Quadratic Gain Research Articles

Optimal FIR Input Shaper Designs for Motion Control With Zero Residual Vibration

This paper considers the design of input shaping filters used in motion control of vibratory systems. The filters preshape a command or actuation signal in order to negate the effect of vibratory modes. A class of finite impulse response filter satisfying a set of orthogonality conditions that ensure zero residual vibration is introduced. Filter solutions having minimum quadratic gain, both with and without the inclusion of non-negativity (peak gain) constraints, are presented. Unlike impulse-based shapers, the filters have impulse responses with no singularities and therefore automatically remove discontinuities from an input signal. Minimum duration impulse response solutions are also presented. These contain singularities but may also have smooth components. Discrete-time designs can be obtained numerically from system modal parameters, accounting for all modes simultaneously so that convolving single-mode solutions, which leads to suboptimality of the final design, is not required. Selected designs are demonstrated experimentally on a flexible link planar manipulator.

Active Control with Optical Fiber Sensors and Neural Networks. I: Theoretical Analysis

To implement the concept of a smart structure, a smart active control system is presented. Both fiber Bragg grating (FBG) sensors and neural networks are utilized to construct a system similar to the human being. The smart system is comprised of three parts: a structural condition surveillance system, three converters, and a controller. By distributing as many sensors as possible in the key areas in buildings, FBG sensors can be used for assessing structure soundness while acting as dendrites in a neural network system. Comparison of structural responses under an uncontrolled system, traditional optimal linear quadratic gain, and the proposed NEURO-FBG control system verifies the advantages of using this novel technique approach. The system robustness is evaluated under both time delay and disconnection problems. Analytical results demonstrate that the NEURO-FBG system can effectively control the response of the structure and provide a more reliable system than ordinary active control.

Optical klystron and harmonic generation free electron laser

The optical field evolution of an optical klystron free electron laser is analytically described for both low gain and high gain cases. The harmonic optical klystron (HOK) in which the second undulator is resonant on the higher harmonic of the first undulator is analyzed as a harmonic amplifier. The optical field evolution equation of the HOK is derived analytically for both the CHG mode (coherent harmonic generation, the quadratic gain regime) and the HGHG mode (high gain harmonic generation, the exponential gain regime), the effects of energy spread, energy modulation, and dispersion in the whole process are taken into account. The linear theory is given and discussed for the HGHG mode. The analytical formula is given for the CHG mode.

Quadratic L2 gain performance LPV system design by a LTI controller with ILMI algorithm

A quadratic L2 gain performance LPV control system has been designed using a linear time invariant (LTI) output feedback controller with an iterative linear matrix inequality (ILMI) algorithm. A linear parameter varying (LPV) plant is assumed with immeasurable dependent parameter, which varies in a plant parameter space that is a polytope. Different from gain scheduled LPV control, this is a complex control problem with the non-convex constraint that the controller gain matrix is the same for each vertex plant of the LPV system. To solve this control problem, a heuristic iterative algorithm is presented in the form of a linear matrix inequality (LMI) formulation. An effective method of setting an initial value to the ILMI algorithm proposed here promotes convergence to an admissible solution.

A norandom variational approach to stochastic linear quadratic Gaussian optimization involving fractional noises (FLQG)

It is shown that the problem of minimizing (maximizing) a quadratic cost functional (quadratic gain functional) given the dynamicsdx=(fx+gu)dt+hdb(t,a) whereb(t, a) is a fractional Brownian motion of ordera, 0<2a<1, can be solved completely (and meaningfully!) by using the dynamical equations of the moments ofx(t). The key is to use fractional Taylor's series to obtain a relation between differential and differential of fractional order.

Quantum computing of Poincaré recurrences and periodic orbits

Quantum algorithms are built enabling Poincare recurrence times and periodic orbits of classical dynamical systems to be found. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of systems. Quadratic gain can be achieved for a larger set of dynamical systems. The simplest cases can be implemented with a small number of qubits.

