Linear Quadratic Technique Research Articles

Optimal output-feedback temperature regulation of a catalytic reverse flow reactor PDEs model

In this work, control and estimation problems have been studied for a catalytic reversal flow reactor (CFRR). A stabilizing compensator is developed on the basis of the infinite-dimensional state-space description of the CFRR. Linear–quadratic technique is used to design both an optimal state-feedback controller and an output injection operator. The later is developed based on the duality fact between regulation and estimation. Indeed, the output injection operator is the adjoint of the feedback control operator of the dual process. The developed compensator is tested numerically for the catalytic combustion of lean methane emissions.

Duality-based optimal compensator for boundary control hyperbolic PDEs system: Application to a tubular cracking reactor

This paper is devoted to the design of an optimal stabilizing compensator for a boundary control distributed parameter system that is described by a set of hyperbolic partial differential equations (PDEs). The standard reformulation of a boundary control system is adopted here to write the system under a regular infinite-dimensional linear system. A finite-dimensional boundary optimal controller is designed based on the linear quadratic technique and the corresponding operator Riccati equation. On the other hand, a Luenberger observer is designed based on the duality between the control and the estimation problems. Combination of the designed controller and observer is performed to construct a stabilizing compensator. A case study of tubular cracking chemical reactor is used to test the performances of the developed algorithm.

No such thing as a perfect hammer: comparing different objective function specifications for optimal control

Linear-quadratic (LQ) optimization is a fairly standard technique in the optimal control framework. LQ is very well researched, and there are many extensions for more sophisticated scenarios like nonlinear models. Conventionally, the quadratic objective function is taken as a prerequisite for calculating derivative-based solutions of optimal control problems. However, it is not clear whether this framework is as universal as it is considered to be. In particular, we address the question whether the objective function specification and the corresponding penalties applied are well suited in case of a large exogenous shock an economy can experience because of, e.g., the European debt crisis. While one can still efficiently minimize quadratic deviations around policy targets, the economy itself has to go through a period of turbulence with economic indicators, such as unemployment, inflation or public debt, changing considerably over time. We test four alternative designs of the objective function: a least median of squares based approach, absolute deviations, cubic and quartic objective functions. The analysis is performed based on a small-scale model of the Austrian economy and illustrates a certain trade-off between quickly finding an optimal solution using the LQ technique (reaching defined policy targets) and accounting for alternative objectives, such as limiting volatility in economic performance. As an implication, we argue in favor of the considerably more flexible optimization technique based on heuristic methods (such as Differential Evolution), which allows one to minimize various loss function specifications, but also takes additional constraints into account.

LQ bumpless transfer between two tracking controllers

In this article, a linear quadratic (LQ) scheme is proposed for bumpless transfer between two tracking controllers. The controllers have integral actions which are used to eliminate the steady-state tracking errors. A compensator is designed using the LQ technique to minimise the differences between two sets of signals, the differences between two control signals as well as the differences between the two input signals which drive the two controllers. Under such circumstances, complete information of the system is taken into account and utilised for achieving satisfactory control. It is shown that the ideal bumpless transfer is achievable with the proposed control scheme. Moreover, the results are extended to discrete-time systems. Finally, simulation results are given to demonstrate the effectiveness of the proposed control scheme.

CI-based design of a satellite attitude controller

This work presents the embedding of Computational Intelligence (CI) mechanisms in well-known techniques available for control system design, applied to satellite attitude control by using a reaction wheel. It is shown that effective search and scoring procedures can replace human-performed trial-and-improvement actions for gain computation of four types of controllers (including linear-quadratic and H2), and produces performance indexes and torque levels compatible with real world specifications. The CI mechanisms are: (i) a genetic algorithm, which generates, combines and selects controllers candidates, and (ii) a fuzzy system, for scoring performance indexes and torque levels of the controller candidates, which are subsequently used by the genetic algorithm. Not only the controller gains their selves are used as candidates, but also weighting matrices (for the linear quadratic technique) and weighting signals (for the H2 technique). Finally, a comparison of the controllers found by each technique is provided, according the hypothetical example FireSat.

Optimal Control of Tandem Cold Rolling Using A Pointwise Linear Quadratic Technique With Trims

The tandem cold rolling of metal strip is a complex multivariable process whose control presents a significant engineering challenge because of the complex interaction between the process variables, the nonlinearities (which change with operating conditions), and the interstand time delays (which change significantly with the mill speed). The present technology generally relies on a control structure that has been successful in producing an acceptable output, but has limited capability for improvement in performance. This paper describes a new strategy for control of the mill that overcomes many limitations of the present controllers. The new strategy is based on a pointwise linear quadratic technique wherein a state-dependent algebraic Riccati equation is solved pointwise to establish a control law for a multiinput–multioutput controller, with appropriate trimming functions. For this application, the features of this novel strategy compare favorably to those of other techniques for control of nonlinear systems in the areas of simplicity of implementation, provision for the use of physical intuition in the design process, and strong robustness to disturbances and uncertainties. During simulations using the new controller coupled to a nonlinear model of the process, the tolerance in mill exit thickness was ∼0.2% for several rolling schedules using mild steel during operations at steady speed and during speed changes, and in the presence of typical disturbances with uncertainties in modeling and measurement. This offers the potential for improvement over present industrial controllers, which typically hold the tolerance in mill exit thickness to within 0.5–0.8%. In addition, excursions in the individual mill stand output thicknesses and interstand tensions are reduced, which contributes to the stability of the rolling process.

