A neural network enhanced generalized minimum variance self-tuning proportional, integral and derivative control algorithm for complex dynamic systems

A neural network enhanced proportional, integral and derivative (PID) controller is presented that combines the attributes of neural network learning with a generalized minimum-variance self-tuning control (STC) strategy. The neuro PID controller is structured with plant model identification and PID parameter tuning. The plants to be controlled are approximated by an equivalent model composed of a simple linear submodel to approximate plant dynamics around operating points, plus an error agent to accommodate the errors induced by linear submodel inaccuracy due to non-linearities and other complexities. A generalized recursive least-squares algorithm is used to identify the linear submodel, and a layered neural network is used to detect the error agent in which the weights are updated on the basis of the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model, and therefore the error agent is naturally functioned within the control law. In this way the controller can deal not only with a wide range of linear dynamic plants but also with those complex plants characterized by severe non-linearity, uncertainties and non-minimum phase behaviours. Two simulation studies are provided to demonstrate the effectiveness of the controller design procedure.

Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality

An efficient model identification algorithm for a large class of linear-in-the-parameters models is introduced that simultaneously optimises the model approximation ability, sparsity and robustness. The derived model parameters in each forward regression step are initially estimated via the orthogonal least squares (OLS), followed by being tuned with a new gradient-descent learning algorithm based on the basis pursuit that minimises the l(1) norm of the parameter estimate vector. The model subset selection cost function includes a D-optimality design criterion that maximises the determinant of the design matrix of the subset to ensure model robustness and to enable the model selection procedure to automatically terminate at a sparse model. The proposed approach is based on the forward OLS algorithm using the modified Gram-Schmidt procedure. Both the parameter tuning procedure, based on basis pursuit, and the model selection criterion, based on the D-optimality that is effective in ensuring model robustness, are integrated with the forward regression. As a consequence the inherent computational efficiency associated with the conventional forward OLS approach is maintained in the proposed algorithm. Examples demonstrate the effectiveness of the new approach.

Impact of variable atmospheric and oceanic form drag on simulations of Arctic sea ice

Over Arctic sea ice, pressure ridges and floe andmelt pond edges all introduce discrete obstructions to the flow of air or water past the ice and are a source of form drag. In current climate models form drag is only accounted for by tuning the air–ice and ice–ocean drag coefficients, that is, by effectively altering the roughness length in a surface drag parameterization. The existing approach of the skin drag parameter tuning is poorly constrained by observations and fails to describe correctly the physics associated with the air–ice and ocean–ice drag. Here, the authors combine recent theoretical developments to deduce the total neutral form drag coefficients from properties of the ice cover such as ice concentration, vertical extent and area of the ridges, freeboard and floe draft, and the size of floes and melt ponds. The drag coefficients are incorporated into the Los Alamos Sea Ice Model (CICE) and show the influence of the new drag parameterization on the motion and state of the ice cover, with the most noticeable being a depletion of sea ice over the west boundary of the Arctic Ocean and over the Beaufort Sea. The new parameterization allows the drag coefficients to be coupled to the sea ice state and therefore to evolve spatially and temporally. It is found that the range of values predicted for the drag coefficients agree with the range of values measured in several regions of the Arctic. Finally, the implications of the new form drag formulation for the spinup or spindown of the Arctic Ocean are discussed.

Facile strategies for the synthesis and crystallization of linear trinuclear nickel(II)-Schiff base, complexes with carboxylate bridges: Tuning of coordination geometry and magnetic properties

Three new linear trinuclear nickel(II) complexes, [Ni-3(salpen)(2)(OAc)(2)(H2O)(2)]center dot 4H(2)O (1) (OAc = acetate, CH3COO-), [Ni-3(salpen)(2)(OBz)(2)] (2) (OBz=benzoate, PhCOO-) and [Ni-3(salpen)(2)(OCn)(2)(CH3CN)(2)] (4) (OCn = cinnamate, PhCH=CHCOO-), H(2)salpen = tetradentate ligand, N,N'-bis(salicylidene)-1,3-pentanediamine have been synthesized and characterized structurally and magnetically. The choice of solvent for growing single crystal was made by inspecting the morphology of the initially obtained solids with the help of SEM study. The magnetic properties of a closely related complex, [Ni-3(salpen)(2)(OPh)(2)(EtOH)] (3) (OPh = phenyl acetate, PhCH2COO-) whose structure and solution properties have been reported recently, has also been studied here. The structural analyses reveal that both phenoxo and carboxylate bridging are present in all the complexes and the three Ni(II) atoms remain in linear disposition. Although the Schiff base ligand and the syn-syn bridging bidentate mode of the carboxylate group remain the same in complexes 1-4, the change of alkyl/aryl group of the carboxylates brings about systematic variations between six- and five-coordination in the geometry of the terminal Ni(II) centres of the trinuclear units. The steric demand as well as hydrophobic nature of the alkyl/aryl group of the carboxylate is found to play a crucial role in the tuning of the geometry. Variable-temperature (2-300 K) magnetic susceptibility measurements show that complexes 1-4 are antiferromagnetically coupled (J = -3.2(1), -4.6(1). -3.2(1) and -2.8(1) cm(-1) in 1-4, respectively). Calculations of the zero-field splitting parameter indicate that the values of D for complexes 1-4 are in the high range (D = +9.1(2), +14.2(2), +9.8(2) and +8.6(1) cm(-1) for 1-4, respectively). The highest D value of +14.2(2) and +9.8(2) cm(-1) for complexes 2 and 3, respectively, are consistent with the pentacoordinated geometry of the two terminal nickel(II) ions in 2 and one terminal nickel(II) ion in 3. (C) 2009 Elsevier Ltd. All rights reserved.

