Goro Obinata

Model Reduction for Control System Design

An approach and a technique for effectively obtaining reduced order mathematical models of a given large order model for the purposes of synthesis, analysis and implementation of control systems is developed. This approach involves the use of an error criterion which is the H-infinity norm of a frequency weighted error between the full and reduced order models. The weightings are chosen to take into account the purpose for which the reduced order model is intended. A previously unknown error bound in the H-infinity norm for reduced order models obtained from internally balanced realizations was obtained. This motivated further development of the balancing technique to include the frequency dependent weightings. This resulted in the frequency weighted balanced realization and a new model reduction technique. Two approaches to designing reduced order controllers were developed. The first involves reducing the order of a high order controller with an appropriate weighting. The second involves linear quadratic Gaussian synthesis based on a reduced order model obtained with an appropriate weighting.

Restoration and analysis of standing-up in complete paraplegia utilizing functional electrical stimulation

OBJECTIVEnRestoration of stand-up motion in patients with complete paraplegia utilizing multichannel functional electrical stimulation, and analysis of the restored motion.nnnDESIGNnNonrandomized control trial.nnnSETTINGnGeneral community, a referral center, institutional practice, and ambulatory care:nnnPATIENTSnTwelve volunteer samples were used for the collection of normal data. Two complete paraplegics received treatment for the restoration of stand-up motion.nnnMAIN OUTCOME MEASURESnThe electromyogram, joint angle, and floor reaction force were investigated during standing-up with arms crossed in front of the chest, and hands-assisted standing-up using parallel bars. The maximum knee joint torque during standing-up without hands-assists was calculated using a three-segment link model. Standing-up motion in complete paraplegics was restored, and then analyzed using the three-dimensional floor reaction force and the hip, knee, and ankle angles.nnnRESULTSnMain muscles used to stand up were the quadriceps, tibialis anterior, and paraspinal muscles. Hands-assists reduced the muscle activity and the vertical floor reaction force. Peak muscle activity was less during hands-assisted standing-up, except for the rectus femoris and the iliopsoas muscle. The maximum knee joint torque during standing-up was 1.6Nm/kg for both knees. Two complete paraplegics were able to stand up smoothly from a wheelchair based on stimulation data obtained from normal subjects. The characteristic pattern during standing-up was knee flexion preceding extension.nnnCONCLUSIONnStand-up motion was restored utilizing electromyogram data and knee joint torque data from normal subjects.

An electrical knee lock system for functional electrical stimulation

An electrical knee lock system that can be combined with functional electrical stimulation was designed for paraplegic patients. This knee system unlocks the knee electrically and allows knee flexion during the swing phase of the gait. When the knee is extended by electrical stimulation of the knee extensors, the knee is automatically locked by the weight of the locking bar, and the stimulation of the knee extensors is stopped. Since the knee extensors are stimulated for only a short period, muscle fatigue of the knee extensors seldom occurs. We applied this system to a T8 completely paraplegic patient. Standing-up, standing, walking, and sitting-down motions were all restored by our hybrid system. No electrical stimulation was necessary during standing, and the knee extensors were stimulated during only a small percentage of the 1-gait cycle.

Hybrid functional electrical stimulation for energy-efficient restoration of standing-up motion

OBJECTIVEnTo find the most energy-efficient standing-up motion for quadriceps and to restore that motion in a person with complete paraplegia by using hybrid functional electrical stimulation.nnnDESIGNnNonrandomized control trial.nnnSETTINGnA referral center and institutional practice providing outpatient care.nnnPARTICIPANTSnTwenty-nine volunteer samples were used to collect normal data. One patient with complete paraplegia received treatment for the restoration of standing-up motion.nnnMAIN OUTCOME MEASUREMENTSnJoint angles and ground reaction forces were investigated during the standing-up motion with arms crossed in front of the chest with an ankle-foot orthosis set at various angles. The electromyogram (EMG) was performed during the standing-up motion with and without the orthosis. The energy costs of quadriceps during the standing-up motion were calculated using a mathematical model. Standing-up motion in a person with complete paraplegia was restored and then analyzed by measuring the vertical ground reaction force and the hip and knee angles.nnnRESULTSnQuadriceps energy cost was lowest (p < .05) in subjects wearing the ankle-foot orthosis set at neutral with a flat sole line. In the integrated EMG the peak value of rectus femoris contraction was larger with the orthosis than without it (p < .05). A patient with complete paraplegia was able to stand up smoothly from a wheelchair based on stimulation patterns obtained from healthy subjects.nnnCONCLUSIONSnEnergy-efficient standing-up motion in a patient with complete paraplegia was restored when the patient used an ankle-foot orthosis set at neutral with a flat sole line.

Sensitivity analysis for simultaneous optimization of controlled structures

Integrated design for actively controlled systems is considered in this paper. The improvement can be obtained in the overall performance of an actively controlled structure by simultaneously optimizing the structural and control design. The purpose of this paper is to analyze the existence condition of optimal solutions for structural parameters. A quadratic index is used to evaluate the system performance and its sensitivities to structural parameter changes are derived to study the conditions for the optimal solution. The effect of an active control on the existence condition is discussed.

Integrated optimal design of passive and active elements for hard disk servo systems

To achieve high density and high speed access of magnetic disk drives, integrated optimization method is applied for designing the head-suspension assembles. Approximation is used to the model of a head-suspension assembly, which makes it possible to obtain a nice analytical result on Riccati equations. Using this approach, we can obtain an explicit expression of the optimal controller in a state space form. Based on this setup, the simultaneous optimization problem both on active and passive parameters is reduced to a simpler one. A numerical example is given to show that a better performance of a magnetic disk drive can be obtained by the simple design procedure.

Methods for Model Reduction

The aim of this book is to introduce the reader to problems of model and controller reduction, with an emphasis on the latter. The book is restricted to considering linear, time-invariant models and controllers.

Low Order Controller Design

Simple linear controllers are normally to be preferred to complex linear controllers for linear time-invariant plants. There are fewer things to go wrong in the hardware or bugs to fix in the software, they are easier to understand, and the computational requirements (and associated hardware requirements) are less. On the other hand, many plants are of high order, Therefore, there is a desire to have methods available for the design of controllers which have order significantly less than the order of the plant they are controlling.

Model and Controller Reduction Based on Coprime Factorizations

In balanced truncation and Hankel norm reduction, any instabilities if present can only be treated by copying them into the reduced order object, which differs from the original object only through reduction of the stable part. This conclusion applies to frequency weighted reduction also, and thus to the controller reduction methods we have examined.

Structural design for reduced-order H/sub /spl infin// controller

We consider an integrated design problem of structural and control systems. Using the reduced-order H/sub /spl infin// controller design method proposed by Mustafa and Glover (1991), we formulate the integrated design as a simultaneous design of the structural design parameter and the reduced order H/sub /spl infin// controller. The formulated problem does not need to take an iterative procedure (controller synthesis and structural modification) which is employed in most integrated design.