滑模控制与观测器设计详解：案例丰富的教材

需积分: 16 48 浏览量更新于2024-07-18 1 收藏 8.42MB PDF 举报

《滑模控制与观测：理论与实践》是一本深入探讨滑模控制（Sliding Mode Control, SMC）及其观测器设计的重要教材，由业内权威专家共同编撰，包括Yuri Shtessel、Christopher Edwards、Leonid Fridman、Arie Levant等人。该书聚焦于自动化领域的控制工程，着重介绍滑模控制这一动态控制策略，其特点是能够有效地处理非线性系统中的不确定性、快速切换和鲁棒性。书中首先阐述了滑模控制器的设计方法，强调了如何通过设计特定的控制律，使系统的状态能够在有限的时间内进入一个稳定的“滑动区域”，从而实现对系统性能的精确控制。滑模控制因其在诸如定位、伺服系统、电力电子等领域广泛应用而备受关注，它能够应对系统参数变化和外部干扰，保持系统的稳定性和快速响应能力。观测器的设计部分则是为了实现系统的状态估计，即使在没有完全信息的情况下也能保证控制的准确性。这部分内容讲解了如何构建有效的观测器模型，确保系统的可观测性，并讨论了与滑模控制相结合时可能出现的挑战，如观测器的稳定性、抗噪声性能以及与控制器的协同作用。作者们来自全球知名学府，如美国马里兰大学、墨西哥国家自治大学等，他们的深厚学术背景使得本书理论严谨，案例丰富，适合研究生和工程师作为学习参考资料。此外，书后还提供了系列链接，读者可以进一步探索滑模控制的更多研究进展和后续出版物。《滑模控制与观测》是一本全面且实用的教材，涵盖了滑模控制的基础理论、设计原则、实际应用以及前沿发展，对于希望深入了解滑模控制技术的读者来说，无论是理论研究者还是工程实践者，都是一份不可或缺的学习资料。

