In this paper, we present a PID controller design based on H_∞-loop shaping method and LMI optimization method. Since the order of the conventional H_∞-loop shaping controller is as high as the plant order, the method can not be applied to PID control design directly. However, the robust stability problem used in H_∞-loop shaping method can be modified to one block problem with a right inverse graph K of the controller and a parameter Q. Then controllers with fixed structure can be designed by using LMI optimization. Furthermore, this method can be extended to a design problem of controllers with fixed poles which is necessary for PID design. Major advantage of our design method is that robust stability as well as nominal stability is guaranteed at design stage which is difficult with classical PID designs such as the Ziegler-Nicholas method. Furthermore, the design can be applied to multi-input multi-output plants and it can be extended to simultaneous control design for multiple plants.

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In this paper, controller order reduction methods based on model matching of loop transfer function's frequency response are proposed. By these methods, a PID controller can be obtained by reducing a high order controller, which is designed by H_∞ control or μ synthesis, etc. Since the controller order reduction is performed such that the frequency response of the loop transfer function matches to a high order controller's loop transfer function in cut-off frequency band, the reduced order controller provides almost the same performance as the high order controller in considerable cases. The methods have very small computation effort because the reduced order controller is derived using the least squares method, and the methods could be applied for multivariable controller design.

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Proportional, Integral, and Differential controller (PID controller) is the most popular elment in industrial control applications. One of the applications of hot strip mill in steel-making industry is mill drive system which is composed of many masses and shafts, and which has many torsional vibration modes. Due to this vibration, response of drive control system is not sufficient for strip thickness accuracy. Authors have aimed to use popular PID controller in order to improve response specification, and certificated usefulness of PID controller with some kind of filters at suppressing torsional vibrations. Finally in real hot strip mill, strip thickness has been improved with new drive control syetem added by vibration suppression controller.

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A PID setting procedure is presented to provide a critically damped response to a reference change for a first-order lag process with time delay. It is shown that the optimized PID settings based on the ISE (Integral of Squared Error) has a significant disadvantage in that it tends to be more sensitive to modeling errors. To reduce the sensitivity, a method of optimizing the PID setting is developed by incorporating a constraint on the manipulated variable. It is found a remarkable improvement of control performance against modeling errors.

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In recent years, the structure and the mechanism of the human brain have been clarified partially, and their knowledges are formulated as neural network systems. Furthermore, there have been applications of neural networks to pattern matching problems, pattern recognitions, learning controls and so on. Especially, neural network techniques have widely used in adaptive and learning control schemes for nonlinear systems. However, generally, it costs a lot of time for learning in the case applied in control systems. Furthermore, the physical meaning of neural networks constructed as a result, is not obvious. In this paper, a design method of self-tuning PID controllers is proposed, which has a fusional structure of self-tuning and neural network schemes. This method enables us to understand a physical meaning of the control parameters, and also to adjust PID gains quickly. Finally, in order to show the effectiveness of the proposed self-tuning PID control scheme, a numerical simulation example is illustrated.

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This paper provides a simple and a safe automatic P, I, D gains tuning method using relay control, for typical marine controllers with PID control law. The on-board computer control system using relay control is applied to typical three types of ship's controller; (1) autopilot system, (2) yaw control system through bow-thruster and(3) diesel engine governor system, and the results of the full scale experiments using a small training ship are discussed.

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Moire topography has an advantage of measuring 3D shape of object using only one image. However, since classical moire topography can hardly discern orders of moire stripes, this method has difficulties in judging convex/concave of the object. Phase-shifting is an efficient method to solve the problem of judging the surface unevenness. This method is not only deliver a way to uneven shape but also improve the sensitivity. This method is, however, on condition that images of different phase have to be obtained, and this method cannot be calculated orders of discontinuous stripes.
In order to solve the above problems, we propose an intensity modulated moire topography. The key point is to use the intensity modulated light source. This method enables us to get the relationship between order and this intensity of moire stripe. Moreover, we can embed this method to slit-pattern projection method to calculate the order of slit-light and to judge an edge by only use fewer image.

