Nominal model manipulation for enhancement of stability robustness for disturbance observer-based control systems

Disturbance observer-based control systems often encounter the stability problem due to modeling uncertainties. In such cases, the disturbance observer (DOB) may have to be re-designed by narrowing the bandwidth of the Q-filter to enhance stability robustness, but this approach to stability enhancement deteriorates the performance of DOB. In order to improve robust stability while maintaining the performance of DOB, this paper proposes a method that manipulates the nominal plant model in the DOB; the parameters of the discretized nominal model are optimized to improve robust stability in the discrete time domain. For the optimization of nominal model, it is assumed that the closed-loop poles of DOB are subjected to multiplicative uncertainties, and the maximum allowable magnitude of uncertainties is utilized as the measure of stability robustness. Then, the proposed method changes the location of closed-loop poles to maximize the robustness margin. This paper provides a case study that includes experimental results.     

Yet another tutorial of disturbance observer: robust stabilization and recovery of nominal performance

This paper presents a tutorial-style review on the recent results about the disturbance observer (DOB) in view of robust stabilization and recovery of the nominal performance. The analysis is based on the case when the bandwidth of Q-filter is large, and it is explained in a pedagogical manner that, even in the presence of plant uncertainties and disturbances, the behavior of real uncertain plant can be made almost similar to that of disturbance-free nominal system both in the transient and in the steady-state. The conventional DOB is interpreted in a new perspective, and its restrictions and extensions are discussed.     

Adding robustness to nominal output-feedback controllers for uncertain nonlinear systems: A nonlinear version of disturbance observer

The linear disturbance observer (DOB) approach has been successfully employed as a tool for robust control and disturbance rejection in practice. In this paper, we present a nonlinear DOB which inherits all the benefits of the classical linear DOB approach. In particular, we prove that the proposed nonlinear DOB recovers not only the steady-state performance but also the transient performance of the nominal closed-loop system under plant uncertainties and input disturbances. One novel feature of the proposed controller is that it is an add-on type inner-loop output-feedback controller; thus any type of outer-loop controller can be combined to enhance the closed-loop system performance. Our result is a semi-global one and the stability proof is given when the nonlinear system has a well-defined relative degree with a stable zero dynamics.     

保证闭环系统鲁棒稳定性的干扰观测器系统性设计方法

研究带有干扰观测器(Disturbance observer,DOB)的反馈控制系统对模型不确定性鲁棒稳定的充分条件,在此基础上,选取满足此充分条件的加权函数,使得标准H∞干扰观测器设计方法保证对受控对象参数变化的鲁棒稳定性.提出了在H∞干扰观测器设计中兼顾鲁棒性设计指标和结构约束的频率加权函数的选取方法.利用加权函数选取的自由度,在干扰观测器低通滤波器设计中,实现Q—滤波器在截止频率上的高峰幅度与干扰抑制性能之间的最佳折中,使得干扰观测器在满足其幅度指标的条件下,具有最优干扰抑制性能.实验结果表明该方法保证了闭环反馈系统的鲁棒稳定性,同时,具有实现其他设计指标的自由度.     

An almost necessary and sufficient condition for robust stability of closed-loop systems with disturbance observer

The disturbance observer (DOB)-based controller has been widely employed in industrial applications due to its powerful ability to reject disturbances and compensate plant uncertainties. In spite of various successful applications, no necessary and sufficient condition for robust stability of the closed loop systems with the DOB has been reported in the literature. In this paper, we present an almost necessary and sufficient condition for robust stability when the Q-filter has a sufficiently small time constant. The proposed condition indicates that robust stabilization can be achieved against arbitrarily large (but bounded) uncertain parameters, provided that an outer-loop controller stabilizes the nominal system, and uncertain plant is of minimum phase.     

基于干扰观测器的不确定线性多变量系统控制

针对不确定线性多变量系统,提出一种基于干扰观测器(Disturbance observer,DOB)的保证系统内部稳定性的控制策略.以简单的结构和少量的计算代价实现鲁棒的控制效果,补偿外界干扰以及内部模型误差.通过引入一个闭环稳定性等价系统,辅助分析基于干扰观测器的多变量控制系统的内部稳定性,探讨在存在外部扰动及内部模型不确定性的情况下系统保证内部稳定的充分条件,指导外环控制器及内环干扰观测器中Q滤波器的设计.通过数值模型上的仿真验证了提出的控制方法的有效性.     