Contents xv

4.7 Variable-Gain Super-Twisting Control ............................... 170

4.7.1 Problem Statement ........................................... 171

4.7.2 The Variable-Gain Super-Twisting Algorithm.............. 172

4.8 Case Study: The Mass–Spring–Damper System ..................... 176

4.8.1 Model Description ........................................... 176

4.8.2 Problem Statement ........................................... 177

4.8.3 Control Design ............................................... 178

4.8.4 Experimental Results ........................................ 179

4.9 Notes and References.................................................. 179

4.10 Exercises ............................................................... 182

5 Analysis of Sliding Mode Controllers in the Frequency Domain ....... 183

5.1 Introduction ............................................................ 183

5.2 Conventional SMC Algorithm: DF Analysis ......................... 184

5.3 Twisting Algorithm: DF Analysis .................................... 193

5.4 Super-Twisting Algorithm: DF Analysis ............................ 196

5.4.1 DF of Super-Twisting Algorithm............................ 196

5.4.2 Existence of the Periodic Solutions ........................ 198

5.4.3 Stability of Periodic Solution ............................... 200

5.5 Prescribed Convergence Control Law: DF Analysis ................ 201

5.6 Suboptimal Algorithm: DF Analysis ................................. 203

5.7 Comparisons of 2-Sliding Mode Control Algorithms ............... 205

5.8 Notes and References.................................................. 208

5.9 Exercises ............................................................... 208

6 Higher-Order Sliding Mode Controllers and Differentiators ........... 213

6.1 Introduction ............................................................ 214

6.2 Single-Input Single-Output Regulation Problem..................... 216

6.3 Homogeneity, Finite-Time Stability, and Accuracy .................. 217

6.4 Homogeneous Sliding Modes ......................................... 222

6.5 Accuracy of Homogeneous 2-Sliding Modes ........................ 223

6.6 Arbitrary-Order Sliding Mode Controllers ........................... 225

6.6.1 Nested Sliding Controllers .................................. 225

6.6.2 Quasi-continuous Sliding Controllers....................... 227

6.7 Arbitrary-Order Robust Exact Differentiation ....................... 228

6.8 Output-Feedback Control ............................................. 230

6.9 Tuning of the Controllers.............................................. 233

6.9.1 Control Magnitude Tuning .................................. 233

6.9.2 Parametric Tuning............................................ 233

6.10 Case Study: Car Steering Control..................................... 234

6.11 Case Study: Blood Glucose Regulation .............................. 237

6.11.1 Introduction to Diabetes ..................................... 237

6.11.2 Insulin–Glucose Regulation Dynamical Model ............ 240

6.11.3 Higher-Order Sliding Mode Controller Design............. 241

6.11.4 Simulation .................................................... 244

xvi Contents

6.12 Notes and References.................................................. 247

6.13 Exercises ............................................................... 248

7 Observation and Identiﬁcation via HOSM Observers .................. 251

7.1 Observation/Identiﬁcation of Mechanical Systems .................. 252

7.1.1 Super-Twisting Observer .................................... 253

7.1.2 Equivalent Output Injection Analysis ....................... 255

7.1.3 Parameter Identiﬁcation ..................................... 259

7.2 Observation in Single-Output Linear Systems ....................... 265

7.2.1 Non-perturbed Case.......................................... 265

7.2.2 Perturbed Case ............................................... 266

7.2.3 Design of the Observer for Strongly Observable

Systems ....................................................... 268

7.3 Observers for Single-Output Nonlinear Systems..................... 274

7.3.1 Differentiator-Based Observer .............................. 275

7.3.2 Disturbance Identiﬁcation ................................... 278

7.4 Regulation and Tracking Controllers Driven by SM Observers ..... 280

7.4.1 Motivation .................................................... 280

7.4.2 Problem Statement ........................................... 281

7.4.3 Theoretically Exact Output-Feedback

Stabilization (EOFS) ......................................... 282

7.4.4 Output Integral Sliding Mode Control ...................... 283

7.4.5 Precision of the Observation and Identiﬁcation

Processes ..................................................... 284

7.5 Notes and References.................................................. 286

7.6 Exercises ............................................................... 286

8 Disturbance Observer Based Control: Aerospace Applications ........ 291

8.1 Problem Formulation .................................................. 291

8.1.1 Asymptotic Compensated Dynamics ....................... 292

8.1.2 Finite-Time-Convergent Compensated Dynamics.......... 293

8.1.3 Sliding Variable Disturbed Dynamics....................... 294

8.1.4 Output Tracking Error Disturbed Dynamics................ 294

8.2 Perturbation Term Reconstruction via a Disturbance Observer ..... 295

8.2.1 SMDO Based on Conventional SMC ....................... 295

8.2.2 SMDO Based on Super-Twisting Control .................. 296

8.2.3 Design of the SMC Driven by the SMDO .................. 297

8.3 Case Study: Reusable Launch Vehicle Control ...................... 298

8.3.1 Mathematical Model of Reusable Launch Vehicle ......... 298

8.3.2 Reusable Launch Vehicle Control Problem Formulation .. 300

8.3.3 Multiple-Loop Asymptotic SMC/SMDO

Design ........................................................ 301

8.3.4 Flight Simulation Results and Analysis..................... 305

Contents xvii

8.4 Case Study: Satellite Formation Control ............................. 309

8.4.1 Satellite Formation Mathematical Model .................. 310

8.4.2 Satellite Formation Control in SMC/SMDO ............... 313

8.5 Simulation Study ...................................................... 314

8.6 Notes and References.................................................. 316

8.7 Exercises ............................................................... 318

A Mathematical Preliminaries ................................................ 321

