Search MathWorks. Open Mobile Search. Off-Canvas Navigation Menu Toggle. Main Content. Robust Control Toolbox Design robust controllers for uncertain plants. Select a Web Site Choose a web site to get translated content where available and see local events and offers. Variables appearing in the in the case of sliding. Violation of the pure rolling constraints can kinematic model are denoted as follows: see Fig.
Steering Angle Bias db Fig. Iz is the inertia moment around z-axis. Notations of sliding effects. Furthermore the dynamic equation describing the relationship between the sideslip angle b and the yaw rate g is considered 3. Sliding angle reconstruction Hiraoka et al. The following equation holds by considering 28 4. Theorem 1. If turbances and the reconstruction errors must be designed. Substituting the reconstructed tire sliding angles Theorem 2.
Please refer to Fang et al. From 60 a2 can be expressed as! The closed- Meanwhile the closed-loop errors can be reduced by increasing loop stability can be achieved via averaging techniques. Besides, the sliding mode fuzzy the proposed algorithms implemented in Matlab. In the simulations, the sideslip angle may be obtained correspondingly. Estimation of kf, kr at speed of 8. Simulation results of robust anti-sliding control 2 In this section, some simulation results of the robust anti-sliding 1.
A reference path consisting of straight lines and curves is followed by the vehicles see Fig. Both the time- 1 varying sine-like lateral disturbances and the side slip angles are introduced into the system. The Normal Lab Values of the side slip 0. To compare with previous works, the control laws of Lenain et al. The result is shown by Fig. Although the anti-sliding controller of Lenain et al. It has good transient responses and is robust against not only the sliding effects but also the time-varying disturbance solid line.
X coordiante m The rotating velocity of the rear wheel was measured by optical Fig. Path to be followed. The actual steering angle of the front wheel was measured by means of absolute encoders and compared with its desired value. Estimation of sideslip angle. The vehicle was maneuvered by a 0. Since the adherence properties of certain kinds of ground do not vary 0. Simulation results of lateral deviation. Also a small amount of recon- struction errors are detected in Fig.
As explained in Section 3. The simulation results of the lateral deviation are shown by Fig. As the control law of Thuilot et al. When the sliding effects Fig. RTV Utility Vehicle. In both cases, sliding occurs inevitably, but the sideslip Fig. Estimation of sideslip angle on dry roads. Mean- while the slip angle on the dry road changes more violently but x with small magnitude. This is due to the fact that the large 4 cornering stiffness kr, kf can provide large tire forces which can correct the tire-sliding more powerfully.
The framework of this two-stage scheme is quite applicable in practice when the tire-ground 1 adhesion property is evenly distributed approximately and leads Histories for estimating to stable and effective behaviors of the whole auto-steering control system. History for using estimated cornering stiffness. Estimation of cornering stiffness.
In real-world applications a reference path consisting of Fig. Estimation of sideslip angle on slippery ground. The lateral deviation is 15 shown by dashed line in Fig. But when 5 the vehicle starts to follow the curves, due to low-grip conditions of the slippery grounds, the tire adherence cannot provide enough 0 lateral forces for the vehicle to track the curve, the tire sliding angles obviously increase Fig.
Sliding Occurs In Fig. But when the vehicle begins to follow the curve, Fig. Orientation error of experimental results. And it is also observed that the slip angle of the front wheel is larger than errors cannot be totally eliminated. This is performance of the vehicle in actual experiments.
The results proposed robust anti-sliding controller, not only the sliding of the anti-sliding controller of Lenain et al. When kinematic observer are also shown in Fig. It is quite interesting to see the different performances of tire-sliding angles and make the vehicle motion robust against those two kinds of the controllers. The robust controller can the inaccuracy of the sliding angle reconstruction and the lateral provide satisfactory lateral accuracy at the expense of high-gain disturbances Solid line in Fig.
The orientation errors are and un-smooth control. Consequently, it can yield small mean displayed in Fig. This second edition of Mathematical Methods in the Robust Control of Linear Stochastic Systems includes a large number of recent results in the control of linear stochastic systems. Self-contained introduction to control theory that emphasizes on the most modern designs for high performance and robustness. It assumes no previous coursework and offers three chapters of key topics summarizing classical control.
To provide readers with a deeper understanding of robust control theory than would be otherwise possible, the text incorporates mathematical derivations and proofs.
The last thirty years have witnessed an enormous effort in the field of robust control of dynamical systems. The main objective of this book is that of presenting, in a unified framework, the main results appeared in the literature on this topic, with particular reference to the robust stability problem for linear systems subject to time-varying uncertainties.
The book mainly focuses on those problems for which a definitive solution has been found; indeed most of the results we shall present.
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