基于高阶未知输入观测器的MIMO系统输出控制方法研究

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"基于高阶未知输入观测器的无匹配干扰的MIMO系统输出控制" 本文研究了基于高阶未知输入观测器的无匹配干扰的MIMO系统输出控制问题。该问题对现有的控制系统具有重要的实际意义，因为在实际应用中，系统的输入和输出信号可能会受到未知干扰的影响，从而影响系统的性能和稳定性。首先，本文提出了基于高阶未知输入观测器的控制策略，该策略可以实时估计系统的状态和干扰信息，并基于这些信息设计控制律以达到输出控制的目的。该策略的核心是高阶未知输入观测器（HOUIO），它可以实时估计系统的状态和干扰信息，并提供了充分的信息基础以设计控制律。在设计控制律时，本文采用了smooth backstepping控制策略，该策略可以确保系统的输出信号逐渐收敛到零，同时也可以减少控制律中的抖振现象。与传统的sliding mode控制策略相比，该策略不包含任何switching函数，从而可以有效地减少控制律中的抖振现象。此外，本文还对所提出的控制策略进行了仿真实验，结果表明该策略可以有效地控制MIMO系统的输出信号，达到输出控制的目的。本文的研究成果对于MIMO系统的输出控制具有重要的理论和实际意义，可以为实际应用提供有价值的参考。知识点摘要： 1. 基于高阶未知输入观测器的控制策略可以实时估计系统的状态和干扰信息，并设计控制律以达到输出控制的目的。 2. 高阶未知输入观测器（HOUIO）可以实时估计系统的状态和干扰信息，并提供了充分的信息基础以设计控制律。 3. Smooth backstepping控制策略可以确保系统的输出信号逐渐收敛到零，同时也可以减少控制律中的抖振现象。 4. 该控制策略可以减少控制律中的抖振现象，并可以有效地控制MIMO系统的输出信号。 5. 该研究成果对于MIMO系统的输出控制具有重要的理论和实际意义，可以为实际应用提供有价值的参考。关键词：高阶未知输入观测器、MIMO系统、输出控制、smooth backstepping控制策略、抖振现象。

International Journal of Control, Automation and Systems 15(2) (2017) 575-584

http://dx.doi.org/10.1007/s12555-015-0429-9

ISSN:1598-6446 eISSN:2005-4092

http://www.springer.com/12555

Output Control of MIMO System with Unmatched Disturbance based on

High-order Unknown Input Observer

Jiancheng Zhang and Fanglai Zhu*

Abstract: In this paper, the output control for a general MIMO linear system subjected to unmatched disturbance is

considered. A smooth backstepping control law is developed under the assumption that the state and disturbance as

well as its derivatives are known ﬁrstly. Then in order to estimate the required information, a high-order unknown

input observer (HOUIO) is developed, and it is proven that based on the estimation by such the HOUIO, the designed

controller can compensate all the disturbances from output channels and asymptotically drive the output to zero.

Comparing with the traditional sliding mode control laws, the control law we design does not contain any switching

function, so it can effectively reduce the chattering. Finally, simulation results are given to show the effectiveness

of our methods.

Keywords: High-order unknown input observer, MIMO systems, smooth controller, unmatched disturbance.

1. INTRODUCTION

Uncertainties in dynamic systems, including parameter

perturbation and external disturbances, can bring adverse

effects to system performance and even cause unstable dy-

namic behaviors. Many scholars have devoted themselves

to address this practical issue, and up to now, many ef-

fective control schemes, including robust H

∞

control

[1–4], adaptive control [5–7], sliding mode control [8–10],

and backstepping control [11] and so on, have been put

forward.

On the one hand, the methods mentioned above are usu-

ally good at dealing with systems with matching uncer-

tainty. For systems with unmatched disturbances, how-

ever, they can not compensate the uncertainty effects com-

pletely. On the other hand, the systems subjected to un-

matched disturbances are very common in engineering

application. In fact, the MAGLEV suspension vehicle

[12], the PMSM systems [13, 14] and the magnetically

suspended balance beam system [15] are examples of sys-

tems affected by unmatched uncertainties [16]. So, how to

design control law to reach the unmatched disturbance re-

jection purpose becomes one of the major considerations

recently and, of course, many control techniques, such

as Riccati approach [17], LMI-based control [18], sliding

mode control (see [19–22]), backstepping method [23–27]

and disturbance observer-based compensation strategies

[12, 28, 29], have been developed. In [23], a backstepping

control scheme is proposed to tackle the exact tracking

Manuscript received November 14, 2015; revised April 5, 2016; accepted June 5, 2016. Recommended by Associate Editor Nam H. Jo un-

der the direction of Editor Duk-Sun Shim. This work is supported by the National Nature Science Foundation of China under grant 61573256.

Jiancheng Zhang and Fanglai Zhu are with the College of Electronics and Information Engineering, Tongji University, Shanghai (201804),

China (e-mails: jcz1919@163.com, 1987jcz@tongji.edu.cn (J. Zhang), zhufanglai@tongji.edu.cn (F. Zhu)).

* Corresponding author.

issue in the presence of matching and unmatched distur-

bances for the system with block controllable form. In

[22] and [25], the control schemes for some certain vari-

ables of systems with unmatched disturbances are pro-

posed based on the exact identiﬁcation of state and dis-

turbance. The former control law design is sliding mode

scheme, and the latter is a continuous one with chatter-

ing attenuation. In [30], the authors proposed a high order

augmented state observer based control such that the out-

put tracking error can be global ultimate bounded, and the

disturbance there is assumed to be in the polynomial func-

tion form. More recently, for these unmatched disturbance

rejection issues, several sliding mode control combining

with disturbance observer design methods were reported,

such as [12, 16, 28, 29, 31, 32] and so on. In particular,

based on a second-order system, [28] proposed a new con-

trol scheme such that the output y can be steered to zero

in the presence of unmatched disturbance d(t) which sat-

isﬁes lim

t→∞

d(t) = 0 . Assumption lim

t→∞

d(t) = 0 im-

plies that the d(t) is a constant or an incipient disturbance

and obviously it is too restrictive. To relax this restriction,

[31] developed a new disturbance observer-based control

method which can deal with high-order time-varying dis-

turbance signals, and then they extended the results in [28]

to n-order system. In addition, in [16] and [32], a nonsin-

gular terminal sliding mode controller and a continuous

controller are constructed, respectively, where the exact

identiﬁcation of disturbance was incorporated into such

the control laws so that the inﬂuence of the disturbance

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