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Two of several critical nozzles were connected in series to calibrate the downstream one at low pressure against the upstream one kept at the atmospheric pressure. The measured discharge coefficients of Venturi nozzles machined by super-accurate lathes distributed along a fitted curve, which had been measured with homologous nozzles using a constant volume tank system at the atmospheric pressure, with deviations of less than ±0.04%. The discharge coefficient of quadrant nozzles had a smaller Reynolds number dependence than those of Venturi nozzles. Stability of the critical flow of the downstream nozzles was measured with varying their downstream pressure in the same configuration. Flow rates of all the nozzles with the throat diameters of 0.5-13.4mmφ with the Reynolds number of 1.7×10³-8.6×10⁴ did not vary more than ±0.02% when they are in the critical condition. Their critical pressure ratios decreased suddenly from certain values near the theoretical ones to 0.5 when the Reynolds numbers are decreased, but they remained at around 0.5 with the Reynolds number down to 1.7×10³. Detachable diffusers for short nozzles were shown to be effective to make their characteristics similar to those with integrated diffusers in spite of a small step at the contact plane. A new method to test a flowmeter at various volume flowrates by using only one critical nozzle is shown to be possible by controlling the pressure at the upstream of the nozzle.

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A new method to calibrate a critical nozzle against the other two, which have been already calibrated, was developed. The method bases on the linear dependency of the pressure between nozzles connected in series on the ratio of their flow rate. Two reference nozzles and the one under test are connected in turn at the upstream of another arbitrary critical nozzle to compare the pressure between the nozzles. The flow rate can be calculated from a linear interpolation between the two reference flow rates by using the difference of the pressure between the nozzles. No instruments other than a pressure gauge, which must be linear in a narrow pressure range, are required, that is, the system need few procedure to keep its accuracy for a long period. An analysis showed that the uncertainty of the method was almost the same as that of the reference nozzle. This was demonstrated by a realized system by calibrating the nozzles which have been already calibrated by a constant volume tank system. The system is fully automated except for installing the nozzle under test and so efficient that one calibration takes only about 10 minutes.

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A tapping stylus for surface topographical measurements by using a quartz fork of watch has been developed. The principle is based on a fact that output voltage of the quartz folk driving circuit is a function of the distance from the surface, as one of the vibrating legs is tapping the surface periodically. A servosystem is constructed to maintain the distance between the leg and surface to a constant gap, with an x-y piezodriven scanner just like other SPMs. Some examples of the measurement are compared with SEM micrographs and profiles obtained by an optical stylus tester. Although measurement time is not so fast, this system has a fine resolution of several nm in vertical direction, and that of tens of nm in horizontal direction.

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Phase Doppler anemometry (PDA) is one of the useful and reliable optical methods for sizing small spherical particles. However, this method is sensitive to the Gaussian beam effect which can cause phase fluctuation and therefore erroneous measurements. This paper theoretically studies the mechanism of the phase fluctuation. A detailed and systematic estimation of the phase fluctuation is performed by using geometrical optics. The validity of this estimation is confirmed by numerical simulations based on the generalized Lorenz-Mie theory. Moreover, we discuss the optimum measuring conditions which can minimize the phase fluctuation.

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In this paper, we experimentally evaluate the accuracy of parallel mechanism using Laser Tracking Coordinate Measuring System. The system has 4 tracking laser interferometers to measure the distance from retroreflector incrementally. Redundant 4 measurements enable us to identify relative location of each laser. Then the coordinate of retroreflector can be estimated precisely. We test the repeatability of parallel mechanism, and find that positioning error is less than 0.099mm. Then we calibrate the kinematic model of parallel mechanism to improve its absolute accuracy. The positions and poses of the endplate are measured and used for reference data of calibration and the kinematic parameter is modified to minimize the positioning error. Its maximum error is 0.98mm.

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Longitudinal controllers are derived for an automated car driving. Two types of information sources are considered: the first-order information includes locations and speeds of following and leading cars, while the second-order information contains accelerations/decelerations in addition to the first-order information. A proper headway distance is defined for a variable speed of a leading car, sliding mode and adaptive sliding mode control theories then become applicable, and stable and robust longitudinal controllers are derived. The acceleration/deceleration information available through the modern inter-vehicle communication and sensing technologies significantly improve the control performance. The adaptive sliding mode controller yields better results because it includes a stable and swift estimation mechanism for the maximum disturbance value.

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In this paper, we consider an H_∞ problem with unstable weighting functions. Such weightings are used to achieve asymptotically disturbance attenuation and/or asymptotically tracking to reference input. Such problems cannot be handled by the standardH_∞ control theory. To this problem, we present a necessary and sufficient condition for the existence of a solution by using Riccati inequalities. This condition needs no assumptions on the jω invariant zeros of G₁₂ and G₂₁.