Disturbance observer for non-minimum phase linear systems

Disturbance observer (DOB) approach has been widely employed in the industry thanks to its powerful ability to attenuate disturbances and compensate plant uncertainties. Motivated by the fact that the application of the DOB approach has been limited to minimum phase systems, we propose a new DOB configuration for non-minimum phase systems. Rigorous analysis for robust stability and performance recovery is presented in terms of a new filter Θ (s). By restricting the plant uncertainty to a multiplicative perturbation, we also present a systematic design methodology for the filter Θ(s) by virtue of the H_∞ synthesis technique. An illustrative example of autopilot design is presented to show the effectiveness of the proposed method for which it is not easy to design H_∞ controller to achieve some control goals. The simulation results show that the response of the perturbed system in the presence of disturbance can be recovered to the nominal system response in the absence of disturbance.     

Analysis the robustness of control systems based on disturbance observer

Disturbance observer (DOB) estimates the system disturbances by using the inverse of the nominal plant model and a low pass filter (LPF). Although the LPF provides the properness in the inner-loop, it is the main design constraint of the control systems based on DOB. The bandwidth of the LPF is designed as high as possible so that the DOB can estimate the disturbances in a wider frequency range. However, its bandwidth is limited by noise and robustness of the system. The robustness limitation is directly related with the robustness analysis methods, and they significantly affect the performance of the DOB based control systems. In this paper, three different robustness analysis methods are implemented into the DOB based control systems, and the relation between the robustness of the system and bandwidth of DOB is clearly explained. The conservatism, which is the main drawback of the conventional analysis methods, on the bandwidth of DOB is removed by proposing a new real parametric uncertainty based analysis method. The proposed methods are compared in detail, and simulation results are given to show the validation.     

Design and evaluation of disturbance observer algorithm for cable-driven parallel robots

Recently, a cable-driven parallel robots (CDPRs) has been applied to radio telescope as the accurate actuator, that is the five-hundred-meter aperture spherical telescope. It can be affected by the disturbances such as wind, earthquake and so on. Therefore, this paper developed a disturbance observer (DOB)-based control suitable for CDPR. The propose of the control is to reduce the effects of disturbance while the end-effectors maintains the same position even though the disturbance affects it. The key component of the DOB controller is a disturbance observer, which includes inverse nominal plant for each cable. So, a system identification test was carried out firstly. Then, the simulation and experiment were also carried out to evaluate the performance of the algorithm in CDPR. The results showed that the designed DOB algorithm could effectively reduce disturbances.

     

含有不确定因素的模型检验及其非伪概率估计*

本文研究了在控制对象的模型具有不确定的建模误差时的模型检验问题，并给邮了控制对象的模型不能被实验数据所否定的概率的估计。     

Approximate model reference adaptive mechanism for nominal gaindesign of fuzzy control system

The difficult design of fuzzy logic control (FLC) can be processed in two separate stages: nominal design and optimal adjustment. The nominal design intends to figure out the nominal model of FLC including rule base, membership functions (MF's), and scaling gains. Different parameters require different design methods. A quantitative approach is presented in this paper to design the nominal scaling gain by using the idea of classical adaptive control. This adaptive mechanism requires only an approximate reference model of the plant, but it tolerates much more system uncertainties due to the inherent nonlinear feature of FLC. In reality, a first-order linear model is usually sufficient for achieving a reasonable performance. This approximate model reference based adaptive fuzzy control system is more robust than its classical counterpart in complex environment without deteriorating the original system stability. Therefore, it is an effective method to determine proper scaling gains for FLC.     

采用改进型扰动观测器的控制方法

提出一种适用于非最小相位对象的改进型扰动观测(DOB)结构.通过新增两个控制器,该结构不但对标称性能控制器输出进行动态补偿,而且还补偿了系统输出反馈信号.因此,基于新DOB的控制结构不但能在低频段很好的抑制外部干扰,消除实际被控模型摄动对闭环系统的输出性能的影响,更重要的是提高了抑制高频测量噪声的能力.最后,讨论了该控制结构的内部稳定性和鲁棒稳定性.     

Monotonic Convergence of Iterative Learning Control for Uncertain Systems Using a Time-Varying Filter

Iterative learning control (ILC) is a learning technique used to improve the performance of systems that execute the same task multiple times. Learning transient behavior has emerged as an important topic in the design and analysis of ILC systems. In practice, the learning control is often low-pass filtered with a ldquoQ-filterrdquo to prevent transient growth, at the cost of performance. In this note, we consider linear time-invariant, discrete-time, single-input single-output systems, and convert frequency-domain uncertainty models to a time-domain representation for analysis. We then develop robust monotonic convergence conditions, which depend directly on the choice of the Q-filter and are independent of the nominal plant dynamics. This general result is then applied to a class of linear time-varying Q-filters that is particularly suited for precision motion control.     

