A novel anti-windup framework for cascade control systems: An application to underactuated mechanical systems

This paper describes the anti-windup compensator (AWC) design methodologies for stable and unstable cascade plants with cascade controllers facing actuator saturation. Two novel full-order decoupling AWC architectures, based on equivalence of the overall closed-loop system, are developed to deal with windup effects. The decoupled architectures have been developed, to formulate the AWC synthesis problem, by assuring equivalence of the coupled and the decoupled architectures, instead of using an analogy, for cascade control systems. A comparison of both AWC architectures from application point of view is provided to consolidate their utilities. Mainly, one of the architecture is better in terms of computational complexity for implementation, while the other is suitable for unstable cascade systems. On the basis of the architectures for cascade systems facing stability and performance degradation problems in the event of actuator saturation, the global AWC design methodologies utilizing linear matrix inequalities (LMIs) are developed. These LMIs are synthesized by application of the Lyapunov theory, the global sector condition and the _?2${?}_2$ gain reduction of the uncertain decoupled nonlinear component of the decoupled architecture. Further, an LMI-based local AWC design methodology is derived by utilizing a local sector condition by means of a quadratic Lyapunov function to resolve the windup problem for unstable cascade plants under saturation. To demonstrate effectiveness of the proposed AWC schemes, an underactuated mechanical system, the ball-and-beam system, is considered, and details of the simulation and practical implementation results are described.     

Constrained control of hot air blower system under output delay using globally stable performance-based anti-windup approach

This paper describes the design and implementation of a linear controller with an Anti-Windup Compensator (AWC) for a hot air blower system having output delays, under actuator saturation constraint and noise. Traditional Anti-Windup (AW) schemes for timedelay systems are based on either local stability or global stability with performance restrictions. We modify an existing AWC architecture using a time-delay term in the compensator in order to ensure global stability and performance. It is also shown that the existing Linear Matrix Inequalities (LMIs) based optimization schemes for AWC, which are derived using the decoupled architecture and coprime factorization, can be applied to the modified AWC architecture. This modified delay independent AWC scheme is applied to a hot air blower system and practical results are discussed. This paper aims to support the industrial application of the modified AWC ensuring global stability and performance, by applying it to a hot air blower system under actuator situation and output delay as well as electrical and thermal noises.     

Molecular dynamics simulation of polyethylene under cyclic loading: Effect of loading condition and chain length

Two nano-blocks of polyethylene (PE) are made and subjected to cyclic deformation with various loading conditions, i.e., strain vs. stress control, zero lateral strain vs. zero lateral stress, and different load amplitude by using the coarse grained molecular dynamics simulation. The one block is filled with 1000 random coil chains of [-CH₂-]³⁰⁰ (long chain), while the other 10 000 chains of [-CH₂-]³⁰ (short chain). The random coil chains are freely grown and relaxed in a simulation box of , then compressed to and relaxed to obtain a stress-free equilibrium. Under the zero lateral stress condition, σ^′=0, the long-chain block shows a leaf-like hysteresis curve both in the stress- and strain-controlled cyclic loading. The area of the hysteresis loop increases as the maximum load is changed to , and , respectively. The “Mullin's effect” is also observed, i.e., the stress-strain curve depicts lower path in the 2nd or later loading, although the target is never a rubber with filler. Under the zero lateral strain condition, ε^′=0, the long-chain block shows little hysteresis with the stress amplitude of 100 MPa, while it shows rapid or unstable elongation around at ε=0.35 in the simulation of ε_max=0.5 and . The short-chain block also shows unstable elongation under the ε^′=0 condition even with the stress amplitude of 100 MPa, noting that it has an upper yield point of at ε=0.35 and lower one around at ε=1.6. On the other hand, the short-chain block is stretched without remarkable stress increase up to the strain around 1.0, under the lateral condition of σ^′=0. Then the block shows “strain hardening” and comes up to the external stress of 100 MPa. It is worth noting that the block shows a leaf-like hysteresis in the 2nd or later cycle; the stress goes back to zero around ε=1.0 in the unloading process and rises up immediately when the load is reversed, as same as the long-chain block.     

