Adaptive tracking control design of constrained robot systems

Both dynamic state feedback as well as output feedback tracking control designs are presented in this paper for constrained robot systems under parametric uncertainties and external disturbances. The previous studies on tracking control design, not considering the velocity measurements, address only the unconstrained robot design. In contrast, a dynamic output feedback controller based on a linear and reduced-order observer that uses only position measurements is proposed here for the first time to treat the trajectory tracking control problem of constrained robot systems. Both adaptive state feedback control schemes and adaptive output feedback control schemes with a guaranteed H^∞ performance are constructed. It is shown that all the variables of the closed-loop system are bounded and a pre-assigned H^∞ tracking performance is achieved, in the sense that the influence of external disturbance on the tracking motion error can be attenuated to any specified level. Moreover, it is also shown that the motion and force trajectories asymptotically converge to the desired ones as the dynamic model of robot systems is well-known and the external disturbance is neglected. Finally, simulation examples are presented to illustrate the tracking performance of a two-link robotic manipulator with a circular path constraint by the proposed control algorithms. © 1998 John Wiley & Sons, Ltd.     

Two-degrees-of-freedom speed control of resonant mechanical system based on H∞ control theory

In industrial motor drive systems such as those used in industrial plants and robots, a torsional vibration is often generated as a result of the elastic elements present in the torque transmission systems. This vibration makes it difficult to achieve quick speed responses and may result in plant damage. Such systems are simply modeled as two-mass mechanical systems. The H^∞ control theory is applied herein to design a speed controller for the two-mass system. This controller determines closed-loop characteristics, including suppression of torsional vibration, rejection of torque disturbance and robust stability. Moreover, two types of two-degrees-of-freedom control systems, which includes the H^∞ controller, are proposed to improve command response. One is based on the TDOF PI control, in which the PI controller included in the H^∞ controller is rearranged for the TDOF system. Another is based on the model matching feedforward control, in which the prefilter and the feedforward compensator are added to the H^∞ controller. The proposed control system is applied to two types of resonant mechanical systems having different inertia ratio. Several examinations demonstrate that the proposed speed control system is useful for a resonant mechanical system.     

Teaching sampled‐data H∞ control theory using arm robot experiment system

This paper explains how to use an arm robot experiment system to teach sampled‐data H_∞ control theory. A design procedure is presented for a digital tracking control system for a continuous plant with structured uncertainties; the target is the positioning control of an arm robot. To guarantee the robust stability of the closed‐loop system and provide the desired closed‐loop performance, the design problem is first formulated as a sampled‐data H_∞ control problem, and is then transformed into an equivalent discrete‐time H_∞ control problem. Finally, linear matrix inequalities are used to obtain a reduced‐order output‐feedback controller and a static state‐feedback controller. In a course, the design procedure is explained and practice is provided through simulations and experiments. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Non-linear learning control of robot manipulators without requiring acceleration measurement

A new class of non-linear learning control laws is introduced for a robot manipulator to track a given trajectory in performing a series of tasks. The learning control scheme is applicable to robots with both resolute and prismatic joints, requires only position and velocity feedback, and removes the acceleration measurement required by the existing results. It has been shown that under the proposed learning control the tracking errors are always guaranteed to be asymptotically stable with respect to the number of trials. The proposed control is robust in the sense that exact knowledge about the non-linear dynamics is not required except for bounding functions on the magnitudes. In addition, the new learning scheme can be used without assumptions such as repeatability of robot motion, repeatability of tasks and resetting of initial tracking errors.     

