Final-State Control Using a Time-Symmetric Polynomial Input

For information devices such as hard disk drives, actuators must be controlled quickly and precisely as much as possible. To satisfy these requirements, feedforward input design is very important. For this problem, we have proposed a frequency-shaped final-state control method. This method can obtain a feedforward input that has lower spectrum at desired frequency points so as to reduce residual vibration after positioning. Furthermore, the method has been extended to generate the feedforward input by a polynomial. By using the polynomial, the required memory size can be drastically reduced because it only requires to store the coefficients of polynomial. However, in the frequency-shaped final-state control method by polynomial input, it is not guaranteed that the solution always exist theoretically. In order to solve this problem, final-state control methods in which the feedforward input is generated by both of a polynomial and time-series data are proposed. The effectiveness of the proposed methods are verified by simulation using the plant model of the HDD benchmark problem. The simulation results show that the proposed method outperform the conventional methods.

We have proposed a frequency-shaped final-state control method that can reduce a residual vibration after positioning by minimizing Fourier gain of feedforward input at desired frequency points. In this method, the feedforward input is obtained as a time series data, therefore, it requires a large memory size to store them in an embedded controller. In this paper, we propose a final-state control method based on a polynomial input. It only requires to store the coefficient of the polynomial, and the required memory size can be drastically reduced. Furthermore, by considering the time symmetry of input, a method to reduce the order of the polynomial without a performance degradation is proposed. The effectiveness is verified by simulations.

As a method to generate a feedforward input that achieves high speed and high precision positioning,a polynomial-input-type final-state control has been proposed.This method can generatea feedforward input that which drives an initial state to a final state in a finite time.However,the existence of the solution is not always ensured for any initial and final states.To solve this problem, a final-state control method using a polynomial and time-series data has been proposed,though,it requires an extra memory to store the time-series data.In this research,we propose a method that does not require the time-series data by introducing a negligibly-sinall final-state error.The effectiveness of the proposed method is verified by performing simulations.

This paper proposes a new design method of track-seeking trajectory for hard disk drives by using final-state control method. The proposed method can obtain a feedforward control input whose frequency components are minimum at the desired frequency points. In our approach, the control input is evaluated in continuous-time domain, and the frequency components higher than the Nyquist frequency can be also optimized. Simulation and experimental results are shown to evaluate the effectiveness of the proposed method.

In this paper we deal with active control of shock in a collision problem between two objects. In order to make it clear how the deformation of the shock-receiving object can be maximized while minimizing the deformation of the shock-giving object and how energy can be transmitted unilaterally, the relationships among contact stiffness, deformation time, deformation ratio and energy balance are discussed. The final-state control is applied to obtain a feedforward input to deform the shock-receiving object by a desired amount in a predetermined time. Thus, the energy balance and the energy efficiency are verified. Furthermore we examine the conditions necessary to realize a ‘dynamical diode’ that can transmit energy unilaterally from the shock-giving object to the shock-receiving object. It is demonstrated experimentally that the appropriate feedforward input can be obtained by final-state control under specified conditions of contact stiffness and deformation time.

This paper discusses an improvement of final-state control (FSC). FSC is a control method for transferring the state of a dynamic system to specified states at a specified terminal time by using an external input. So far, it is mainly applied to motion control problems such as servo control of hard disk drives. However, FSC cannot deal with time-varying specified states. For example, when an operator pushes a cart and attempts to connect with another stopped cart without any stop, the stopped cart should accelerate to the same velocity as the running cart within a specified time. Here, the velocity of the running cart is time-varying, and a control method which can deal with such time-varying specified states is required. In this paper, in order to deal with the time-varying states, an updating final-state control (UFSC) technique is introduced. UFSC updates the initial and ideal final states at every sample. However, the equation of UFSC algorithm includes inverse matrix computations and the computation process is complicated. Moreover, most computed inputs will not be applied because of updating. So, in order to reduce the computational load, this paper also introduces a device to extract the requisite computation for simple controlled models. The effectiveness of the proposed method is verified by simulations in a case of connection control problem of two carts.

