A. Johnson

New Lyapunov Robustness Bounds for Pole-Assignment in a Specified Region

Abstract In this paper we present new Lyapunov robustness bounds for pole-assignment in a specified region to guarantee a certain performance robustness of linear systems described by state-space models with structured or unstructured uncertainties. Examples are given to show the improvements of proposed methods over previous ones.

Optimization of Fed-batch Biotechnical Processes

Abstract Linear-quadratic (LQ) optimal control theory is applied to the problem of optimizing the time-dependent process conditions affecting the fed-batch production of biomass. Two linear models are derived which are suitable for model-based optimization. Neither model assumes a particular time behaviour of the specific growth rate. The minimization of three different quadratic cost or performance criteria is solved; two by means of a standard LQ result and the last by a recent extension to the LQ theory.

PC Implementation of Optimal Sampled-Data Control for Robotic Manipulators

Abstract A stochastic optimal sampled-data tracking controller is implemented to control anindustrial X-V robot using a personal computer. The controller, incorporating a Kalman filter, takes account of theinter-sample behavior of the controlled system by using a continuous-time cost criterion, allowing the use of large sampling intervals. Most computations can be performed off-line. The experimental results show that the tracking accuracy and the sensitivity to the payload are good

Environmental Control of a Fed-batch Fermentation Process

Abstract It is common practice to regulate the respiratory quotient of a fed-batch fermentation process in order to optimize the biomass production. Certain process variables, such as air flowrate, pH and temperature, which determine the environment in which the cell culture is to grow are held constant, or within bounds, by separate control loops. By studying the transport phenomena involved in the fermentation process together with the dynamics of the actuators and measuring instruments robust controllers for these environmental variables have been developed. These perform well in conjunction with the self-tuning control of the respiratory quotient. Experimental results, taken from a baker’s yeast fermentation in a 100-liter pilot plant are presented to validate this claim.

A Model for the Nonlinearities of Extrusion and other Flow Processes

Abstract In order to optimize the startup phase of an extrusion process it is necessary to accurately model both the static and dynamic nonlinearities inherently associated with the process. A single multivariable nonlinear model is presented for this purpose. By means of two algebraic transformations a linear, state space model may be obtained. Thus, not only are the properties of the proposed model easily inferred but established linear controller design techniques may be employed, and existing methods used to estimate or determine any unknown parameters. An application to the modelling of a twin-screw plastics extruder is presented. It is believed that many nonlinear dynamic processes, in particular those associated with flow phenomena, could also usefully be modelled in this way.

Stability robustness analysis and design for linear systems with structured time-invariant uncertainty

A new sufficient condition is derived from a general framework for linear state space models maintaining asymptotic stability in spite of existence uncertainty. Constant structured design problem is solved by using a numerical optimization program. In all examples we examined the results of stability robustness analysis and synthesis based on our sufficient condition are less conservative than those of existing methods.<<ETX>>

The Theory of LQ Optimization of Fermentation

Abstract Linear-quadratic (LQ) optimal control theory is applied to the problem of optimizing the time-dependent process conditions affecting the fed-batch production of blomass. Two linear models are derived which are suitable for model-based optimization. Neither model assumes a particular time behaviour of the specific growth rate. The minimization of three different quadratic cost criteria is solved. The first optimization problem is to maximize the blomass production. This results in a undesirable specific growth rate trajectory, so that In the second optimization problem an additional constraint to minimize the specific growth rate Is incorporated, leading to an exponential substrate feed rate trajectory. The third problem considered is when the specific growth rate must follow a predetermined trajectory while at the same time the blomass production must be maximized. The result of this optimization gives useful insight into how competing requirements can be met In an optimal fashion. Finally, the problem of on-line parameter estimation is addressed and a solution proposed in the form of a (standard) Kalman Filter.

Minimax Guaranteed Cost Control for Linear Systems with Large Uncertain Parameters - Riccati Equation Approach

Abstract Given a linear system with large but bounded time-varying uncertainty and a quadratic cost criterion, the Minimax Guaranteed Cost Control (MGCC) robust design method proposed in this paper results in a simple linear feedback control law to guarantee both the asymptotic stability of the closed-loop system and the minimized maximal performance bound over all possible parameter perturbations. A comparative study of two illustrative examples show the improvements and advantages of the proposed method over previous ones.

Model Reduction of An Oxygen Enriched Industrial Waste-water Treatment Process

Abstract This paper describes the reduction of a 10th order nonlinear model of an oxygen enriched industrial waste-water process to a 3rd order linear model. With the aim of providing good control of the settling tank sludge volume a model has been developed which describes the dynamical behaviour of the bioreactor and settling tank. Two crucial properties of the reduced model are: (i) that it variables may still be associated with the physical variables of the waste-water treatment process, (ii) that all the unknown parameters of the reduced model may be estimated from steady-state measurements.

Optimization of the Operating Variables of an Industrial Wastewater Treatment Process

Abstract The Complex Method of optimization has been applied to minimize the operating costs of a large (1200 m3/hr effluent with an average of 1500 gCOD/m3) chemical effluent processing plant. The process, an oxygen enriched activated sludge process, consists of 3 parallel trains of UNOX bioreactors, each of four compartments, followed by 3 settling tanks. The five most important operating variables for a given recycle and waste sludge flowrate are the amount of gas vented to the atmosphere from the last compartment of each bioreactor train and the submersion depths of the electrically driven aerators in each bioreactor compartment. Using the cost prices of oxygen and electricity these five operating variables have been incorporated into a cost function which, subject to various constraints, must be minimized. The constraints are described by a steady-state, nonlinear model in which the concentrations of the dissolved oxygen in each compartment of each reactor are expressed in terms of the operating variables. The model parameters have been estimated from steady-state measurements. The result of the optimization is a simple strategy, independent of any of the model parameters, which fixes the depths of submersion of the aerators. The amount of gas vented to the atmosphere can be calculated regularly offline by means of a numerical search procedure. Savings in the order of Hfl. 15, 000 to Hfl. 30, 000 per year can be predicted from this study.