Time-optimal Transition Research Articles

Time-Optimal Transition Method for Six-Step Operation of PMSM via Geometric Prediction of Flux Trajectory

Time-Optimal Transition Method for Six-Step Operation of PMSM via Geometric Prediction of Flux Trajectory

Time-optimal control of piecewise affine bistable gene-regulatory networks: preliminary results

In this preliminary work we give a geometric characterization of the time-optimal trajectories for a piecewise affine bistable switch. Such hybrid models play a major role in systems biology, as they can expressively account for the behaviors of simple gene-regulatory networks. A key example of these biological circuits is the genetic toggle switch, for which the optimality of a state switch has not been studied to the present day. The main tool of this work is an adaptation of the Hybrid Pontryagin's Maximum Principle to our setting, which allows to prove that the optimal control strategy is indeed a simple bang-bang feedback control law. In opposition to previous works, we show that a time-optimal transition between states should pass by an undifferentiated state, well known in cell biology for playing a major role in fate differentiation of cells. We conclude by showing numerical simulations of optimal trajectories illustrating the structure of the bang-bang optimal control for different scenarios.

(B.6)Corner trajectory smoothing with asymmetrical transition profile for CNC machine tools

The linear toolpaths, so-called G01 blocks, are widely used in CNC machining. Since this non-smooth path only achieves position continuity at the corner junction, it is prone to cause speed fluctuations and excite structural vibrations, which is not conducive to high-speed and high-accuracy machining. To solve the problem, typical corner smoothing methods generate a symmetrical cornering transition profile around the angle bisector, while respecting the given error tolerance. In this paper, a one-step corner smoothing approach with asymmetrical transition profile and limited jerk was proposed. The proposed approach can attain high reproducibility to guarantee good surface finish in back-and-forth parallel raster toolpaths, and is different from two-step corner path smoothing approaches which geometrically replace the sharp corner with a pre-specified curve. The near time-optimal transition parameters are obtained in one step, subject to the geometric error tolerance and kinematic limits. Since the proposed approach does not require a symmetrical cornering profile, the performance of the drives can be utilized more fully to obtain better cycle time than other approaches. Experimental results demonstrate the effectiveness of the proposed method on cycle time and contour accuracy.

Robust incoherent control of qubit systems via switching and optimisation

A robust incoherent quantum control scheme via projective measurements plus unitary transformations is proposed for driving a qubit system from an unknown initial mixed state to an arbitrary target pure state. This scheme consists of two main steps: projective measurement on the initial mixed state and optimal control between two pure states. The first step projects the initial state into an eigenstate of the qubit system by projective measurement and guarantees that the proposed scheme is robust to different initial mixed states. The second step finds a set of suitable optimal controls to drive the qubit system from the conditional eigenstate to the target pure state. The connection between the two steps is accomplished by a switching strategy. To accomplish the second step, two approaches are presented in detail. These approaches are time-optimal transition with unbounded control and bang-bang control with minimal switches. The minimal time and minimal number of switches in these approaches can be calculated by simple analytical expressions. The proposed approaches provide two relatively straightforward optimal design methods.

Alternator Field Control of an HVDC Link

The paper describes the design and simulation of a computer control scheme for a high voltage DC link supplied from an isolated alternator. For economy an uncontrolled rectifier is employed and control of line current achieved through adjustment of alternator excitation. For large disturbances in line current or large scheduled changes time optimal control is used to obtain a rapid response. The field voltage is switched between two levels depending on the state of the system in relation to a switching curve stored in a control computer. For small disturbances or under steady state conditions, time optimal control causes unacceptable fluctuations in line current and needless switching of the alternator field. Thus at the completion of a time-optimal transition control is switched to a linear digital algorithm. The design is implemented on an electromechanical HVDC simulator controlled by an online minicomputer.

A near-time-optimal control approach for third- and fourth-order relay control systems

A predictive strategy is proposed which gives near-time-optimal control for third and fourth-order relay control systems. By direct application of the strategy, equivalent near-time-optimal feedback control laws are derived for third and fourth-order pure integrator plants. For the triple-integrator plant, the equivalent feedback control law of the predictive strategy is shown to be remarkably similar to the known time-optimal control law and, with the exception of a certain set of initial states, gives time-optimal transition to the state origin. For the fourth-order pure integrator plant, it is established that the equivalent feedback control law of the predictive strategy yields near-optimal settling times, typically within 26% of the corresponding minimum values. Furthermore, it is demonstrated that the strategy (or its equivalent feedback control law) also gives near-time-optimal control when applied, by a state variable transformation method, to more general fourth-order plants having real non-posit...

Proof of the time-optimality of a predictive control strategy for systems of higher order

For a plant of higher order with a control subject to a saturation constraint, Gulko has given a predictive control strategy which involves the use of nested models operating on fast time scales. In the present paper it is proved that the strategy gives time-optimal transition to the state origin.