A nonlinear disturbance-decoupled elevation axis controller for the Multiple Mirror Telescope

Sparse aperture telescopes represent a promising technology for increasing the effective diameter of an optical system while reducing the weight and the size. Multiple-mirror telescope (MMT) and multiple-telescope telescope (MTT) are two types of sparse aperture systems. The primary mirror of MMT consists of a number of segments that are all parts of a single primary-mirror conic. The configuration of the sparse aperture is related to the performance of the MMT. Golay configuration is nonredundant sparse aperture. Entrance pupil characteristics of Golay 6 MMT are studied to research the relationships between the sub-mirrors on the primary mirror and the shapes of sub-apertures on the entrance pupil of Golay 6. Overlay factor and efficiency factor are proposed to achieve the optimal fill factor on the entrance pupil. Given the relative aperture of Golay 6 MMT, there is some concern that the fill factor on the entrance pupil is larger than the overlay fill factor on the spherical sparse aperture primary mirror. The maximum fill factor and the maximal overlay factor are discussed, and the tangency condition when sub-mirrors of Golay 6 MMT are tangency is derived. Two Cassegrain telescopes having a spherical primary mirror with Golay6 configuration and with an aspherical secondary mirror are designed. The fill factor on the entrance pupil can be larger than the overlay factor on the primary mirror at the certain occasion. Based on the relationships between the fill factor and the overlay factor, the rational parameters of sub-mirrors on the primary mirror can be selected.

The multiple mirror telescope (MMT), a joint project of the University of Arizona and the Smithsonian Institution, is in many ways a pioneering instrument that helped pave the way for the new class of 8 to 10 meter optical telescopes in use today. Part of the telescope facility upgrade to a 6.5m primary mirror is improved servos for pointing and tracking of sufficient quality to support the latest generation of wide-field and adaptive-optics instruments. This discussion presents the current and future work in servo development at the MMT.

A preliminary optical design is proposed to convert the existing Multiple Mirror Telescope (MT) on Mount Hopkins to the maximum diameter, filled-aperture optical/infrared telescope that can be accommodated by the existing telescope mounting and building without substantial modification. The design utilizes a 256-inch diameter f/1.00 primary mirror which is chosen to be parabolic in order to provide adequate field of view at the required f/45.0 infrared Cassegrain focus. A 40-arcmin-diameter flat field of view is provided at an f/4.5 optical Cassegrain focus such that the resulting image scale gives a sampling factor of 3.5 (27 μ) pixels per (2/3 arcsec) spatial information element. The three-element refracting field corrector contains material for an atmospheric dispersion compensator (ADC) and it is fully color-corrected such that the entire passband from 0.33 μ to 1.60 μ can be imaged simultaneously. An f/9.0 Cassegrain focal expander-corrector with (ADC) is provided which uses the f/4.5 secondary mirror and enables the new telescope optics to be coupled to existing ancillary MMT instrumentation without substantial modification to the latter. A two-element all-spherical null-lens design is presented which provides a diffraction limited optical null-test arrangement for the unprecedentedly large f/1.00 parabolic primary mirror.

A new interim adaptive system—FASTTRAC IT—has been developed for near-infrared imaging for the Multiple Mirror Telescope (MMT), prior to upgrade to a single 6.5 m mirror. The system employs a real-time adaptive beam combiner consisting of six mirror facets which control the tip and tilt for each of the 1 .8 m primary mirrors. Since the overall piston of the mirrors is not controlled, the light from the six MMT mirrors adds incoherently at the focal plane, producing an image with the diffraction limit of a single mirror but with flux corresponding to a filled 4.5 m aperture. In operational mode the tilts over each of the 1.8 m mirrors will be sampled using a sodium laser guide star. Overall tilt is compensated using a field star imaged in the visible. We present a brief discussion of the various error sources entering into the system performance. Simulations of performance are presented showing the dependence on field star magnitude and angle. the time delay between sense and application of the required correction, and the angle between laser guide star and field position. These simulations demonstrate that FASTTRAC II should readily achieve diffraction limited imaging for a 1.8 m aperture with 6 times the light collection at near-infrared wavelengths.

An Analysis of Differential Geometric and Differential Algebraic Method for Disturbance Decoupling of Nonlinear Systems

This paper presents the design of a novel nonlinear position controller for an interior permanent-magnet synchronous motor (IPMSM) servo drive. The motor model equations provide the basis for the proposed controller, which is designed with the adaptive backstepping technique. Various system uncertainties, particularly mechanical-parameter uncertainties, are incorporated in the design of the controller. Using Lyapunov's stability theory, it is verified that the control variables are asymptotically stable. The complete drive system is then simulated with MATLAB/Simulink software. Performance of the proposed adaptive-backstepping-based nonlinear position controller (ABNPC) is investigated under different dynamic operating conditions such as step changes in command positions, step changes in load, and parameter variations. The results indicate that the proposed ABNPC-based IPMSM drive could be a candidate for real-time industrial servo motor drive applications.

We present a nonlinear control scheme that permits to solve, at the same time, the disturbance decoupling and output trocking problems for a class of nonlinear systems. The control scheme proposed needs a state vector observer so, a minimal nonlinear observer is included in the control structure. The nonlinear control law, with the observer included, was applied to the model of binary distillation column.