High-precision stages require high-speed and high-precision control to improve their production throughput and quality. However, it is expected that their motion speed and accuracy will reach a limit in the near future if the structure of the conventional high-precision stage is used. Therefore, the authors designed and fabricated a stage called the catapult stage which has a decouplable structure consisting of a fine stage and a coarse stage. This stage is different from conventional dual stages in which the fine stage would be disturbed by the coarse stage since they contact with each other. This paper proposes a novel control system design for the catapult stage, and a settling time shortening control method using final-state control (FSC). So far, FSC is mainly applied to the applications such as hard disk drives whose initial states are the zero. However, it is important to consider the initial states for the catapult stage since the initial position, velocity and acceleration of the catapult stage are not equal to zero. Simulations and experimental results demonstrate the effectiveness of the proposed methods.

This paper proposes a design method for short track-seeking control based on one-degree-of-freedom (ODOF) control and initial value compensation (IVC). IVC utilizes non-zero initial values of the feedback controller to improve the step reference response of the ODOF tracking control system. This makes feedforward control unnecessary to shape the transient response of short track-seeking. As a result, the amount of computation during short track-seeking may be kept minimal. The proposed design method minimizes tracking errors in multi-rate control frame work for a step reference input taking into account the inter-sampling behavior. The effectiveness of the proposed method is shown by simulations.

Galvano scanners are used as laser beam scanners in laser drilling machines. The galvano scanner requires high-speed and high-precision control for more precise laser processing with high throughput. Heat generated by current amplifiers becomes problematic as the positioning speed of the galvano scanner increases. We propose a final-state control (FSC) method that considers voltage constraint of the current amplifiers. By considering the constraint of the applied voltage on the motor, the power supply voltage of the current amplifier can be lowered. Therefore, the electricity consumption and the heat generated by the current amplifier can be reduced. Experimental results show the effectiveness of the proposed method.Copyright © 2012 by ASME

A Design Method of Bilateral Control of Teleoperators with Uncertain Communication Time-Delay

The catapult stage is a high-precision dual stage with a new structure which, by allowing contact between fine and coarse parts, is compatible with increasing size and acceleration. Impact force occurs in acceleration and deceleration regions, and may degrade a stage. This paper thus proposes a control method to reduce the impact force that considers the thrust limitation by combining model prediction and final-state control. In the proposed method, the timing to activate the fine stage is automatically determined by solving an optimization problem. Simulation and experimental results demonstrate that the method can significantly reduce the impact force between the fine and coarse parts.

In this paper, the authors develop a new design method of the reference trajectory for hard disk drives. The control input is assumed to be generated through zero-order-hold and the reference trajectory is designed so that the frequency component of the control input is minimized over the desired frequency points. Input constraints can also be incorporated into the design. Simulation results are shown to evaluate the effectiveness of the proposed method.

In this paper, we develop a new design method of feedforward control input by using final-state control method. The feedforward input can be obtained so as to reduce the spectrum at the desired frequency. The proposed method is applied to short seek control of hard disk drives. The experimental results show the effectiveness of our method.

A new tuning method for proportional-integral-derivative (PID) controller design is proposed for a class of unknown, stable, and minimum phase plants. We are able to design a PID controller to ensure that the phase Bode plot is flat, i.e., the phase derivative w.r.t. the frequency is zero, at a given frequency called the "tangent frequency" so that the closed-loop system is robust to gain variations and the step responses exhibit an iso-damping property. At the "tangent frequency," the Nyquist curve tangentially touches the sensitivity circle. Several relay feedback tests are used to identify the plant gain and phase at the tangent frequency in an iterative way. The identified plant gain and phase at the desired tangent frequency are used to estimate the derivatives of amplitude and phase of the plant with respect to frequency at the same frequency point by Bode's integral relationship. Then, these derivatives are used to design a PID controller for slope adjustment of the Nyquist plot to achieve the robustness of the system to gain variations. No plant model is assumed during the PID controller design. Only several relay tests are needed. Simulation examples illustrate the effectiveness and the simplicity of the proposed method for robust PID controller design with an iso-damping property.

In this paper, we propose the design method for memory sampled-data controller for the depth control of an autonomous underwater vehicle (AUV) using exponential time-varying gains. To this end, the depth system of an AUV is represented as a Takagi-Sugeno (T-S) fuzzy model. When constructing the controller, the exponential time-varying gains are used to reduce the convergence time. Furthermore, using the Lyapunov-Krasovskii functional (LKF), a sufficient condition guaranteeing exponential stability is derived in terms of linear matrix inequality (LMI). Finally, the validity of the proposed design method is demonstrated by a simulation example.