A jerk-constrained time-optimal servo with disturbance compensation

For positioning servo-systems, this paper presents a jerk-constrained time- optimal control (JCTOC) scheme, augmented with an improved disturbance rejection method. In mechanical systems, the jerk that is the time derivative of acceleration may cause many unwanted results when too high. Thus, the JCTOC method is proposed to constrain the system׳s jerk and also obtain a time-optimal characteristic with the constrained jerk. However, because the JCTOC relies on the accuracy of the plant׳s model, system uncertainties and disturbances can adversely affect the output response. Thus, a disturbance observer (DOB) is added for compensation of the perturbation. The DOB used in this paper is in an integral form, and is thus referred to as an integral DOB (IDOB). The IDOB is further enhanced with a dynamic compensator to provide both better noise immunity and asymptotic compensation for disturbances of various orders.     

Design and stability analysis of a variable structure adaptive backstepping controller

This paper presents the design and stability analysis of a Variable Structure Adaptive Backstepping Controller (VS‐ABC) for linear plants with relative degree one, using only input/output measurements. Instead of traditional integral adaptive laws for estimating the plant parameters, switching laws are proposed to increase robustness to parametric uncertainties and disturbances, as well as to improve transient response. Moreover, the controller design is more intuitive when compared with the original adaptive backstepping controller, since the relay amplitudes are related to the plant nominal parameters and their respective uncertainties. Simplified algorithm versions are also presented, named Compact and Relay VS‐ABC, which reduce the practical implementation complexity, and encourage applications in industrial environments. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust Stabilization and Performance Recovery of Nonlinear Systems With Unmodeled Dynamics

In this technical note we present a time-scale separation redesign for stabilization and performance recovery of nonlinear systems with unmodeled dynamics. The unmodeled dynamics studied do not change the relative degree of the plant and are minimum phase. We design two sets of high gain filters—the first to estimate the uncertain input to the plant over a fast time-scale, and the second to force this estimate to converge to the nominal input on an intermediate time-scale. The control input then acts over the slow time-scale and guarantees that the closed-loop trajectories approach those of the nominal system.      

Comparative study of discretization zero dynamics behaviors in two multirate cases

It is well known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems. When the usual digital control with zero-order hold (ZOH) or fractional-order hold (FROH) input is used, unstable zero dynamics inevitably appear in the discrete-time model even though the continuous-time system with relative degree more than two is of minimum phase. This paper investigates the zero dynamics, as the sampling period tends to zero, of sampled-data models composed of a generalized sample hold function (GSHF), a continuous-time nonlinear plant and a sampler in cascade. More precisely, we show how an approximate sampled-data model can be obtained for nonlinear systems with two special GSHF cases such that sampled zero dynamics of the resulting model can be arbitrarily placed. Further, two GSHFs with appropriate parameters provide nonlinear zero dynamics as stable as possible, or with improved stability properties even when unstable, for a given continuous-time plant. It is also shown that the intersample behavior arising from the multirate input can be localised by appropriately selecting the design parameters based on the stability condition of the zero dynamics. The results presented here generalize well-known ideas from the linear to nonlinear cases.     

Linear Model‐based Feedforward Control for Improving Tracking‐performance of Linear Motors

The main purpose of this article is to propose a linear model‐based approach for improving the tracking performance of linear motors. In particular, P‐ and PI‐controllers, augmented with a linear‐model‐based feedforward controller and disturbance observer (DOB), were utilized in this research. Experimental results show that the feedforward controller can substantially reduce the phase‐delay problem resulting from the limitation of closed‐loop bandwidth. In addition, the DOB can reject nonlinear behaviors to keep a motor‐system close to our nominal linear model. Compared with the results of using P‐ and PI‐controllers only, tracking errors were reduced from 4.44% to 0.67% of the desired trajectory. Therefore, the proposed method provides a solution for improving the tracking performance of linear motors.     

基于Hankel范数模型降价的控制对象的名义模型选择

研究了控制对象具有多个模型时,求取其适合鲁棒控制器设计的名义模型的问题. 提出了一种基于Hankel范数模型降阶的名义模型选择算法.仿真结果确认了算法的有效 性.