| Model-based control design is an important approach in developing control theory, such that the ana-lytic (i.e., closed-form) dynamical model serves as the foundation of the control design, meanwhile, the inverse dynamics analysis can help the engineer to understand the kinetic characteristics more clearly.However,the current dynamics modeling approaches, in obtaining the model of a mechanical system, is either difficult to manipulate, too complex in calculation, or can not obtain the dynamics model analyti-cally,thus can not serve control design well, and the uncertainty of the system model necessarily affects the inverse dynamics analysis. Therefore, finding a concise and easily manipulated approach to obtain the analytic equation of motion as well as perform the inverse dynamics analysis becomes an important basisfor motion control of mechanical system. In addition, handling the disturbance of uncertainty, is another important problem in present developing control theory. There are two types of uncertainty of the deter-ministic ones and the fuzzy ones. Since the handle manners and control logic are different for different types of uncertainty, choosing appropriate approach to describe and handle the uncertainty is the other importation basis for motion control of mechanical system. What more, with the development of control theory, adjusting the relation between the system performance and the uncertainty to obtain an optimal control, which renders optimal disturb of uncertainty, control cost and system performance, has already been a hot topic in motion control of mechanical system.For above problems, in this dissertation, analytic dynamics modeling and inverse analysis of the con-strained mechanical systems is considered firstly, and in turn, for uncertain mechanical systems the prob-lem of motion control is proposed. The proposed controllers can deal with both deterministic and fuzzy uncertainty in the systems.First, some basic concepts and essential theories about analytic dynamics modeling and inverse anal-ysis of constrained systems are organized. The vector-matrix notation shows us how to put the equation motion of a high dimensionality system in vector-matrix form; the generalized inverse of matrix and (non-holonomic and holonomic) constraints are frequently-used concepts in constraint analysis; the Udwadia-Kalaba theory is referred for analytic dynamics modeling of constrained dynamic systems; the Leitmann’s inverse theory introduces us to do inverse analysis on the motion of constrained mechanical systems.Then, with above theory foundation, analytic dynamics modeling and inverse analysis of the Brachis-tochrone system with and without Coulomb friction is proposed. First, by using the Udwadia-Kalaba theory, we subsume the Coulomb friction force as a non-ideal constraint, thereby, the analytic equation of motion for a particle mass moving along the Brachistochrone cycloid curve with Coulomb friction is obtained. Second, while the Brachistochrone cycloid curve is given, we seek the corresponding minimiz-ing object with and without friction. Third, we return to the search for a curve subject to a minimization principle, with the total travel time as the minimizing object, which was addressed in the classical Brachis-tochrone problem. All three analysis come to meet at the special case when there is no friction.For the motion control of uncertain mechanical systems, we first consider the deterministic uncertainty control problem. This control problem is formulated as to drive the control system to follow certain prescribed constraints, that is approximate constraint following. A high-order adaptive robust control is proposed under the assumption that the system uncertainty is (possibly) time-varying and bounded, but the bound is unknown. An adaptive law is designed. The control guarantees uniform boundedness and uniform ultimate boundedness even in the presence of the uncertainty. Furthermore, the system performance,including the finite entering time, constraint-following error, and control magnitude, can be improved by changing the control order.Furthermore, in the deterministic uncertainty control problem, we take the design uncertainty into consideration. For the motion control of uncertain mechanical systems, an unprecedented control scheme,namely adaptive-adaptive robust control is proposed. The system uncertainty is bounded while the bound may be unknown. Two classes of robust controls are proposed, with the first class featuring leakage type and the second class featuring dead-zone type. Each class involves an adaptive law mimicking the uncertainty bound. However, there is a design uncertainty related to the choice of a design parameter in the adaptive law. An adaptive law for this design parameter is then constructed; hence rendering the adaptive-adaptive robust control. The control guarantees uniform boundedness and uniform ultimate boundedness of a β-measure of the system performance, regardless of both system uncertainty and design uncertainty.It allows the system, instead of the designer, to determine certain design parameters adaptively.Motion control for fuzzy mechanical systems is also formulated as approximate constraint following.But in this formation, fuzzy theory is applied to handle the uncertainty, which is (possibly) fast time-varying but is bounded,and the bound is unknown,but is assumed to be within a prescribed fuzzy set.A robust control is proposed specially for nonlinear mechanical systems. Both the mechanical system and the control are deterministic, and is not if-then fuzzy rule-based. A fuzzy-based performance index is designed. Then deterministic performance is guaranteed, regardless of the uncertainty. Meanwhile,the minimization of a fuzzy-based performance index is guaranteed by seeking an optimal control design parameter.Besides the theoretical derivation and validation in above works, the simulation results are given out to corroborate the theoretical findings at the ending of each part. |
