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1 Introduction: Intuitive Theory of Sliding Mode Control |
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1 | (42) |
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1.1 Main Concepts of Sliding Mode Control |
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3 | (6) |
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1.2 Chattering Avoidance: Attenuation and Elimination |
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9 | (8) |
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1.2.1 Chattering Elimination: Quasi-Sliding Mode |
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9 | (2) |
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1.2.2 Chattering Attenuation: Asymptotic Sliding Mode |
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11 | (6) |
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1.3 Concept of Equivalent Control |
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17 | (1) |
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1.4 Sliding Mode Equations |
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18 | (1) |
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1.5 The Matching Condition and Insensitivity Properties |
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19 | (1) |
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1.6 Sliding Mode Observer/Differentiator |
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20 | (3) |
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1.7 Second-Order Sliding Mode |
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23 | (4) |
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1.8 Output Tracking: Relative Degree Approach |
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27 | (13) |
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1.8.1 Conventional Sliding Mode Controller Design |
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28 | (2) |
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1.8.2 Integral Sliding Mode Controller Design |
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30 | (3) |
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1.8.3 Super-Twisting Controller Design |
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33 | (3) |
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1.8.4 Prescribed Convergence Law Controller Design |
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36 | (4) |
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40 | (1) |
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41 | (2) |
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2 Conventional Sliding Modes |
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43 | (62) |
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43 | (7) |
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44 | (3) |
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2.1.2 Concept of Equivalent Control |
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47 | (3) |
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2.2 State-Feedback Sliding Surface Design |
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50 | (11) |
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53 | (2) |
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2.2.2 Eigenvalue Placement |
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55 | (3) |
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2.2.3 Quadratic Minimization |
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58 | (3) |
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2.3 State-Feedback Relay Control Law Design |
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61 | (7) |
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2.3.1 Single-Input Nominal Systems |
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61 | (1) |
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2.3.2 Single-Input Perturbed Systems |
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62 | (5) |
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2.3.3 Relay Control for Multi-input Systems |
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67 | (1) |
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2.4 State-Feedback Unit-Vector Control |
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68 | (7) |
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2.4.1 Design in the Presence of Matched Uncertainty |
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68 | (3) |
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2.4.2 Design in the Presence of Unmatched Uncertainty |
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71 | (4) |
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2.5 Output Tracking with Integral Action |
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75 | (2) |
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2.6 Output-Based Hyperplane Design |
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77 | (12) |
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2.6.1 Static Output-Feedback Hyperplane Design |
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78 | (5) |
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2.6.2 Static Output-Feedback Control Law Development |
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83 | (2) |
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2.6.3 Dynamic Output-Feedback Hyperplane Design |
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85 | (2) |
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2.6.4 Dynamic Output-Feedback Control Law Development |
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87 | (1) |
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2.6.5 Case Study: Vehicle Stability in a Split-Mu Maneuver |
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88 | (1) |
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2.7 Integral Sliding Mode Control |
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89 | (7) |
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2.7.1 Problem Formulation |
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90 | (1) |
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2.7.2 Control Design Objective |
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91 | (1) |
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91 | (3) |
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2.7.4 ISM Compensation of Unmatched Disturbances |
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94 | (2) |
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96 | (3) |
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99 | (6) |
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3 Conventional Sliding Mode Observers |
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105 | (38) |
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105 | (1) |
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3.2 A Simple Sliding Mode Observer |
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106 | (5) |
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3.3 Robustness Properties of Sliding Mode Observers |
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111 | (10) |
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3.4 A Generic Conventional Sliding Mode Observer |
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121 | (7) |
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3.5 A Sliding Mode Observer for Nonlinear Systems |
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128 | (5) |
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3.6 Fault Detection: A Simulation Example |
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133 | (3) |
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136 | (1) |
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137 | (6) |
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4 Second-Order Sliding Mode Controllers and Differentiators |
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143 | (40) |
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143 | (4) |
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4.2 2-Sliding Mode Controllers |
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147 | (8) |
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4.2.1 Twisting Controller |