The control problem of the single machine infinite bus system with TCSC is dealt with. Based on the maximization of the external disturbances on the system model, an adaptive nonlinear controller for large disturbance attenuation and a parameter updating law are designed by using the backstepping method. The parameter uncertainty of the transmission line is considered, as well as the influences of large external disturbances to the system output are mainly discussed. The nonlinear controller does not have the sensitivity to the influences of external disturbances, but also has strong robustness for system parameters variation. The simulation results show that the control effect of the large disturbance attenuation controller more advantages by comparing with the control performance of conventional nonlinear robust controller.

Control of the optical surface of a thin, deformable primary mirror with application to an orbiting astronomical observatory

ABSTRACTHeart rate can be used to define exercise intensity; feedback control systems for treadmills which automatically adjust speed to track arbitrary heart rate target profiles are therefore of interest. The aim of this study was to compare linear (L) and nonlinear (NL) controllers using quantitative performance measures. Sixteen healthy male subjects participated in the experimental L vs. NL comparison. The linear controller was calculated using a direct analytical design that employed an existing approximate plant model. The nonlinear controller had the same linear component, but it was augmented using static plant-nonlinearity compensation. At moderate-to-vigorous intensities, no significant differences were found between the linear and nonlinear controllers in mean RMS tracking error (2.34 vs. 2.25 bpm [L vs. NL], p=0.26) and average control signal power (51.7 vs. m2/s2, p=0.16), but dispersion of the latter was substantially higher for NL (range 45.2 to 56.8 vs. 30.7 to m2/s2, L vs. NL). At low speed, RMS tracking errors were similar, but average control signal power was substantially and significantly higher for NL (28.1 vs. m2/s2 [L vs. NL], p<0.001). The performance outcomes for linear and nonlinear control were not significantly different for moderate-to-vigorous intensities, but NL control was overly sensitive at low running speed. Accurate, stable and robust overall performance was achieved for all 16 subjects with the linear controller. This points to disturbance rejection of very-low-frequency heart rate variability as the overriding challenge for design of heart rate controllers.

This article proposed a nonlinear robust controller to achieve vehicle creep for dual-clutch transmission. The control problem is summarized as the tracking control, and linear quadratic approach is adopted to define the trajectory of the clutch slip before the controller design. The control scheme is derived from an error affine nonlinear system; meanwhile, by combining nonlinear H∞ method with the backstepping technique, the nonlinear controller is programmed to achieve the tracking of the clutch slip trajectory against the model uncertainties or disturbance. The designed controller is evaluated by simulation model including the dynamic powertrain and hydraulic actuator model, and the results show that the nonlinear controller is effective in clutch slip tracking control and has better control performance than that of the proportional–integral–derivative in terms of disturbance attenuation.

In response to the non-linear and underactuated characteristics of quadrotor UAV suspension transportation system, this paper proposes a novel control strategy aimed at achieving precise position control, attitude control, and anti-swing capabilities. Firstly, a dynamical model required for controller design is established through the Newton-Euler method. In the controller design process, the paper employs the energy method and barrier Lyapunov function to design a double-closed-loop nonlinear controller. This controller is capable of not only accurately controlling the position and attitude angles of the quadrotor UAV suspension transportation system but also effectively suppressing the swing of the payload. Building on this, considering the elastic deformation of the lifting cable, and by analyzing the forces in the Newton-Euler equations, this paper proposes an adaptive control design for the case where the length of the cable connecting the UAV and the payload is unknown. To validate the effectiveness of the proposed control scheme, comparative experiments were conducted in the MATLAB simulation environment, and the results indicate that the method proposed in this paper exhibits superior control performance compared to traditional controllers.

The biological fermentation process has the characteristics of nonlinearity and multivariable coupling. To improve the performance of decoupling control in the fermentation process, a disturbance decoupling control based on the Lie symmetry method is proposed to obtain the analytical feedback control for a class of biological fermentation systems with single input single output (SISO). Firstly, the state-space equations and the disturbance decoupling model for a class of SISO biological fermentation systems are defined; Secondly, the key technologies and algorithm approaches of Lie symmetry theory for differential equations are introduced, and the conditions and the properties of Lie symmetry for nonlinear control systems under group action are given in detail; Finally, the derived distribution of Lie symmetric infinitesimal generators is used to prove the sufficient conditions for local disturbance decoupling in the system, and the closed-loop state feedback analytical law of the system is constructed. The proposed control method is applied to the disturbance decoupling control of mycelium concentration and substrate concentration in the biological fermentation process. Numerical simulation results show that the proposed control method can effectively improve the system decoupling control performance. Meanwhile, using Lie symmetry, the cascade decoupling standard form and the static state feedback law of biological fermentation systems can be constructed.

This paper is concerned about the finite-time stabilizability and instabilizability for a class of delayed memristive neural networks (DMNNs). Through the design of a new nonlinear controller, algebraic criteria based on M -matrix are established for the finite-time stabilizability of DMNNs, and the upper bound of the settling time for stabilization is estimated. In addition, finite-time instabilizability algebraic criteria are also established by choosing different parameters of the same nonlinear controller. The effectiveness and the superiority of the obtained results are supported by numerical simulations.

Considering generator rotor and valve by external disturbances for turbine regulating system, the nonlinear large disturbance attenuation controller and parameter updating law of turbine speed governor system are designed using backstepping method. The controller not only considers transmission line parameter uncer-tainty, and has attenuated the influences of large external disturbances on system output. The nonlinear con-troller does not have the sensitivity to the influences of external disturbances, but also has strong robustness for system parameters variation, which is because of the transmission line uncertainty being considered in internal disturbances. The simulation results show that the control effect of the large disturbance attenuation controller more advantages by comparing with the control performance of conventional nonlinear robust controller.