Switching of H∞ controller under constraints and decision of controller state at instance of the controller switching

In real control systems, certain constraints are placed on the input, state, and output values. If such constraints are violated, the system may become unstable, in a worst‐case scenario. One of the promising approaches to solving this problem is to switch the controller according to the state of the closed‐loop system. No useful design strategy for each controller, however, has yet been developed. In addition, the determination of the controller state at the instant of controller switching has not been investigated. First, this paper presents a new design methodology which merges the switching control and H_∞ controller design into one design algorithm. Second, this paper presents a way of determining the controller state at the instant of controller switching. Finally, the proposed method is applied to force control of a one‐DOF manipulator in order to demonstrate the usefulness of the proposed method. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 142(2): 68–75, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10082     

悬停状态下旋翼飞行机器人自适应鲁棒控制

针对加装二自由度绳驱动机械臂的旋翼飞行机器人在悬停条件下的抗干扰控制,提出了一种自适应终端滑模控制策略.将系统分成四旋翼飞行器和机械臂两个子系统,分别采用拉格朗日法与牛顿-欧拉法获得各自的动力学模型.在Lyapunov稳定性框架下设计了旋翼飞行器人的抗干扰轨迹跟踪控制器,并引人自适应策略来估计扰动上界.通过3个仿真算例验证了所设计控制器的有效性,结果表明,与其他控制器相比,本控制器具有较高的跟踪精度、较强的鲁棒性以及较好的抗干扰能力;机械臂质量的变化主要影响x通道和y通道的控制性能;本控制器基本能满足旋翼飞行机器人悬停作业的工作需求,具有一定的工程参考意义.     

不确定刚性机械臂的鲁棒输出控制

针对不确定刚性机械臂系统的鲁棒控制和抖振问题,在仅有精确关节位置反馈的情况下,通过引入速度滤波器生成伪速度信号,并利用反推补偿设计滤波增益,提出了一种基于速度估计的鲁棒输出反馈控制策略。滤波器-控制器设计中不合有开关控制项,有效避免了控制抖振现象。该算法对采样频率无严格限制,最终可确保系统闭环半全局一致有界收敛。通过两关节机械臂的仿真实例验证了所提算法的有效性。     

Vibration control of two-mass system with low inertia ratio considering practical use

In some industrial motor-drive systems, a torsional vibration is often generated because of an elastic element in torque transmission. Such a mechanical system is modeled as a two-mass system and it is well-known that the suppressing vibration of a low inertia ratio two-mass system where the motor inertia is larger than the load inertia is very difficult. This paper proposes a speed control system of a low-inertia ratio system, taking into account not only the dynamic responses but also a robust stability. The proposed control system is based on the H^∞ control theory and the resonance ratio control due to the feedback of the estimated shaft torque. Combining the H^∞ controller with the resonance ratio controller, the control system with high robust stability can be obtained comparing with the conventional resonance ratio control. The variable feedback gain system and the construction of the disturbance observer are discussed in order to reject the effects of noise. The simulated and experimental results show that the proposed speed control system is useful for the two-mass system with low inertia ratio. ©1998 Scripta Technica, Electr Eng Jpn, 125(2): 1–9, 1998     

Robust decentralized neural networks based LFC in a deregulated power system

In this paper, a decentralized radial basis function neural network (RBFNN) based controller for load frequency control (LFC) in a deregulated power system is presented using the generalized model for LFC scheme according to the possible contracts. To achieve decentralization, the connections between each control area with the rest of system and effects of possible contracted scenarios are treated as a set of input disturbance signals. The idea of mixed H₂/H_∞ control technique is used for the training of the proposed controller. The motivation for using this control strategy for training the RBFNN based controller is to take large modeling uncertainties into account, cover physical constraints on control action and minimize the effects of area load disturbances. This newly developed design strategy combines the advantage of the neural networks and mixed H₂/H_∞ control techniques to provide robust performance and leads to a flexible controller with simple structure that is easy to implement. The effectiveness of the proposed method is demonstrated on a three-area restructured power system. The results of the proposed controllers are compared with the mixed H₂/H_∞ controllers for three scenarios of the possible contracts under large load demands and disturbances. The resulting controller is shown to minimize the effects of area load disturbances and maintain robust performance in the presence of plant parameter changes and system nonlinearities.     

