Proximate Time-optimal Control Research Articles

Stability Analysis of a Proximate Time Optimal Controlled Electrostatic Suspension System Using Piezo Actuator via Lyapunov Functional Approach

An electrostatic suspension of silicon wafer using proximate time optimal control has been successfully developed. In this system, the movable electrodes which are supplied by constant voltage and actuated by the piezoelectric (PZT) actuator are used instead of stationary electrodes like previous systems. The changing of the gap length between movable electrodes and the suspended object will create varying capacitances that can control the electrostatic forces. To overcome the problem of actuator saturation of the piezo actuator, a proximate time optimal control is used to stabilize the system. The system stability is theoretically investigated using Lyapunov’s function. The constant voltage supplying to the electrode is an important parameter, and it is also determined. The paper presents series of the simulation and experimental results that prove completely suspension of 4-inch silicon wafer without any mechanical contact.

Approximate Time-Optimal Control Considering System Bandwidth and Saturation

Time-optimal (TO) control is promising in many fields since it ensures to accomplish a task in minimum time. However, its direct application may cause oscillations or even limit cycles due to the restriction of the sampling period, state measurement accuracy and so on. To solve these problems, a compound proximate time-optimal (PTO) control law is proposed by considering system bandwidth and saturation in this paper. With the help of the phase plane, the switching zone and linear zone of the PTO control law are constructed. When the system state lies outside of both switching and linear zones, the bang-bang optimal scheme is adopted to achieve rapidity. And when the system state enters the switching zone, the bang-bang suboptimal scheme is developed to avoid oscillations or even limit cycles. Proportional-derivative (PD) scheme is applied in the linear zone to obtain local asymptotic stability around the origin. Numerical simulations are carried out to corroborate the advantages of the PTO control law.

Proximate time optimal for the heading control of underactuated autonomous underwater vehicle with input nonlinearities

In this paper, a modified proximate time-optimal control (PTOC) is proposed based on reduced order extended state observer (RESO) and controller scaling method, for the heading control of underactuated autonomous underwater vehicles (AUV) with input nonlinearities. First, a simple and practical modified ADRC is proposed for heading control with input nonlinearities. The non-symmetric dead-zone with unknown parameters is modeled as a combination of linear input and bounded disturbances, and the RESO is designed to estimate and compensate it. The influence of actuator saturation constraint is reduced by limiting the control signal before it goes into the RESO. Then, a parameter self-tuning strategy is proposed for the feedback controller with the changed control gain by the controller scaling method. The control gain is quadratic respect to the velocity of AUV, the active disturbance rejection control (ADRC) controller parameters can be adjusted based on the AUV velocity using the strategy. And finally, the modified PTOC, based on RESO and with an updating strategy for the limit of linear region, is proposed to improve the control performance. Several simulation experiments are carried out, the effectiveness of self-tuning modified ADRC is verified, and the proposed modified PTOC shows better performance.

Soft-Switching Proximate Time Optimal Heading Control for Underactuated Autonomous Underwater Vehicle

In this paper, a soft-switching proximate time-optimal control (PTOC) is proposed based on the model-compensation extended state observer (ESO) and Takagi-Sugeno fuzzy switching, for the fast set-heading tracking of underactuated autonomous underwater vehicle (AUV). First, based on Pontryagin's maximum principle, a time-optimal control (TOC) law is derived for the first-order Nomoto model of the underactuated AUV. Then, a model-compensation active disturbance rejection control (ADRC) is developed; the outstanding characteristic is that the nonlinear heading dynamic model is compensated to a first-order Nomoto model rather than by a double integral system through implementing a model-compensation ESO (MC-ESO). The regular ESO is replaced with a reduced-order ESO (RESO) to reduce complexity, and the model-compensation RESO (MC-RESO) is designed by adding the known partial model to RESO. Based on the controller scaling method, a parameter self-tuning strategy is proposed for model-compensation ADRC (MC-ADRC) with changed plant parameters at different velocities. Finally, the soft-switching PTOC is developed for heading control, and the MC-RESO is adopted to estimate the unmeasured velocity and unknown total disturbances for feedback and compensation. The TOC with an unsaturated region (RTOC) is employed to enhance the robustness by using a switching region to replace the switching curve, and a soft-switching strategy between ADRC (near the origin) and RTOC (far from origin) is designed based on the Takagi-Sugeno fuzzy mode. Several simulations are carried out, the effectiveness of self-tuning MC-ADRC is verified, and the proposed soft-switching PTOC shows better performance compared with MC-ADRC.

Proximate Time-Optimal Control of a Harmonic Oscillator

This paper considers near-time-optimal setpoint tracking of a second-order oscillator. First, the time-optimal setpoint tracking feedback law is derived by recasting the problem as a regulator problem in the error coordinates with shifted control limits. This result is used to construct a derated approximation of the optimal control. Initially, the control law is derived as a regulator controller. This result is then extended to include setpoint tracking. Global stability is proven for the setpoint tracking controller in the zero-damping case. A scaling method is developed, which allows an efficient implementation of the control laws using a single lookup table. Both the damped and undamped controllers are validated experimentally.

Parameterised design of robust point‐to‐point fast motion controller

A dual-parameter design of expanded proximate time-optimal controller is proposed for fast point-to-point motion in typical electromechanical servo systems with a damping element. The controller initially resorts to a saturated control signal for the fastest acceleration or braking if possible and then seamlessly gives way to a linear control strategy once the motion slows down. The damping ratio and natural frequency of the linear control law are chosen as the design parameters to allow for a better tuning of the control performance. An extended-state observer is also included for simultaneous estimation of system speed and disturbance. Experimental verification is conducted on a DC motor position servo system using a TMS320F28335 board, and the effectiveness of the proposed design is demonstrated.

