Hiroshi Oku

Brief Recursive 4SID algorithms using gradient type subspace tracking

Sometimes we obtain some prior information about a system to be identified, e.g., the order, model structure etc. In this paper, we consider the case where the order of a MIMO system to be identified is a priori known. Recursive subspace state-space system identification algorithms presented here are based on the gradient type subspace tracking method used in the array signal processing. The algorithms enable us to estimate directly the subspace spanned by the column vectors of the extended observability matrix of the system to be identified without performing the singular value decomposition. Also, a new convergence proof of the gradient type subspace tracking is given in this paper. Under the condition of a step size between 0 and 1, we prove the convergence property of the recursive equation of the gradient type subspace tracking. A numerical example illustrates that our algorithm is more robust with respect to the choice of the initial values than the corresponding PAST one.

Washout Control for Manual Operations

It is known that limitations of human accuracy in manual manipulation hinder the quality of work performed by human operators of manual control systems. Indeed, movements of operators are apt to cause undesirable vibrations in manual control systems. In this paper, we propose a new operator-support control scheme for suppressing harmful oscillatory motions in such systems without disturbing human operators manipulation. The proposed scheme is based on the fact that steady-state blocking zeros of a feedback controller do not affect the steady-state control input. A finite-dimensional feedback controller with steady-state blocking zeros, called a washout controller in this paper, plays the central role in support for operators manipulation. However, the dynamics of a manual control system may become different significantly from its initial model used for the design of an initial washout controller when it is applied to the manual control system. Such difference can result in poor performance of operator-support control. In order to improve it, an iterative procedure is presented for redesign of washout controllers based on closed-loop subspace identification. Closed-loop identification is performed to refine the model for the control design, and then a more sophisticated washout controller is obtained using the identified model. The effectiveness of the proposed scheme is demonstrated by an experiment on manual control of an inverted pendulum.

Change detection in the dynamics with recursive subspace identification

We propose a tracking mechanism to follow time-variations in the dynamics of a linear system with a recursive identification of the PI-MOESP scheme. The proposed mechanism consists of change detection scheme followed by a re-initialization of the recursive calculations. The change detection is based on the least-squares interpretation of the calculation in the subspace scheme and detects whether the estimates of the recursive solution without exponential forgetting lies in the confidence interval of the estimates obtained with a second finite-window length solution to the least-squares problem. When a change has been detected, the estimate by the recursive implementation is re-initialized via the solution of a constrained least-squares problem. One numerical example is presented to illustrate that our change detection and reinitialization scheme can detect incipient changes in the system dynamics without detecting changes in input dynamics.

Direct subspace model identification of LTI systems operating in closed-loop

In this paper, a subspace identification method of estimating the input-output relation of a linear system operating in closed-loop is presented. The proposed method is a straightforward consequence of the integration of the two-stage method with PI-MOESP type subspace identification method. It is shown that such integration brings the omission of the first stage identification, i.e., the omission of the identification of the sensitivity function of closed-loop and subsequent reconstruction of the fictitious input sequence. Therefore, the proposed method is able to estimate the input-output relation of a linear system in closed-loop directly from sampled sequences of observed signals.

Application of a recursive subspace identification algorithm to change detection

Abstract This paper presents a new change detection method with the aid of subspace identification. The proposed method is based on monitoring a change in variance of a statistic generated by a recursive subspace identification algorithm. An asymptotic property of the statistic is presented. Without changes during sampling, it is shown that, under relevant assumptions. the statistic converges in probability to a stack of noise vectors multiplied from the left side by a Toeplitz matrix. A numerical example illustrates that the proposed method can detect changes in the dynamics of a system, without being disturbed by changes in the dynamics of an input signal which are not our concern.

MIMO closed-loop subspace model identification and hovering control of a 6-DOF coaxial miniature helicopter

This paper concerns black-box modeling of a radio-controlled (RC) coxial miniature helicopter by closed-loop subspace model identification with a multi-input and multi-output (MIMO) state space model, as well as model-based control design of hovering flight using the identified black-box model. The RC helicopter has 6 degrees of freedom (6-DOF) in its motions, namely, the lateral (left/right), vertical (up/down), longitudinal (fore/aft), pitching, rolling and yawing axes. These 6 parameters of the position and posture, as the outputs of the RC helicopter, are measured by a motion capture system with 6 high-speed cameras. The helicopter maneuvers, as the inputs, are done by the aileron, elevator, rudder and throttle. A closed-loop system identification experiment of the hovering RC helicopter is performed. CL-MOESP, which is one of closed-loop subspace model identification methods, is applied to the sampled closed-loop data in order to obtain a state-space model with an estimated order. Using the identified model, an LQ controller with a full-state observer is designed. Finally, as verification of the identified model, an experiment of hovering flight of the helicopter is performed with the implementation of the feedback controller.

Estimation error analysis of system matrices in some subspace identification methods

Explicit formulation of dominant parts of the estimation errors of system matrices in PO-MOESP method and a robust N4SID like method are derived based on a proposing lemma on a gap between two singular subspaces. By considering the gap instead of the perturbations of the singular vectors, it is shown that the estimate in PO-MOESP method is unbiased while the estimate in the robust N4SID like method has an asymptotic bias when the past horizon p is finite.

MIMO Closed-Loop Subspace Model Identification and Hovering Control of a Coaxial Mini Helicopter with 3 DOFs

Abstract This paper reports the experimental results of the dynamic modelling using MIMO closed-loop system identification, controller design and implementation for hovering flight of a coaxial radio-controlled helicopter. The helicopter is set on our handcrafted supporting device, and it has the roll, side-to-side and up-and-down motions. The maneuvers are done by the aileron and the throttle. Hence, our system is with 2 inputs and 3 outputs. A dynamic model is derived for hovering flight conditions from closed-loop system identification experiments with the MOESP-type closed-loop subspace model identification method (CL-MOESP). Then, LQR with a full state observer is designed and implemented.

Asymptotic Properties of Bias Compensated State Space Model Identification Method

Abstract The authors proposes a bias-compensated state space model identification (BCSS) method in order to relax the order of the persistent excitation (PE) condition. Most of the subspace identification methods utilize instrumental variables (IV) to obtain an unbiased estimate while the proposed method introduces a bias compensation technique to the Ordinary MOESP type method. In this paper, S/N ratios of certain matrices in the proposed method and the PI-MOESP method are analyzed and compared. It is shown that the S/N ratio in the proposed method is better than that in the PI-MOESP method especially when a pole of the plant is near 1 and the number of the block rows of the IV matrix is small.

Adaptive modeling and compliance control for RC servo motor

This paper concerns compliance motion control for joints of a humanoid robot for the external force. Our strategy is to estimate the amount of the external force by measuring the motor drive current of the RC servo motor since auxiliary current sensors can be attached easily. However, we did not consider about the dynamics of RC servo motor. The aim of this paper is to propose the adaptation scheme to identify the dynamics model of RC servo motor. We construct a time-varying adaptive identifier of the parameters with adaptation law based on adaptive control theory and give successful results in our numerical simulation.