Inteligent Control Of A Class Of Nonholonomic Underactuated Mechanical Systems

The control of nonholonomic underactuated systems is an important field in nonlinear control. This thesis uses the example of an acrobot to illustrate the intelligent control of such systems. The acrobat is a two-link manipulator operating in a vertical plane. It consists of one joint each at the shoulder and elbow with a single actuator at the elbow. The control objective is to swing it up from a stable downward equilibrium position to the unstable straight-up equilibrium position and balance it there. To solve problems with controlling the acrobot, this thesis proposes intelligent integrated control methods based on fuzzy control, variable structure control and LQR control.Chapter 1 explains the purpose and significance of studying an acrobat, and goes on to describe the current state of the art regarding control of an acrobat and exiting problems in this area.Chapter 2 describes a dynamic model of the acrobat is established based on homogeneous transformation. First, the concept of homogeneous transformation is explained, including the coordinate translation and rotation. Next, a dynamic equation is derived from the Lagrangian equation for the energy of the acrobat. The method requires only to compute the kinetic and the potential energies. It is simple, and describes the characteristics of the acrobat very well.In chapter 3, the motion space is divided into a swing-up area and a balance area from the inherence and the motion characteristics of the acrobat. Then, an intelligent integrated control strategy combining fuzzy control and LQR control is proposed. In the swing-up area, the control law for the torque derived from the energy of the acrobat guarantees that the energy of the acrobat increases with each swing. The fuzzy controller is designed to reduce the amplitude of the control torque as the energy increases, which makes the transition from the swing-up area to the balance area smooth. In the balance area, an LQR controller is designed using a linear approximate model of the unstable equilibrium position to accomplish balance control. The validity of the intelligent integrated control strategy is demonstrated by simulation results.Chapter 4 presents a balance control method that employs a Takagi-Sugeno (TS) fuzzy model to enlarge the region for the balance control. First, a TS fuzzy model is constructed to approximate the nonlinear characteristics through linearization of the local area according to the dynamics of the acrobat. This model describes nonlinear characteristics of the acrobat with a satisfactoryapproximated precision over a large region. A set of local controllers are designed by means of pole assignment. The frizzy controller is obtained by the fuzzy blending of the local controllers. The stability of balance control is analyzed by the method of linear matrix inequalities. Finally, an intelligent integrated control strategy based on fuzzy control is proposed. The fuzzy control desinged in section 3 is used in the swing-up area, and the fuzzy control based on the TS model is used in the balance area. The validity of the control strategy is demonstrated by simulation results.Furthermore, chapter 5 proposes an intelligent integrated control strategy based on fuzzy control and variable structure control. Fuzzy control based on energy is used to swing the acrobat up. Fuzzy variable structure control is used to make the transition from the swing-up area to the balance area quick. Fuzzy control based on the TS model is employed to balance the acrobat. The fuzzy variable structure controller consists of a variable structure controller and two fuzzy controllers. The variable structure controller makes the two links of the acrobat extend naturally and easily enter the balance area when the potential energy of the acrobot reaches the amount appropriate for the unstable equilibrium position. During this process, the fuzzy controllers regulate the parameter to keep the energy unchanged. The control strategy solves the problem of quickness of the transition from the swing-up...