Simultaneous Energy-vibration-optimal Trajectory Planning Method For Flexible Servo Motion Systems

Flexible servo motion systems(FSMS)have a wide range of applications in industrial equipments.In such FSMS,the point-to-point(PTP)trajectory planning is one of the main challenges and has attracted much attention.To enhance the equipments’ performance and productivity,lower energy consumption and better motion accuracy are demanded for FSMS.Therefore,it is theoretically and practically meaningful to generate energy-vibration-optimal(EVO)trajectory for both saving energy consumption and suppressing residual vibration.Addressing the PTP trajectory planning problem for FEMS and aiming at achieving simultaneous EVO performance,this dissertation focuses on the researches of the global optimization,the robust performance and the real-time generation for EVO trajectories.To achieve both zero residual vibration and globally energy optimal for FEMS,the dissertation proposes a globally EVO trajectory planning method based on the zero residual energy constraint.Firstly,the EVO trajectory generation is newly modeled while both satisfying the zero residual energy constraint and minimizing the total energy loss.The physical interpretation of such problem statement is that the residual vibration energy is separated form the total energy and is preferentially constrained to zero.Subsequently,by means of convexification and discretization,the trajectory planning is reformulated as a convex quadratic programming problem which can be solved with global convergence.Finally,to improve the solving precision and efficiency of the problem,an improved algorithm combined with a Hamiltion-based method and a precision-control mechanism is developed.Overall,the proposed globally EVO trajectory can both suppress the residual vibration to zero and minimize the total energy consumption.To improve the performance robustness of the EVO trajectory to parametric uncertainties,the dissertation proposes a robust EVO trajectory planning method based on the sensitivity-function-based constraints of the residual energy.Firstly,we prove that the time-domain sensitivity-function-based constraints is equivalent to place double zeros at the pole of FEMS in the frequency domain.In this way,it is possible to consider the robustness of EVO trajectories in the frequency domain besides the classical time-domain formulations.Then,inspired by the robustness enhance method for filters and input shapers,we generalize the double zeros placement to the so called one-hump and multi-hump zero placements,and propose the corresponding time-domain constraints of the residual energy.The proposed robust EVO trajectory not only suppresses the residual vibration and minimize the total energy consumption,but also has significant robustness to parametric model mismatches.To reduce the computation time of the EVO trajectory for industrial practices,the dissertation proposes a real-time EVO trajectory planning method based on trapezoidal velocity profile(T-curve)and S-curve due to their widely use.Firstly,the globally and the robust EVO trajectory planning problems are simplified into two parameter optimization problems in the parameter spaces of T-curve and S-curve,respectively.The resultant parameter optimization problems are both nonlinear integer programming problems(NIPPs).Subsequently,an algorithm to solve the NIPP for T-cuve is proposed using the continuous relaxation method,and an algorithm to solve the NIPP for S-curve is proposed based on the enumeration near the approximate extreme point.These two algorithms both involve analytical calculations and a one-dimensional search,and therefore are computation-efficient.The proposed EVO trajectories based on T/S-curve not only optimize the vibration and energy consumption performance,but also can be generated in real time for industrial practices.Finally,based on a rotary flexible joint plant system,comparative simulations and experiments are carried out to verify the superior performances of the proposed methods.The proposed globally EVO trajectory suppresses 96% residual vibration and saves 25% energy consumption;the proposed robust EVO trajectory suppresses 90% residual vibration with 20% parametric uncertainties while only sacrifices a small amount of energy saving;the proposed EVO trajectory based on T/S-curve sacrifices part of the EVO performance,but only takes about 160 microseconds to be used in real time.