Optical deflection measuring system

A system for accurate real-time measurement of deflections was developed. A stable laser source is, by means of a single-mode fiber, coupled to an optical head located at one end of deformed structure. A detector circuit with a quadrant detector and processing electronics, located at the other end of the structure, communicates the resolved 2D position of the incident beam over a common digital bus. Experiments using interferometers were conducted in a climate-controlled chamber to evaluate system performance and verify the accuracy. A resolution of 0.1  m is attainable in dynamic measurements. The system was calibrated and tested to yield measurement accuracy of ± 0.8  m for ± 2σ probability over the measurement range of ± 300  m. Drift of the system in the experimental setup was determined to be less than 2  m for measurement in both degrees of freedom within the 10 h period under constant environmental conditions.     

Enhancing the performance of parallel cascade control using Smith predictor

Parallel cascade controllers are used in chemical processing industries to improve the dynamic performance of a control system in the presence of disturbances. In the present work, a delay compensator has been incorporated in the primary loop of the parallel cascade control system. The secondary controller is designed using the internal model control (IMC) method. The primary controller is designed based on a direct synthesis method for the delay-free system. Design of controllers for slow (when the secondary loop dynamics is slow i.e. process contains poles sufficiently slower than the desired closed loop response) as well as fast dynamics (when the inner loop dynamics is fast i.e. process contains poles sufficiently faster than the desired closed loop response) of the secondary process is considered. The method provides robust control performances. Significant improvement in the closed loop performances are obtained with the delay compensator over that of a conventional parallel cascade control system. Several case studies are considered to show the advantage of the proposed method when compared to other recently reported methods.     

Report of the Italian inter-laboratories comparison of high dc resistance on the calibration of a and a resistors

A national comparison of high dc resistance at and level was organized by the Electromagnetic Division of National Institute of Metrological Research (INRIM, Italy) and piloted by the high dc resistance Laboratory of the same Division. This comparison took place between January and April 2008 with the participation of 8 Secondary Laboratories accredited by the Italian Service of Accreditation of Calibration Laboratories (SIT). The travelling package included one wire-wound standard and one thick film-type standard in a wooden anti-shock container designed by INRIM. The obtained results indicate that the relative differences at and between each Laboratory’s value and the respective reference value are all within the expanded relative uncertainties of these differences at a 2σ confidence level.     

Transverse and longitudinal vibrations of a frame structure due to a moving trolley and the hoisted object using moving finite element

This paper aims at presenting a technique to replace the moving load by an equivalent moving finite element so that both the transverse and the longitudinal inertial effects due to the moving mass may easily be taken into account simultaneously. Where the mass, damping and stiffness matrices of the moving finite element are determined by the transverse () inertia force, Coriolis force and centrifugal force of the moving mass, respectively. From the numerical examples illustrated, it has been found that, in addition to the conventional transverse () responses, the inertial effects of the moving load also affect the longitudinal () responses of the portal-frame structure significantly.     

Repeatable and accurate assembly of X-ray foil optics

Repeatable and accurate assembly of thin, foil optics is crucial to meeting performance goals in optical systems such as grazing-incidence X-ray telescopes and diffractive lithography tools. Our previous work in proving key technologies for assembly has been motivated by the need to meet spectral resolution goals for the NASA Constellation-X mission. We report a new generation of technology that makes strides towards simulating actual telescope assembly conditions. Our technology is based on the use of micromachined silicon tooling that we call microcombs. Theoretical error budgeting and analytical models were applied to a mechanical design with an isolated metrology frame and high-resolution actuation with feedback. Experimental testing has yielded assembly results with sub-micron repeatability and accuracy. For complete foil reassembly, placement errors are approximately 0.3  m over a 140 mm× 100 mm× 0.4 mm foil. Accuracy of assembly in pitch and yaw are 0.34 and 2.01  m, respectively. This performance meets the 1  m telescope assembly accuracy goal with the exception of yaw accuracy, which is under continued development.     

Auto-tuning of cascade control systems

In this paper, a novel auto-tuning method for a cascade control system is proposed. By employing a simple relay feedback test, both inner and outer loop model parameters can be simultaneously identified. Consequently, well-established proportional-integral-derivative (PID) tuning rules can be applied to tune both loops. Compared with existing methods, the new method is simpler and yet more effective. It can be directly integrated into commercially available industrial auto-tuning systems. Some examples are given to illustrate the effectiveness and robustness of the proposed method.