Research On Extended Cascading Modeling And The Constraint-following Control Of Multi-body Systems

By generating appropriate constraint force, servo controls render system to follow design constraints. It is one of the few frontiers in multi-body systems control. In the past, the constraint is followed by Nature that the structure of the system and environment can automatically generate the required constraint force. In contrast to the passive manner, servo constraint control takes a different perspective to follow the constraint by using servo controls. There still exist several difficult problems in constraint-following control of multi-body systems, such as the modeling approach, the description of uncertainty, the control of nonlinear system with uncertainty. For the issues above, we need to explore a new efficient modeling method to get the explicit model, introduce a new exact and realistic description method for uncertainty, and seek for a general nonlinear control method and its optimal design for the constraint-following control. The main contents and contributions are as follows:(1) Based on the Udwaid-Kalaba theory, a new approach for the dynamic modeling of multi-body systems is established as an extend method of cascading and clustering method, which can resolve the singular mass matrix problem and decouple the model of given force that depends on the constraint force; the explicit model constructed by the new approach is applicable for the constraint-following control; by using the Udwaid-Kalaba theory, the paper justifies the Rosenberg’s embedding method and provides a valid way to embed the nonholonmic constraints in the modeling procedure.(2) Based on the explicit model of multi-body system, an adaptive robust servo constraint-following control for the uncertain multi-body system is constructed; the control can simulate the Nature and provide the appropriate constraint force which is the smallest one that can render the system to follow the constraint; for ideal and nonideal design constraint, two adaptive robust control designs are proposed to guarantee the system performace under uncertainty; the control design contains nonideal constraint force model to compensate the friction force of system; the system uncertainty is time-varying and bounded, the bound information of it can be estimated by an adaptive parameter; the estimated bound information could be utilized to design the robust control gain; the leakage term of control may reduce the adaptive parameter when the following error goes down, which can manage the robust gain; the dead zone design would simplify the adaptive law and improve the speed of the control.(3) From the constraint-following perspective, a trajectory tracking control is turned into a constraint-following control; a new constraint equation for the trajectory-tracking problem is formulated; by transforming the constraint equation into a second order form, the constraint-following control is designed; compared with current trajectory-tracking control methods, the new method is simple for control design and suitable for online control.(4) By using the fuzzy description of system uncertainty, the paper proposed a constraint-following control and an optimal design for multi-body systems; the control of system is deterministic and can guarantee the performance of the system, which is unlike the traditional fuzzy control methods based on the IF-THEN rules; the paper designed a quadratic performance index for multi-body systems which is the function of D-operation; for the proposed fuzzy system performance index, the paper transforms the optimal control design into a constrained optimization problem; it is proven that the global solution to this problem always exists and is unique; the closed form solution and minimum performance index are derived.(5) Taking the excavator robot as the application object, the explicit dynamic model of the robot is established by using the extended modeling method; the friction force of the load is decoupled with constraint force; the decoupled model is precise and prone to be used in control design; based on the established dynamic model, adaptive robust constraint-following controls of robot are proposed for different constraints; the simulation of the control system justifies the modeling method and the control design.