A.1 Linear Algebra ......................................................... 321

A.1.1 Rank and Determinant ....................................... 321

A.1.2 Eigenvalues and Eigenvectors ............................... 322

A.1.3 QR Decomposition........................................... 323

A.1.4 Norms......................................................... 323

A.1.5 Quadratic Forms ............................................. 324

B Describing Functions ........................................................ 327

B.1 Describing Function Fundamentals ................................... 327

B.1.1 Low-Pass Filter Hypothesis and Describing Function ..... 328

B.1.2 Limit Cycle Analysis Using Describing Functions......... 328

B.1.3 Stability Analysis of the Limit Cycle ....................... 329

C Linear Systems Theory ...................................................... 331

C.1 Introduction ............................................................ 331

C.1.1 Linear Time-Invariant Systems.............................. 331

C.1.2 Controllability and Observability ........................... 332

C.1.3 Invariant Zeros ............................................... 333

C.1.4 State Feedback Control ...................................... 334

C.1.5 Static Output Feedback Control ............................. 335

D Lyapunov Stability ........................................................... 337

D.1 Local Results........................................................... 338

D.2 Global Results ......................................................... 338

D.2.1 Quadratic Stability ........................................... 339

Bibliography ...................................................................... 343

Index ............................................................................... 353

Chapter 1

Introduction: Intuitive Theory of Sliding

Mode Control

In the formulation of any practical control problem, there will always be a

discrepancy between the actual plant and its mathematical model used for the

controller design. These discrepancies (or mismatches) arise from unknown exter-

nal disturbances, plant parameters, and parasitic/unmodeled dynamics. Designing

control laws that provide the desired performance to the closed-loop system in the

presence of these disturbances/uncertainties is a very challenging task for a control

engineer. This has led to intense interest in the development of the so-called robust

control methods which are supposed to solve this problem. One particular approach

to robust controller design is the so-called sliding mode control technique.

In Chap. 1, the main concepts of sliding mode control will be introduced

in an intuitive fashion, requiring only a basic knowledge of control systems.

The sliding mode control design techniques are demonstrated on tutorial examples

and via graphical exposition. Advanced sliding mode concepts, including sliding

mode observers/differentiators and second-order sliding mode control, are studied

at a tutorial level. The main advantages of sliding mode control, including ro-

bustness, ﬁnite-time convergence, and reduced-order compensated dynamics, are

demonstrated on numerous examples and simulation plots.

For illustration purposes, the single-dimensional motion of a unit mass (Fig. 1.1)

is considered. A state-variable description is easily obtained by introducing vari-

ables for the position and the velocity x

D x; x

DPx

so that

(

D x

D u C f.x

;t/

.0/ D x

;

(1.1)

where u is the control force, and the disturbance term f.x

;t/,whichmay

comprise dry and viscous friction as well as any other unknown resistance forces,

is assumed to be bounded, i.e.,

f.x

;t/

 L>0. The problem is to design a

feedback control law u D u.x

/ that drives the mass to the origin asymptotically.

In other words, the control u D u.x

/ is supposed to drive the state variables to

Y. Shtessel et al., Sliding Mode Control and Observation, Control Engineering,

DOI 10.1007/978-0-8176-4893-0

剩余368页未读，继续阅读

黎明雨水

粉丝: 0
资源: 5

滑模控制与观测器设计详解：案例丰富的教材

滑模控制理论Sliding mode control Utkin

SlideMode:处理2.x的演示模式

Sliding Mode Control and Observation

Sliding Mode Control and Observation-03Conventional Sliding Mode Observers.pdf

Sliding Mode Control and Observation-00Front Matter.pdf

Sliding Mode Control and Observation-01Introduction_Intuitive.pdf

Sliding Mode Control and Observation -02Conventional Sliding Modes.pdf

Sliding Mode Control and Observation-productFlyer-EAST_978-0-8176-4892-3.pdf

Stability analysis for an Euler-Bernoulli beam under local internal control and boundary observation

NDBC Processing, Display, and Observation

最新资源