Force‐based disturbance observer for dynamic force control and a position/force hybrid controller

In this paper, a force‐based disturbance observer (DOB) and a force control system using the DOB are proposed to obtain dynamic force control under disturbances. A DOB can reduce the effect of disturbances and modeling errors on robots. In a conventional DOB, an acceleration response is fed back to a reference, enabling highly precise position control. In other words, the effect of disturbances is decreased by emphasizing the effect of inertial forces. When a force controller is implemented, however, inertial forces are regarded as disturbances respect to a force response. Because inertial forces increase according to the acceleration, conventional DOBs are not suitable for dynamic force control. In the proposed DOB, a force response is fed back instead of an acceleration response. The effect of inertial forces is thus eliminated, thereby improving the tracking performance of force controllers. The proposed method's validity is verified analytically and experimentally. A position/force hybrid controller and a DOB for the controller are proposed as an extension of the proposed DOB. A bilateral controller is given as an example of the proposed hybrid controller, and its tracking performance is demonstrated experimentally. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

This paper considers the problem of adaptive robust H_∞ state feedback control for linear uncertain systems with time‐varying delay. The uncertainties are assumed to be time varying, unknown, but bounded. A new adaptive robust H_∞ controller is presented, whose gains are updating automatically according to the online estimates of uncertain parameters. By combining an indirect adaptive control method and a linear matrix inequality method, sufficient conditions with less conservativeness than those of the corresponding controller with fixed gains are given to guarantee robust asymptotic stability and H_∞ performance of the closed‐loop systems. A numerical example and its simulation results are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Active vibration control of a motor system by using H∞ control theory

This paper considers the vibration control of a motor system which has a motor and a load connected with a flexible shaft. However, this system often generates a shaft torsional vibration. Traditional methods of treating this problem to adjust the PID controller so that the closed-loop frequency response is slower than that of the vibration mode. On the other hand, one method has already been proposed in which the vibration is suppressed by a disturbance observer. This paper proposes a new approach based on H_∞ control theory. For comparison, a PI control system based on classical control theory also is constructed. The results of several experiments show that compared with the PI control system, the H_∞ control system is effective in suppressing the vibration. Further, the H_∞ controller obtained in the study consists of a PI controller and a series compensator that functions as an active vibration controller.     

A design method of digital robust speed servo system considering output saturation

When a robust servo system having an integral element has a large error input, it often reveals windup phenomena caused by output saturation. It is very difficult for a strictly proper and high‐order controller to avoid having windup phenomena caused by output saturation. This paper newly proposes the digital robust speed servo system with a complete algorithm for consideration of output saturation. The proposed algorithm completely considers the output saturation of a robust speed controller connected to a PI current controller in series. Moreover, this method can be applied to both a PI speed controller and an H^∞ speed controller. The experimental results show that a robust speed servo system using the proposed algorithm has a good and stable response for a large step speed command. © 2000 Scripta Technica, Electr Eng Jpn, 132(3): 68–78, 2000     

Adaptive motion/force tracking control of holonomic constrained mechanical systems: a unified viewpoint

This paper proposes a robust adaptive motion/force tracking controller for holonomic constrained mechanical systems with parametric uncertainties and disturbances. First, two types of well‐known holonomic systems are reformulated as a unified control model. Based on the unified control model, an adaptive scheme is then developed in the presence of pure parametric uncertainty. The proposed controller guarantees asymptotic motion and force tracking without the need of extra conditions. Next, when considering external disturbances, control gains are designed by solving a linear matrix inequality (LMI) problem to achieve prescribed robust performance criterion. Indeed, arbitrary disturbance/parametric error attenuation with respect to both motion and force errors along with control input penalty are ensured in the L₂‐gain sense. Finally, applications are carried out on a two‐link constrained robot and two planar robots transporting a common object. Numerical simulation results show the expected performances. Copyright © 2006 John Wiley & Sons, Ltd.     

