Output Transition Problem Research Articles

A B-spline-based pseudo-inversion approach for constrained optimal output transition

ABSTRACTThe contribution of this paper is to propose a new method for the continuous-time optimal output transition problem under constraints on the control effort. The new method situates in the recently proposed framework of pseudo-inversion, which proved to be very effective to achieve an almost perfect tracking. The presented method assumes a B-spline function as the external input reference r(t) forcing a given stable closed-loop system. The actual control input u(t) yielded by r(t) and forcing the plant is optimally approximated (in the least square sense) by a B-spline . The control points of the B-spline are chosen in such a way to satisfy the saturation constraints on u(t). The parameters of interest to define the solution of the considered problem are given by the control points of the B-splines r(t) and . These parameters are simultaneously estimated as elements of the vector solving the constrained least-squares minimisation of a suitably defined multi-objective cost functional. If is a sufficiently accurate approximation of u(t), the exact fulfilment of saturation constraints by is transferred to u(t). The simulations on a practical case of a relevant interest show excellent results.

Time-Optimal Output Transition for Minimum-Phase Systems

The time-optimal output transition control problem for stable or marginally stable systems with minimum-phase zeros is discussed in this paper. A double integrator system with a real left-half plane zero is used to illustrate the development of the time-optimal output transition controller. It is shown that an exponentially decaying postactuation control profile is necessary to maintain the output at the desired final location. It is shown that the resulting solution to the output transition time-optimal control profile can be generated by a time-delay filter whose zeros and poles cancels the poles and zeros of the system to be controlled. The design of the time-optimal output transition problem is generalized and illustrated on the benchmark floating oscillator problem.

Time-Optimal Control With Pre/Post Actuation for Dual-Stage Systems

This paper considers the output transition problem, to change the output position, from an initial value to a final value, for dual-stage positioning systems. The main contribution of this paper is to show that the use of pre- and post-actuation input (applied outside the transition interval without changing the output) can reduce the transition time beyond the standard bang-bang-type inputs from the optimal state-transition approach. Moreover, the paper shows that, without pre- and post-actuation, the minimum transition time cannot be lower than the rigid-body, transition time with only the main actuator if the second actuator cannot apply external forces. An example, motivated by the disk-drive application, is used to illustrate the advantages of using: 1) pre- and post-actuation and 2) the second actuator in dual-stage positioning system.

Nonlinear minimum-time control with pre- and post-actuation

This article studies the time-optimal output transition problem to change the system output, from an initial value y ( t ) = y ¯ (for all time t ≤ 0 ) to a final value y ( t ) = y ¯ (for all time t ≥ T ), for invertible nonlinear systems. The main contribution of the article is to show that the use of pre- and post-actuation input outside the transition interval I T = [ 0 , T ] can reduce the transition time T beyond the standard bang–bang-type inputs for optimal state transition. The advantage of using pre- and post-actuation is demonstrated with an illustrative nonlinear example.

Time-Optimal, Dual-Stage, Output Transition: with Pre / Post Actuation

AbstractThis article considers the output transition problem, to change the output position, from an initial value to a final value, for dual-stage positioning systems. The main contribution of the article is to show that the use of pre- and post-actuation input (applied outside the transition interval without changing the output) can reduce the transition time beyond the standard bang-bang-type inputs from the optimal state-transition approach. An example, motivated by disk-drives application, is used to illustrate the advantages of using (a) pre- and post-actuation and (b) the second actuator in dual-stage positioning system.

Optimal Output Transitions for Dual-Stage Systems

This paper solves the minimum-energy output-transition problem for dual-stage systems, such as dual-stage disk-drives, where the second actuator can be used to increase the bandwidth and precision of conventional single-actuator systems. The objective is to find optimal inputs that change the system output from an initial value to a final value during a specified output-transition time interval. The paper shows that, for dual-stage systems, inputs applied outside the output-transition time interval (i.e., pre- and postactuation) can substantially reduce the required input energy. For an experimental dual-stage system, results are presented to show that the input energy can be reduced by 65% with the use of pre- and postactuation inputs when compared to standard methods that do not use such pre- and postactuation.

Design of Feedforward Input for Output-Settling Control With Dual-Stage Actuators

The settling problem is an output transition problem, i.e., given an initial state x(0), the goal is to bring the output to a desired value y(t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> ) = y macr and hold it constant after the end of settling, t > t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> . This article develops the direct solution to the optimal-output-transition (OOT) problem for settling, and develops a method to use postactuation inputs to optimize the settling cost. The approach is illustrated with simulations on an example dual-stage system model. Simulations are also used to illustrate the reduction in the computational burden for online implementation by using linear combinations of precomputed inputs.

Minimum-Energy Output Transitions for Linear Discrete-Time Systems: Flexible Structure Applications

This paper finds minimum-energy inputs to change the position of an output point, on a flexible structure, from one value to another. Current methods transform the output-transition problem into a state-to-state transition problem by constraining the initial and final states of the output transition, for example, to be rest (rigid-body) configurations of the flexible structure. However, the choice of the initial and final states can be ad hoc, and the resulting output-transition cost (input energy) might not be minimum. The contribution of this paper is the direct solution of the optimal output-transition problem; the problem is posed and solved for general linear discrete-time systems. The novelty of the proposed approach is that inputs are not applied just during the output-transition time interval; rather, inputs are also applied outside the output-transition time interval, that is, before the beginning of and after the end of the output-transition time interval. (These inputs are called pre- and postactuation.) The implications of using pre- and postactuation are illustrated by using an example of discrete-time flexible structure model, which consists of a flexible rod connecting two masses. Simulation results are presented, which show substantial reduction of output-transition costs with the use of the proposed method when compared to the use of the standard state-to-state transition approach.

Optimal output-transitions for linear systems

This article addresses the optimal (minimum-input-energy) output-transition problem for linear systems. The goal is to transfer the output from an initial value y(t)= y ̄ (for all time t⩽ t i) to a final output value y(t)= y ̄ (for all time t⩾ t f). Previous methods solve this output-transition problem by transforming it into a state-transition problem; the initial and final states ( x( t i), x( t f), respectively) are chosen and a minimum-energy state-to-state transition problem is solved. However, the choice of the initial and final states can be ad hoc and the resulting output-transition cost (input energy) may not be minimal. The contribution of this article is the solution of the optimal output-transition problem. An example system with elastic dynamics is studied to illustrate the proposed method. Simulation results are presented that show substantial reduction of transition costs with the use of the proposed method when compared to the use of minimum-energy state-to-state transitions.