to that of the single-input single-output (SISO) systems. The theoretical developments are verified through the use of the proposed algorithm to identify a minimal order state space model of a boiler used in the petroleum industry in Kuwait.

Uncorrelated multisymbol signals for MIMO system identification

This paper presents a new approach to the system identification of a two-input two-output multivariable system. In a similar manner to that used for the single-input/single-output system, the multi-input multi-output (MIMO) system response may be obtained directly from measured input output frequency responses. An investigation of compact multifrequency data measurement signals, which have been extensively cataloged by the authors, has provided compact multifrequency ternary and quaternary input signals that have uncorrelated spectra. They are powerful multisymbol, multilevel computer generated measurement signals whose signal power is concentrated in either two or three dominant harmonics. As the signals, which are given in this paper, have six, seven, or eight symbols in their measurement codes, both the computation time for the frequency estimates and the experimental time are minimized. Two multifrequency quaternary signals with uncorrelated spectra are used to identify a simulated distillation column. It is shown that the cross coupling terms between the measurement channels may be removed by these digital measurement signals with the same number of symbols but different measurement codes.