Simplified parameter adaptive control

A simple parameter adaptive controller design methodology is introduced in which steady-state servo tracking properties provide the major control objective. This is achieved without cancellation of process zeros and hence the underlying design can be applied to non-minimum phase systems. As with other self-tuning algorithms, the design (user specified) polynomials of the proposed algorithm define the performance capabilities of the resulting controller. However, with the appropriate definition of these polynomials, the synthesis technique can be shown to admit different adaptive control strategies, e.g. self-tuning PID and self-tuning pole-placement controllers. The algorithm can therefore be thought of as an embodiment of other self-tuning design techniques. The performances of some of the resulting controllers are illustrated using simulation examples and the on-line application to an experimental apparatus.

Self-tuning proportional, integral and derivative controller based on genetic algorithm least squares

A self-tuning proportional, integral and derivative control scheme based on genetic algorithms (GAs) is proposed and applied to the control of a real industrial plant. This paper explores the improvement in the parameter estimator, which is an essential part of an adaptive controller, through the hybridization of recursive least-squares algorithms by making use of GAs and the possibility of the application of GAs to the control of industrial processes. Both the simulation results and the experiments on a real plant show that the proposed scheme can be applied effectively.

Reduced complexity set-point following in self-tuning control

An external input signal is incorporated into a self-tuning controller which, although it is based on a CARMA system model, employs a state-space framework for control law calculations. Steady-state set point following can then be accomplished even when only a recursive least squares parameter estimation scheme is used, despite the fact that the disturbance affecting the system may well be coloured.

Implementation of microprocessor based self-tuning control on a heating system

This paper describes the implementation, using a microprocessor, of a self-tuning control algorithm on a heating system. The algorithm is based on recursive least squares parameter estimation with a state-space, pole placement design criterion and shows how the controller behaves when applied to an actual system.

abctools: an R package for tuning approximate Bayesian computation analyses

Approximate Bayesian computation (ABC) is a popular family of algorithms which perform approximate parameter inference when numerical evaluation of the likelihood function is not possible but data can be simulated from the model. They return a sample of parameter values which produce simulations close to the observed dataset. A standard approach is to reduce the simulated and observed datasets to vectors of summary statistics and accept when the difference between these is below a specified threshold. ABC can also be adapted to perform model choice. In this article, we present a new software package for R, abctools which provides methods for tuning ABC algorithms. This includes recent dimension reduction algorithms to tune the choice of summary statistics, and coverage methods to tune the choice of threshold. We provide several illustrations of these routines on applications taken from the ABC literature.

Variational data assimilation for parameter estimation: application to a simple morphodynamic model

Data assimilation is a sophisticated mathematical technique for combining observational data with model predictions to produce state and parameter estimates that most accurately approximate the current and future states of the true system. The technique is commonly used in atmospheric and oceanic modelling, combining empirical observations with model predictions to produce more accurate and well-calibrated forecasts. Here, we consider a novel application within a coastal environment and describe how the method can also be used to deliver improved estimates of uncertain morphodynamic model parameters. This is achieved using a technique known as state augmentation. Earlier applications of state augmentation have typically employed the 4D-Var, Kalman filter or ensemble Kalman filter assimilation schemes. Our new method is based on a computationally inexpensive 3D-Var scheme, where the specification of the error covariance matrices is crucial for success. A simple 1D model of bed-form propagation is used to demonstrate the method. The scheme is capable of recovering near-perfect parameter values and, therefore, improves the capability of our model to predict future bathymetry. Such positive results suggest the potential for application to more complex morphodynamic models.

Parameter sensitivity and predictive uncertainty in a new water quality model, Q(2)

A new dynamic model of water quality, Q(2), has recently been developed, capable of simulating large branched river systems. This paper describes the application of a generalized sensitivity analysis (GSA) to Q(2) for single reaches of the River Thames in southern England. Focusing on the simulation of dissolved oxygen (DO) (since this may be regarded as a proxy for the overall health of a river); the GSA is used to identify key parameters controlling model behavior and provide a probabilistic procedure for model calibration. It is shown that, in the River Thames at least, it is more important to obtain high quality forcing functions than to obtain improved parameter estimates once approximate values have been estimated. Furthermore, there is a need to ensure reasonable simulation of a range of water quality determinands, since a focus only on DO increases predictive uncertainty in the DO simulations. The Q(2) model has been applied here to the River Thames, but it has a broad utility for evaluating other systems in Europe and around the world.