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148 | (3) |
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4.2.2 Suboptimal Algorithm |
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151 | (1) |
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4.2.3 Control Algorithm with Prescribed Convergence Law |
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152 | (1) |
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4.2.4 Quasi-Continuous Control Algorithm |
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153 | (2) |
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4.2.5 Accuracy of 2-Sliding Mode Controllers |
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155 | (1) |
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4.3 Control of Relative Degree One Systems |
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155 | (6) |
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4.3.1 Super-Twisting Controller |
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155 | (4) |
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4.3.2 First-Order Differentiator |
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159 | (2) |
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4.4 Differentiator-Based Output-Feedback 2-SM Control |
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161 | (2) |
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4.5 Chattering Attenuation |
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163 | (3) |
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4.6 Case Study: Pendulum Control |
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166 | (4) |
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4.6.1 Discontinuous Control |
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167 | (2) |
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4.6.2 Chattering Attenuation |
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169 | (1) |
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4.7 Variable-Gain Super-Twisting Control |
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170 | (6) |
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171 | (1) |
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4.7.2 The Variable-Gain Super-Twisting Algorithm |
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172 | (4) |
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4.8 Case Study: The Mass-Spring-Damper System |
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176 | (3) |
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176 | (1) |
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177 | (1) |
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178 | (1) |
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4.8.4 Experimental Results |
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179 | (1) |
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179 | (3) |
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182 | (1) |
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5 Analysis of Sliding Mode Controllers in the Frequency Domain |
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183 | (30) |
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183 | (1) |
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5.2 Conventional SMC Algorithm: DF Analysis |
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184 | (9) |
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5.3 Twisting Algorithm: DF Analysis |
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193 | (3) |
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5.4 Super-Twisting Algorithm: DF Analysis |
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196 | (5) |
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5.4.1 DF of Super-Twisting Algorithm |
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196 | (2) |
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5.4.2 Existence of the Periodic Solutions |
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198 | (2) |
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5.4.3 Stability of Periodic Solution |
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200 | (1) |
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5.5 Prescribed Convergence Control Law: DF Analysis |
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201 | (2) |
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5.6 Suboptimal Algorithm: DF Analysis |
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203 | (2) |
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5.7 Comparisons of 2-Sliding Mode Control Algorithms |
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205 | (3) |
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208 | (1) |
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208 | (5) |
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6 Higher-Order Sliding Mode Controllers and Differentiators |
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213 | (38) |
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214 | (2) |
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6.2 Single-Input Single-Output Regulation Problem |
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216 | (1) |
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6.3 Homogeneity, Finite-Time Stability, and Accuracy |
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217 | (5) |
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6.4 Homogeneous Sliding Modes |
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222 | (1) |
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6.5 Accuracy of Homogeneous 2-Sliding Modes |
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223 | (2) |
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6.6 Arbitrary-Order Sliding Mode Controllers |
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225 | (3) |
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6.6.1 Nested Sliding Controllers |
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225 | (2) |
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6.6.2 Quasi-continuous Sliding Controllers |
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227 | (1) |
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6.7 Arbitrary-Order Robust Exact Differentiation |
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228 | (2) |
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6.8 Output-Feedback Control |
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230 | (3) |
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6.9 Tuning of the Controllers |
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233 | (1) |
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6.9.1 Control Magnitude Tuning |
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233 | (1) |
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233 | (1) |
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6.10 Case Study: Car Steering Control |
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234 | (3) |
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6.11 Case Study: Blood Glucose Regulation |
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237 | (10) |
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6.11.1 Introduction to Diabetes |
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237 | (3) |
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6.11.2 Insulin-Glucose Regulation Dynamical Model |
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240 | (1) |
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6.11.3 Higher-Order Sliding Mode Controller Design |
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241 | (3) |
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244 | (3) |
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6.12 Notes and References |
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247 | (1) |
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248 | (3) |
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7 Observation and Identification via HOSM Observers |
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251 | (40) |
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7.1 Observation/Identification of Mechanical Systems |