A novel trajectory prediction control for proximate time-optimal digital control DC—DC converters

The purpose of this paper is to present a novel trajectory prediction method for proximate time-optimal digital control DC—DC converters. The control method provides pre-estimations of the duty ratio in the next several switching cycles, so as to compensate the computational time delay of the control loop and increase the control loop bandwidth, thereby improving the response speed. The experiment results show that the fastest transient response time of the digital DC—DC with the proposed prediction is about 8 μs when the load current changes from 0.6 to 0.1 A.

Two-dimensional proximate time-optimal servomechanism

This paper focuses on the development of a proximate time optimal control method for two-dimensional rigid body systems, eg. XY positioning tables. Our approach is based on the traditional proximate time-optimal servomechanism (PTOS), which starts with a near-time-optimal non-linear controller and then switches to a linear controller as the system output approaches the desired target. This work proposes to expand the PTOS, a unidirectional control law to twodimensional systems, in order to perform linear point to point trajectories in minimum time.

Two-Dimensional Proximate Time-Optimal Servomechanism

This paper focuses on the development of a proximate time optimal control method for two-dimensional rigid body systems, eg. XY positioning tables. Our approach is based on the traditional proximate time-optimal servomechanism (PTOS), which starts with a near-time-optimal non-linear controller and then switches to a linear controller as the system output approaches the desired target. This work proposes to expand the PTOS, a unidirectional control law to two-dimensional systems, in order to perform linear point to point trajectories in minimum time.

Analysis of sliding mode proximate time-optimal disk drive servo control

An analysis of a sliding mode proximate time-optimal servomechanism (SPTOS) conducted through simulations and experiments is presented. The sliding mode is utilized to deliver proximate time-optimal performance naturally. We also examine why the SPTOS scheme is superior to the proximate time-optimal servomechanism that is widely used in the disk drive industry. The SPTOS is shown to produce bounded motion along the reference profile, which contributes to accurate reference profile tracking even in the presence of plant uncertainties. The application of the SPTOS yielded accurate reference velocity profile tracking as well as uniformly excellent seek performance regardless of the seek length.

Improved proximate time-optimal sliding-mode control of hard disk drives

An improved proximate time-optimal (PTO) positioning control approach with discrete-time sliding-mode control theory for a Hard Disk Drive (HDD) servo is presented. A third order velocity reference profile is introduced to improve the second order ones in the conventional proximate time-optimal servomechanism (PTOS). The proposed approach eliminates the mode-switching mechanism and dramatically reduces the seek time by 5–50%. Moreover, it is robust to unmodelled dynamics and parameter variations. Its effectiveness is verified in a simulation.

Discrete-time sliding mode proximate time optimal seek control of hard disk drives

The paper presents a new proximate time optimal seek control approach with discrete-time variable structure control theory for a hard disk drive (HDD) servo. It incorporates the time optimal control idea into the time-varying sliding mode control design and derives a class of proximate time optimal control algorithms with robustness. The proposed approach provides one unified framework for both track seeking and track following controller design, it achieves smooth transition from seek control to track-following control naturally, and it eliminates the common chattering and overshoot problem as well. A systematic method is developed for the choice of controller parameters. Simulation results are demonstrated to show the robustness of the proposed method to disturbances, unmodelled dynamics and parameter variations with near time optimal performance.

Robust time optimal controller design for hard disk drives

Robust time optimal control algorithm based on internal loop compensator is proposed. Internal loop compensator effectively isolates the hard disk system from the uncertain disturbances including modeling error, external disturbance, shock, and control torque saturation. We use the H/spl infin/ mixed sensitivity method for the optimization of internal loop compensator and proximate time optimal controller as a feedback controller to provide a time optimal property. The performance of the proposed controller is verified via simulation.

Robust Compensation for Dynamic Friction in Positioning Control of Hard Disk Drives

Friction in actuators of hard disk drives lowers the system gain in low frequency range, which prevents the system positioning accuracy from further improvement. The complexity and multiform of friction make it difficult to obtain a complete friction model. A nonmodel-based robust friction compensation method is introduced, in which the gain decrease in the low frequency domain is compensated by the infinite gain in a bang-bang compensator. The introduced method is simply integrated into the proximate time-optimal servomechanism controller widely used in the current hard disk drives. Simulation results based on a commercial FUJITSU hard disk are presented

Continuous Proximate Time-Optimal Control of an Aerodynamically Unstable Rocket

Continuous Proximate Time-Optimal Control of an Aerodynamically Unstable Rocket

Improved discrete proximate time optimal controller of a disk drive actuator

An important relationship between the acceleration discount factor and the closed loop control poles in a discrete Proximate Time Optimal Servo (PTOS) design has been established. This result enables the PTOS seek and tracking controllers to be designed and optimized independently without being constrained by boundary conditions. During subsequent merging, smooth transition from seek to tracking is obtained by linear, time shrinking of the boundary layer closer to the target track. The proposed controller is applied to R/W head actuation in a hard disk. Significant improvement in head settling is observed compared to conventional PTOS, specifically for longer seeks.

Proximate time-optimal control of third-order servomechanisms

The problem of proximate time-optimal control of third-order systems is considered. Two proximate time-optimal servomechanisms, PTO53 and PTO53 tau , are proposed for type-3 and type-2 third-order plants, respectively. Theorems stating sufficient conditions on each system's control design parameters to ensure global stability are given, and it is shown that the control parameters can be adjusted to accommodate, more or less, disturbances and unmodeled dynamics in the system. The approach used to develop the controllers is that of constructing a 'slab' in three-dimensional state space that describe the 'switching' structure of the control. The technique relies on three-dimensional phase-space analysis, which is rarely applied to systems of order three or higher. Simulation and experimental results demonstrate the performance of the algorithms developed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>