Two-degree-of-freedom Research Articles

Design of two-degree-of-freedom robust controllers for a seeker scan loop system

A mathematical model of a seeker scan loop plant is derived. The scanning accuracy of the seeker scan loop is degraded by modelling uncertainty and disturbance. To satisfy robust stability as well as robust performance, a new two-degree-of-freedom (TDF) robust control is formulated in the framework of H optimization problem. The TDF controller consists of the feedback controller for robust stabilization and the feedforward controller for good command following. Two structures, such as the conventional and modified structures, of TDF control are introduced, and the formulations of the TDF H control are presented for both structures. The feedback and feedforward controllers are designed in a single-step procedure. The proposed formulation is able to reflect not only frequency-domain specifications but also time-domain specifications such as transient response characteristics and multivariable interaction between output channels, differently from the mixed-sensitivity problem. The seeker scan loop system with the TDF control satisfies design requirements and in particular shows good scanning performances for conical and rosette scan patterns.

Two-Degree of Freedom Configulation of Generalized Predictive Control to Increase the Ability of the Disturbance Rejection and the Setpoint Tracking for a Dead Time System

This paper presents a two-degree freedom configuration of Generalized Predictive Control in order to increase the ability of the disturbance rejection and the setpoint tracking for a dead time system. The controller which is designed with the plant model including the feedforward control can prevent the undesirable action which is caused by the feedforward control. Numerical and experimental results demonstrate the effectiveness and the practicableness.

Robust Controller Design by a Combination of Loop Shaping and Frequency Response Approximation

This paper describes a robust control design procedure for ill-conditioned plants. In this procedure the Loop Shaping Design Procedure (LSDP) is combined with the Multi-Model Frequency Response Approximation (MMFRA) method to design robust two-degree-of-freedom (TDF) controllers. The optimization of the feedback controller and the prefilter are carried out in two separate stages. By the design of the feedback controller the weighting function in LSDP is optimized by a modified MMFRA procedure. The design procedure is demonstrated on a well-known benchmark problem.

A Design Methodology for Robust Two-Degree-of-Freedom Digital Repetitive Control

This paper presents a design method for digital repetitive control systems for a plant with structured uncertainties. A two-degree-of-freedom (TDF) control system configuration has been employed in order to achieve the desired feedback and input-output performance independently. The lowest-order feedback repetitive controller is designed to guarantee the robust stability of the closed-loop system and provide the desired closed-loop performance. Afeedforward repetitive deadbeat controller has been designed to obtain the desired transient response.

A Design method for Two-Degree-of-Freedom Controller using the Dynamical Model of the Feedback Controller.

Two-degree-of-freedom (TDOF) system has a characteristic that the feedback property such as disturbance attenuation and the reference response property can be designed separately. But in general the order of TDOF controllers tend to be higher compared with that of one-degree-of-freedom (ODOF) controllers. For this reason, a new design method of the TDOF system using the dynamical model of the feedback controller was proposed by Y. Chida. In this method, the reference response achieved by the feedback controller can be improved by the TDOF controller whose order is same as that of the feedback controller. The TDOF controller is designed as such that minimizes a square integral performance index. But the choice of the weighting parameter of the performance index is difficult and some try-and-error is needed to get a good performance.In this paper, we propose an alternative design method for the TDOF controller proposed by Y. Chida. We introduce a model transfer function and the controller is designed so that the output of the two-degree-of-freedom system follows the output of the model transfer function. Designers need only to choose the model transfer function which has desired time response.Further, we apply this method to the 2-mass control system to improve the reference response. Simulation results are presented to demonstrate the control effects.

Modelling and analysis of non-linear orifice type damping in vibration isolators

The effects of non-linear orifice type damping on the response of one- and two-degree of freedom (DOF) systems are studied. The damping is formulated through the hydraulic resistance of the fluid path as a function of the frequency of flow oscillation and mean flow velocity for the laminar and turbulent flows. A comparison is made to demonstrate the vibration control capability of linear and non-linear damping models in terms of displacement transmissibility ratios for a 1-DOF system and for a 2-DOF system with an optimally tuned absorber, providing the minimum peak displacement of the isolated mass over the complete frequency range of interest. The results show a significant shift in resonant frequency between the linear and non-linear damping approaches.

Experimental evaluation of adaptive and robust schemes for robot manipulator control

In this paper, adaptive and robust control schemes are compared in the tracking control of robot manipulator. In adaptive control, the authors classify the adaptive control laws that have been proposed into three types. They show that the most important difference among them is that in their PD gains. They investigate their tracking performances by laboratory experiment and show that they can have similar performances by adjusting their equivalent PD gains almost equally. In robust control, two degree of freedom (TDOF) controller is examined. The authors demonstrate its strong disturbance rejection performance and robustness to parameter variation by experiment. They analyze the stability of TDOF controller against the payload change. Finally, through these experiments, they consider the advantages of adaptive and robust schemes for robot manipulator control.