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252 | (13) |
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7.1.1 Super-Twisting Observer |
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253 | (2) |
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7.1.2 Equivalent Output Injection Analysis |
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255 | (4) |
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7.1.3 Parameter Identification |
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259 | (6) |
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7.2 Observation in Single-Output Linear Systems |
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265 | (9) |
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265 | (1) |
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266 | (2) |
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7.2.3 Design of the Observer for Strongly Observable Systems |
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268 | (6) |
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7.3 Observers for Single-Output Nonlinear Systems |
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274 | (6) |
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7.3.1 Differentiator-Based Observer |
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275 | (3) |
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7.3.2 Disturbance Identification |
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278 | (2) |
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7.4 Regulation and Tracking Controllers Driven by SM Observers |
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280 | (6) |
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280 | (1) |
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281 | (1) |
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7.4.3 Theoretically Exact Output-Feedback Stabilization (EOFS) |
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282 | (1) |
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7.4.4 Output Integral Sliding Mode Control |
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283 | (1) |
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7.4.5 Precision of the Observation and Identification Processes |
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284 | (2) |
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286 | (1) |
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286 | (5) |
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8 Disturbance Observer Based Control: Aerospace Applications |
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291 | (30) |
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291 | (4) |
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8.1.1 Asymptotic Compensated Dynamics |
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292 | (1) |
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8.1.2 Finite-Time-Convergent Compensated Dynamics |
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293 | (1) |
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8.1.3 Sliding Variable Disturbed Dynamics |
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294 | (1) |
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8.1.4 Output Tracking Error Disturbed Dynamics |
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294 | (1) |
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8.2 Perturbation Term Reconstruction via a Disturbance Observer |
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295 | (3) |
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8.2.1 SMDO Based on Conventional SMC |
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295 | (1) |
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8.2.2 SMDO Based on Super-Twisting Control |
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296 | (1) |
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8.2.3 Design of the SMC Driven by the SMDO |
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297 | (1) |
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8.3 Case Study: Reusable Launch Vehicle Control |
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298 | (11) |
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8.3.1 Mathematical Model of Reusable Launch Vehicle |
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298 | (2) |
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8.3.2 Reusable Launch Vehicle Control Problem Formulation |
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300 | (1) |
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8.3.3 Multiple-Loop Asymptotic SMC/SMDO Design |
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301 | (4) |
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8.3.4 Flight Simulation Results and Analysis |
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305 | (4) |
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8.4 Case Study: Satellite Formation Control |
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309 | (5) |
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8.4.1 Satellite Formation Mathematical Model |
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310 | (3) |
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8.4.2 Satellite Formation Control in SMC/SMDO |
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313 | (1) |
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314 | (2) |
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316 | (2) |
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318 | (3) |
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A Mathematical Preliminaries |
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321 | (6) |
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321 | (6) |
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A.1.1 Rank and Determinant |
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321 | (1) |
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A.1.2 Eigenvalues and Eigenvectors |
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322 | (1) |
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323 | (1) |
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323 | (1) |
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324 | (3) |
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327 | (4) |
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B.1 Describing Function Fundamentals |
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327 | (4) |
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B.1.1 Low-Pass Filter Hypothesis and Describing Function |
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328 | (1) |
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B.1.2 Limit Cycle Analysis Using Describing Functions |
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328 | (1) |
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B.1.3 Stability Analysis of the Limit Cycle |
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329 | (2) |
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331 | (6) |
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331 | (6) |
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C.1.1 Linear Time-Invariant Systems |
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331 | (1) |
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C.1.2 Controllability and Observability |
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332 | (1) |
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333 | (1) |
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C.1.4 State Feedback Control |
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334 | (1) |
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C.1.5 Static Output Feedback Control |
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335 | (2) |
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337 | (6) |
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338 | (1) |
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338 | (5) |
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D.2.1 Quadratic Stability |
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339 | (4) |
Bibliography |
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343 | (10) |
Index |
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353 | |