Optimal Reference Shaping for Dynamical Systems: Theory and by Tarunraj Singh

By Tarunraj Singh

Integrating feedforward regulate with suggestions regulate can considerably enhance the functionality of regulate structures in comparison to utilizing suggestions keep an eye on on my own. targeting feedforward keep watch over suggestions, optimum Reference Shaping for Dynamical structures: conception and functions lucidly covers a number of the algorithms for attenuating residual oscillations which are considering reference inputs to dynamical platforms. The reference shaping options awarded within the publication require the approach to be solid or marginally solid, together with structures the place suggestions regulate has been used to stabilize the method. Illustrates suggestions via Benchmark difficulties After constructing versions for functions within which the dynamics are ruled through calmly damped poles, the ebook describes the time-delay clear out (input shaper) layout approach and studies the calculus of diversifications. It then makes a speciality of 4 keep an eye on difficulties: time-optimal, fuel/time-optimal, gasoline constrained time-optimal, and jerk constrained time-optimal keep an eye on. the writer explains how the minimax optimization challenge will help within the layout of strong time-delay filters and explores the input-constrained layout of open-loop keep watch over profiles that account for friction within the layout of point-to-point regulate profiles. the ultimate bankruptcy provides numerical thoughts for fixing the matter of designing formed inputs. delivering MATLAB® code and a set of real-world difficulties, this e-book offers a rigorous but obtainable presentation of the speculation and numerical recommendations used to form keep watch over process inputs for attaining particular keep watch over while modeling uncertainties exist. It comprises up to date strategies for the layout of command-shaped profiles for targeted, strong, and speedy point-to-point regulate of underdamped structures.

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Panda and Y. Lu. Tutorial on control systems design in tape drives. In ACC, Denver, CO, 2003. [9] P. D. Mathur and W. C. Messner. Controller development for a prototype high-speed low-tension tape transport. IEEE Trans. on Cont. , 6(4):534–542, July 1998. [10] Y. Lu. Advanced control for tape transport. Dissertation, CMU, 2002. [11] H. Mizuguchi, T. Nakagawa, and Y. Fujita. Breaking the 1000 mpm barrier. Elevator World, pages 71–76, September 2005. [12] J. W. Fortune. Mega high-rise elevators. Elevator World, 43(7):63, December 1995.

2 Damped Systems Unlike the jerk limited time-delay filters for undamped systems, the jerk limited time-delay filter for damped systems cannot be solved in closed form. The problem can be solved numerically by posing the design as an optimization problem. 107) To cancel the damped poles of the system at s = σ ¦ jω , we require a pair of zeros of the time-delay filter to be collocated with the plant’s damped poles. 109). 5 Robust Jerk Limited Time-Delay Filter Most systems have errors in estimated damping and natural frequencies which can result in significant residual errors when a rest-to-rest maneuver is performed.

8). 45) where J corresponds to the inertia of the motor. 46) where r is the reference input, is guaranteed to be stable provided the gains K1 and K2 are greater than zero. 48) If 4JK1 K22 , the resulting closed-loop poles result in an underdamped system response. The natural frequency and damping ratios of the closed-loop response are ωn ÖK 1 J ζ Ô K2 2 JK1 which are used to determine the transfer function of the time-delay filters. 9 illustrates the evolution of the angular displacement and the angular velocities of the system where it is assumed that the inertia of the system is exactly known.

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