Decentralized load frequency based on H∞ control

This paper presents a decentralized load frequency control (LFC) based on H_∞ optimal control theory with an observer. A few LFC schemes have been proposed based on the optimal control theory, but they have not considered the change of system parameters in operation and the characteristics of load disturbances in a target system. In this paper, H_∞ robust control is introduced to address such problems. Owing to its practical merit, the proposed control scheme is a decentralized LFC. Employing observer theory, the proposed method requires only frequency and tie‐line power deviation in each area. Numerical simulations are shown to demonstrate the effectiveness of the proposed method. H_∞ control was proven to show greater effectiveness of damping disturbance over the conventional optimal control by the design of control systems aimed at restricting the H_∞ norm of its transfer function. In particular, when a decentralized LFC is applied, by reducing the system size, H_∞ norm is easier to dampen; thus H_∞ control is more effective in the decentralized control. Future research topics include the design of H_∞ control system with a weight on frequency response. © 2001 Scripta Technica, Electr Eng Jpn, 136(3): 28–38, 2001     

DLR/HIT II灵巧手控制系统及基关节同步控制

针对多传感器、多自由度机器人灵巧手,开发了基于DSP＆FPGA的多层控制系统.将手指驱动控制系统和传感器系统集成在手指内部,使得与人手尺寸和活动性相似的DLR/HIT II五指机器人灵巧手得以实现.对于手指基关节差分齿轮的运动协调问题,设计了包含速度和加速度前馈项、同步误差和位置误差反馈项以及平滑鲁棒非线性反馈补偿项的交叉耦合同步控制器,该控制器不需要精确的动力学模型.经与传统的非同步控制PD加摩擦力补偿控制和轨迹跟踪控制对比,实验验证了所设计的控制系统及交叉耦合同步控制器的有效性.     

Stabilization control for multimachine system using decentralized H∞ excitation controller realizing terminal voltage control and damping control

In this paper, to achieve both damping of power system oscillation and terminal voltage control simultaneously on a multimachine power system, we propose a decentralized H_∞ excitation controller. In the proposed method, H_∞ control via the Normalized Coprime Factorization approach is used to achieve the proposed design idea. By the Normalized Coprime Factorization approach, the weighting function in H_∞ control design is simplified, and output feedback controllers that take into account the realities and constraints of the power systems are designed. The proposed controller is subjected to model reduction of H_∞ controllers, and is transformed to a discrete system to perform digital control by computer systems in consideration of application to a real system. We verify that the proposed excitation controller can achieve both damping of power system oscillation and terminal voltage control by computer simulations of a multimachine power system. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 147(1): 33–41, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10254     

An adaptive force/position regulator for robot manipulators

An adaptive force/position regulator for robot manipulators in contact with an elastically compliant surface is proposed in this paper. The controller consists of a PD action on the position loop, a PI action on the force loop, together with estimated gravity compensation and desired contact force feedforward. The closed-loop system is shown to have a unique equilibrium state and asymptotic stability in the neighbourhood of this state is proven via the classical Lyapunov method. To cope with imperfect gravity compensation, the controller is made adaptive with respect to a suitable set of parameters in the gravity term. Numerical case studies are developed for a three-joint elbow manipulator.     

Youla Parameterization Robust Control Strategy Considering Power System Uncertainties

In view of the reduced low-frequency oscillation damping effect caused by inaccurate modeling of the power system due to various uncertainties, a Youla parameterization robust control strategy considering system uncertainties is proposed in this article. First, the uncertainties of the measurement error and parameter estimation are described by the perturbation matrix, and the convex polytopic model is utilized to describe uncertainties caused by variation of the operating point. Then, by solving the H₂/H_∞ inequalities, the Youla parameterization matrix is gained. Finally, the output error of the actual system to the nominal system is introduced to the output feedback control link via the Youla parameterization matrix. Thus, tracking control of the output error can be realized, as well as H₂/H_∞ robust control of the system. Simulation results show that the proposed method is immune to internal and external uncertainties. Compared with control methods without considering uncertainties, the proposed method is capable of damping low-frequency oscillation faster and more effectively with better robust performance.