超音波モータを用いたロボット用アクチュエータの開発 第２報 球面超音波モータの試作

The creation of advanced dexterous mechanical manipulators and actuators is increasingly important for development of intelligent robots, which are capable of performing any human arm task. This paper deals with a spherical ultrasonic motor which is an application of an ultrasonic motor to such a dexterous actuator which has multi-degree of freedom. As a prototypal spherical ultrasonic motor, we have developed successfully two kinds of spherical motor with two-degree of freedom which has a spherical body driven by two pairs of ultrasonic actuator. The spherical ultrasonic motors show good controlability and high accurate positioning.

A Digital H∞ Controller for a Flexible Transmission System

The aim of this paper is to propose two procedures for the design of a robust discrete time controller for the flexible transmission system of Landau et al. (Proc. Europ. Control Conf., Rome, Sept. 1995). The procedures are based on discrete time versions of the two degree offreedom (TDF) methods of Limebeer et al. (Automatica, 29(1), 1993, 157–168) for designing robust controllers. The first method involves designing the feedback controller and prefilter in a single stage using H ∞ optimisation. It is this approach that is evaluated on the flexible transmission problem. The second approach involves two stages in which both the feedback controller and prefilter are optimised separately.

Fuzzy control of a manipulator using the switching motion of brakes

A method of controlling a manipulator with n-degrees of freedom by one actuator and n — 1 brakes using fuzzy inference is described. The manipulator is reduced to have two-degrees of freedom because n — 2 brakes are applied, so that the switching time of the brakes and the torque of the actuator are obtained. The manipulator is assumed to have uncertainty in the model and fuzzy control is determined by learning the dynamic response of the manipulator. The effectiveness of the proposed method is illustrated by a simple example.

Application of a two‐degrees‐of‐freedom controller to chaotic dynamical systems

AbstractWe apply a TDOF (two‐degrees‐of‐freedom) robust controller to chaotic dynamical systems. We show that the TDOF controller is effective not only for rejection of chaotic disturbance but also for control of a chaotic plant.

Active Vibration Control of a 2-mass Spring System using .MU.-Synthesis.

A 2-mass system connected by a non ideal shaft has resonance modes and it is difficult to design a controller suppressing the vibration in the face of parameter variation. In this paper, we propose a method of μ-Synthesis based on the descriptor form representation to deal with parameter uncertainties independently. We first consider a class of parameter uncertainty given in the descriptor form and show how to achieve robust stability and robust performance for this class of perturbed systems. Then we apply this method to the 2-mass spring system with parameter uncertainties of the torsional constant and the load inertia. By using this method these two physical uncertainties are treated independently and a controller is designed to achieve not only robust stability but also robust disturbance suppression. In addition, we also use two-degree freedom control scheme to achieve a good transient response.Simulation results are presented to demonstrate the control effects.

High performance control of robot manipulator without using inverse dynamics

Abstract A novel motion control method of robot manipulator without using inverse dynamics is proposed. First, the disturbance observer based servosystem is introduced. Next, Two-Degrees-Of-Freedom (TDOF) robust servosystem is proposed from more control theoretical point of view. Strongly robustified servosystem realizes completely independent joint control for multi-axis robot manipulators. It is shown that almost all kinds of robot motion control, i.e., impedance, compliant motion, force, and hybrid controls can be implemented in a unified way.

On the design of robust two degree of freedom controllers

The aim of this paper is to introduce two methods of designing robust two degree of freedom (TDF) controllers. Both design procedures will be illustrated and evaluated on a high purity distillation column example. In the first approach the feedback controller and the prefilter are designed in a single step using an H ∞ optimization procedure. The second method optimizes the feedback controller and prefilter in two separate design stages. Roughly speaking, the feedback controller is designed to meet robust stability and disturbance rejection specifications, while the prefilter is used to improve the robust model matching properties of the closed loop system. The single step approach has the advantages that it is easy to use, and that the resulting controller degree is the same as that of the plant. The two stage approach offers greater design flexibility and it may produce robust stability and robust performance margins which are significantly bigger than those achievable with the single stage approach. Set against that, the two stage technique is more difficult to use and it produces controllers which may have an order which is significantly bigger than that of the plant.