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In this paper, a shape tracking control problem for a hyper degrees of freedom manipulator is discussed. The objective of shape tracking is to control its shape, which is characterized by all the link positions, to follow a given time-varying curve. Crucial key to solve this problem is to introduce a 2nd-order estimator that infers the curve parameters corresponding to the target link positions on the curve. The coupled dynamics of the manipulator and this estimator has the same properties as the manipulator dynamics which is useful for control design purposes. Therefore, familiar design methods for manipulator tracking can be utilized to solve the shape tracking problem. The shape tracking control law based on the ID (inverse dynamics)-based method is shown as a exapmle to illustrate how tofind shape tracking laws by using familiar tracking control methods.

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In this paper, two types of identifications are analyzed with respect to the worst case identification error, which is necessary in the ordinary robust control system design. We show that the worst case identification error in deterministic approach is considerably large when I/O signals are corrupted by comparatively large noises. We compare it with the error of the least squares method which exponentially converges to zero as the numbers of data increase when noises obey stochastic processes of normal distribution or uniform distribution, and show the error of the least squares method which is equal to the worst case error of the deterministic approach in size, is exceedingly conservative. We point out the necessity of a modified robust control system design which consists of multiple weights according to the different sizes of uncertainties, and show a numerical example.

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For a conventional modified repetitive control system, designing of its pre-compensator so as to maximize the lowpass filter band width has been considered to contribute to the improvement of its control performance such as its tracking performance for reference input and its insensitivity to disturbance. The control performance of the control system, however, basically depends on its sensitivity function in the main frequency bands possessed by the reference input and disturbance. This fact suggests that the control performance of the control system should be evaluated using its sensitivity function. Therefore, the sensitivity functions of the conventional modified repetitive control system and the modified repetitive control system with corrected dead time already proposed by the authors were first calculated. The results of the calculation showed that the expansion of the lowpass filter band width did not necessarily result in improved sensitivity function of the control system in the intended frequency band.
The results of the investigation, however, indicated that some sensitivity functions of both systems to be compared intersect with each other in the intended frequency bands, suggesting that it is difficult to judge precisely whether the control performance of the system are good or not by its sensitivity function. Therefore, a new design method applicable both for the conventional modified repetitive control system and our proposed modified repetitive control system with corrected dead time was proposed. This newly proposed design method is based on simulation of such a modified repetitive control system to calculate its performance index IAE (integral of absolute value of error) and design the system so as to minimize its IAE.
The overall results of the investigations thus conducted by the authors revealed that a modified repetitive control system with corrected dead time, if so designed using the newly proposed method as to minimize its IAE, can achieve further improvement in its control performance.

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This paper provides a new μ analysis and synthesis method of state feedback systems. First, we derive a necessary and sufficient condition for the system to have μ less than a specified valu γ by using parameter-dependent multipliers and the positive real lemma. Furthermore we give a computable sufficient condition which requires no more computation burden while being less conservative than former methods. Second, based on these results, we give an LMI condition for the existence of a state feedback gain which achieves that μ of the closed loop system is less than given γ. Finally, an illustrative numerical example is given.

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In this paper, we investigate relations between the results of the generalized gradient flow introduced by Helmke & Moore and the geometry of the set of linear systems. We first introduce a metric on the set of Gramians defined by Ohara et al. or Tsumura & Kitamori, and give a gradient flow for a minimization problem of a gap between Gramians. This result is extended to a Gramian assignment problem of state feedback systems. Moreover, we show a result of an approximation problem of system realizations, and finally analyze a duality of the flow on the set of Gramians.

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In this paper, modeling and control of connected two flexible beams are discussed. We derive dynamic equations of the connected flexible beams by means of the Hamilton's principle. As the obtained boundary conditions are nonhomogeneous, we introduce a change of variables to derive homogeneous boundary conditions. By solving the eigenvalue problem related to the distributed parameter system, eigenvalues and corresponding eigenfunctions are obtained. We construct robust controllers to compensate the spillover instability caused by residual modes which are neglected at the controller design phase. Simulations have been carried out.

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This paper deals with a method of wave control for a class of uniform flexible beams (real beam) by introducing an idea of imaginary beam. The imaginary beam is assumed to be connected serially at the free-end of the real beam of interest and to have the distributed viscous damping force whose coefficient is selected optimally in such a way that the total energy generated by traveling waves becomes minimum.

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This paper presents a design method for digital repetitive control systems in which the plant has structural uncertainties. A two-degree-of-freedom control system configuration has been employed in order to achieve the desired feedback and input-output performance independently. Through application of the sampled-data H_∞ control theorem to the design of the feedback controller, a state-feedback repetitive controller that guarantees the robust stability of the closed-loop system and provides the desired closed-loop performance is obtained. A feedforward repetitive deadbeat controller is designed to obtain the desired transient response.

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