Model-Based Control of an Integrated Fuel Cell and Fuel Processor With Exhaust Heat Recirculation

In this paper, we consider the dynamic and controlled operation of an integrated natural gas fuel processor system (FPS), a proton exchange membrane fuel cell (PEM-FC), and a catalytic burner (CB). The FC provides power based on the electrochemical reaction of hydrogen. The FPS generates the hydrogen from natural gas through catalytic partial oxidation (CPOX) and the CB provides the energy for preheating the FPS inlet flows by burning any excess hydrogen from the FC exhaust. The coupling of these three systems poses a challenging optimization and control problem. Optimization is performed to generate the air and fuel flow intake setpoints to the FPS for various load levels. The optimal flow setpoints are used in a static feedforward map that ensures maximum efficiency at steady state. Linear quadratic techniques are then used to develop a controller to mitigate hydrogen starvation in the fuel cell and regulate CPOX reactor temperatures. We show in simulations that the designed observer-based feedback controller, which relies on temperature measurements of two reactors, speeds up the transient response fourfold, as compared to the baseline when the static feedforward controller is employed

Adaptive maneuvering entry guidance with ground-track control

We demonstrate that a three-dimensional entry guidance with accurate ground-track control can be achieved using a combined strategy of proportional down-range maneuvering and linear quadratic (LQ) technique, thereby precluding the necessity of sophisticated nonlinear programming. It is also shown that heating rate and load-factor constraints can be met by a careful but simple selection of LQ gains. Although the speed, flight path angle, and down-range accuracy are comparable to that of a planar guidance strategy, the present technique also demonstrates an accurate cross-range control, which is not possible with a planar strategy. It is shown that adaptive maneuvering produces a superior performance than that of a nonlinear tracking control derived using feedback linearization. The method can handle much larger deviations in the entry conditions than those published previously, and has the important advantage of a relatively simple implementation in a realistic entry scenario. Furthermore, the LQ technique can take advantage of the good robustness properties of a linear Kalman filter based upon the measurement of longitude, latitude, and speed, wherein little deterioration is observed in the closed-loop performance.

Control Design of an Industrial Equalization System - Handling System Contraints, Actuator Faults and Varying Operating Conditions

This paper describes the design and evaluation of a control system for an equalization system at the wastewater treatment plant of a pharmaceutical production facility. The design includes actuator fault tolerance, and measures are included to deal with physical constraints and changing operating conditions. A combination of linear quadratic techniques, fuzzy logic and disturbance accomodation theory is used. The controller is evaluated through simulation and is currently under full-scale test.

Identification and idle speed control of internal combustion engines

This paper presents an integrated approach for the identification and control of internal combustion engines in idle-speed conditions. The inputs of the nonlinear identification model are the position of the idle speed air actuation system and the spark advance, while its outputs are the pressure inside the air intake manifold and the crank shaft speed. The estimated model is then used to synthesize an idle speed controller with the linear quadratic technique. The design procedure outlined here is currently being used by Magneti Marelli for the synthesis of commercial idle-speed regulators. Some identification and control results obtained by applying this method to a 1400 cm 3 commercial engine are reported to witness the effectiveness of the proposed approach.

The Application of Observers in the Control of Macroeconometric Systems

This paper is concerned with evaluating optimal controls for large nonlinear macroeconometric models. The application of optimal control theory with such models has generally been based on nonlinear optimisation or on linear quadratic techniques with linearisations of the model. Here observers based on low order linear models are used with a larger nonlinear macroeconometric model. The advantage of this type of observer is that linear quadratic techniques can be used to calculate controls for the nonlinear model. Further, the observer is independent of the solution techniques (for such things as forward looking behaviour) used in the nonlinear model. Different basis models for the observer are used in a counterfactual optimal control exercise.

Automatic Control of Canal Flow Using Linear Quadratic Regulator Theory

An integrated approach to the design of automatic control systems for canals using Linear Quadratic Regulator theory is developed. The one‐dimensional partial differential equations (PDE) describing open channel flow (Saint‐Venant equations) are linearized about equilibrium flow conditions and discretized spatially to provide a set of approximate ordinary differential equations (ODE) which describe the effects of gate openings on depth and flow rate. Standard linear quadratic techniques are used to design a regulator. The requirement to measure all states is obviated by the construction of an observer using only measurements of depth adjacent to control gates. Simulation results are presented which show dramatic improvements in transient response over the uncontrolled case. Use of these techniques in water conveyance canals facilitates more rapid changes in discharge, and by permitting longer periods of off‐peak pumping could greatly reduce pumping costs.