Two-degree-of-freedom robust speed controller for high-performance rolling mill drives

A scheme is presented for the speed control of rolling mill drives. The proposed speed controller is based on a two-degree-of-freedom (TDF) structure and uses an observer-based state feedback compensator for the major control loop. The control method yields a robust system with respect to system uncertainties and modeling errors and is very effective for vibration suppression. Experimental verification was carried out on a prototype rolling mill minimodel system. The experimental drive system has a three-mass-model structure (motor-gear-load) connected by low stiffness shafts. The mechanical resonances and the inertia ratios between the motor, gear, and load are comparable to those of an actual rolling mill system (resonant frequencies are at 17.4 Hz and 51.3 Hz). The proposed scheme was compared to the conventional PI controller and the performance of each scheme is presented. A high closed loop speed bandwidth was obtained with the proposed TDF speed controller.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust servosystem design with two degrees of freedom and its application to novel motion control of robot manipulators

A novel robust servosystem design method based on the two-degree-of-freedom (TDOF) controller and its application to advanced motion control for a robot manipulator is proposed. This servosystem is derived from the simple parametrization. The command input response and the closed loop characteristics can be specified independently by using two parameters which belong to the ring of stable and proper rational functions. The sensitivity and the complementary sensitivity functions can be determined straightforwardly through the optimization of the two design parameters. The control performance of the servosystem has been demonstrated. A completely decentralized joint control system for multiaxis robut manipulators has been realized. In particular, various kinds of robot motion controls, such as compliance, force, and hybrid controls, are realized in a unified way based on the robust position control. This servosystem has been implemented using DSP. >

ロボットマニピュレータにおける力制御のロバスト化と衝突過程の制御

It is important that we control a robot manipulator considering contact with an object. In force control we have two difficulties caused by (1) environmental parameter change and (2) large contact force at collision. The collision always happens in a short transient period from trajectory control to force control. In this paper, we propose a robustifid force and collision control method. First, we designed TDOF (Two Degrees Of Freedom) force controller. This force controller enables us to obtain stable and fast response in the face of considerable environmental parameter variation. Next, in order to reduce the shock and also to change control modes smoothly from position to force, we proposed a novel collision control method by using feedforward position command together with the robust force controller based on position. We realized these proposals by using a TRANSPUTER based con-troller and confirmed their usefulness with experiments by using a 1-axis and a lifesize 6-axis mani-pulator.

Design of a robust electrical position servo based on dual model matching

This paper deals with the robust control of electrical servomotors with parametric uncertainties and some non-linear factors. A powerful two-degrees-of-freedom (TDOF) approach via sensitivity and complimentary sensitivity functions has been used previously to obtain results, subject to unstructured uncertainties. This approach has the advantages that any stable linear control systems can be realized and also that the reference input response and disturbance supression can be specified independently. In this paper a procedure is proposed for the design of robust electrical position servos based on a novel control system design method called dual model matching (DMM). The DMM approach also possesses the above properties but with additional advantages subject to parametric uncertainties. A comparison of the usual TDOF approach with the DMM approach is discussed. The efficacy of the proposed servos is confirmed with computer simulations and laboratory experiments.

Nonlinear dynamics of two-mode interactions in parametric excitation of surface waves

Parametric excitation of surface waves in a container under vertical forcing is investigated in detail, by an averaged Lagrangian method due to John Miles, and a system of evolution equations of third-order nonlinearity is presented for the case that the forcing frequency is chosen to be near twice the frequencies of two nearly degenerate free modes. The system of first-order differential equations in four variables which are derived from an averaged Hamiltonian is considered in a unified fashion, and the analytical results are compared with three experimental observations. It is found with the help of numerical integration that this dynamical system yields not only excitation of a single-mode state, but also interaction between two modes in which each mode oscillates either periodically or chaotically. These results are in good agreement with the observations, except for one case in which nonlinearity is considered to be too strong. As a fourth case, homoclinic chaos in the Hamiltonian system of two-degrees of freedom without damping is studied numerically. It is suggested that the chaotic mode competition observed in the experiments is different from the homoclinic chaos.

Two-degree-of-freedom dead-beat control system with robustness: multivariable case

Abstract A design procedure for two-degree-of-freedom (TDF) dead-beat controllers for multivariable systems is presented. Based on the parametrization of all stabilizing TDF controllers, a minimal-time dead-beat control system with optimal robustness is constructed for an arbitrary reference input. The optimal robustness is achieved under the constraint of robust tracking. A comparison of a TDF system with a one-degree-of-freedom (ODF) system reveals that, under the same robustness criterion, the optimal robustness of the TDF system is always superior to that of the ODF system irrespective of its settling time. It is also shown that the optimal robustness of the ODF system becomes identical to that of the TDF only when the settling time of the ODF system goes to infinity. Some numerical examples are given to illustrate the theoretical results.