A new two-degree-of-freedom gain scheduling method applied to the Lynx MK7

This paper considers the design of two-degree-of-freedom gain-scheduled controllers for a helicopter system in a new fashion. By taking advantage of a two-degree-of-freedom decoupling scheme, it is possible to generically split the controller synthesis into two parts. One part is concerned with the synthesis of a regulator and the other aims to achieve the tracking requirements. An important feature of the method is that the feedforward filter can be designed by solving a particular full information problem. A robust linear time-invariant (LTI) regulator will be designed and two methods used to synthesize a gain-scheduled feedforward tracking controller will be investigated. The first method is based on a quadratic gain scheduling technique which makes use of a polytopic description of the plant. The second is simpler and uses the concept of linear interpolation of LTI controllers. Both methods are tested on a Lynx MK7 helicopter in simulation. For this application, the benefits and the shortcomings of the respective methods are discussed. Non-linear simulation results show that the gain-scheduled interpolated controller performs remarkably well over the flight envelope.

Robust Multivariable Control of Nuclear Power Plant

The paper presents a design method for robust multiva-riable control design and its application to retrofit a new additional control system in an old pressurized water reactor (PWR) nuclear power plant (NPP). The mathematical model of PWR NPP, used in the design process is briefly described. The 28th dimensional state equation model accounts for the main physical processes and plant subsystems. The optimal and suboptimal linear quadratic gain (LQG) additional control, which provides improved integration of the existing automatic feedback control loops is described and dynamical behaviour of the plant is simulated. Because of the process parameters variations, the design of a robust multivariable control system is considered and a new method which leads to improvement of system robustness is proposed. The method, based on LQG control improves the response of the existing control loops and increases the closed loop system robustness. The dynamical behaviour of NPP Krsko, Slovenia, for specified design plant perturbations is presented and the use of different control systems is compared.

Dynamically similar control systems and a globally minimum gain control technique: IMSC

The concept of dynamically similar control systems is introduced. The necessary and sufficient conditions to minimize a quadratic modal gain measure are given for dynamically similar closed-loop control systems. The globally minimum modal gain is obtained when the independent modal space control (IMSC) is used. Corollaries of the results for the control of infinite-dimensional structural distributed parameter systems (DPS) are given. Based on the results, a modal interaction parameter (MIP) is defined for all control systems. The minimum value of MIP is zero and uniquely corresponds to the IMSC. A nonzero value of MIP corresponds to all other coupled control (CC) designs and implies suboptimality relative to the IMSC design. The relative optimality of the real-space gain matrices of the IMSC and the CC designs depends on the actuator locations for the IMSC. Based on this, a real-space interaction parameter (RIP) is defined. A positive value of RIP renders IMSC optimal in its real-space gain matrix. The MIP and RIP are indications of suboptimality of a particular control technique and can be used to tune-up the control design via actuator locations. Actuator distribution criteria are suggested for both CC and IMSC designs, based on the values of MIP and RIP, respectively.

Spatial mode structure of stimulated Stokes emission from a Raman generator

The spatial mode structure of the stimulated Stokes emission from a H2 Raman generator has been accurately determined by using a linear photodiode array and imaging techniques. The diffraction-limited pump beam was obtained by spatially clipping the output of an injection-locked XeCl laser. The spatial profiles of the stimulated Stokes beam are compared with the predictions of Yariv’s theory of propagation in a quadratic gain medium applied to Raman scattering [ A. Yariv , Quantum Electronics ( Wiley, New York, 1975)]. While the theory compares well with the experimental data at low intensities, the spatial profile develops features at higher intensities that are not predicted by the simple theory.

Intermodal injection locking of semiconductor lasers

Injection locking of a GaAlAs laser by coupling into non-lasing Fabry-Perot modes is described. Locking of a slave laser mode as far as 22 mode spacings (60 Å) away from the gain curve centre is obtained. The dependence of the locking bandwidth on the injected power and the wavelength separation between the free-running and injected mode (Δλ) is described. The dependence of the power required for locking on the magnitude of Δλ is consistent with a 192 Å-wide quadratic gain profile.