L.G. van Willigenburg

Control and optimization

Abstract. A wide range of various classical and modern control methods is classified from the point of view of required information and put in the context of optimization.

Robust optimal receding horizon control of the thermal sterilization of canned foods

Open loop optimal control strategies for the thermal sterilization of canned foods are computed and analysed. The optimal retort temperature profiles ensure that the required degree of sterilization is met whilst minimising costs. The costs are defined in terms of batch time and retention of nutrient value in the food material. The model is a finite dimensional approximation of the infinite dimensional system. The errors due to the finite dimensional approximation and the uncertainty in the thermal diffusivity parameter of the model are considered. Based on the analysis a closed loop receding horizon optimal controller is designed. Simulation experiments reveal the robustness of the receding horizon optimal controller with respect to uncertainty in the thermal diffusivity parameter. The simulations also reveal that the loss of performance is relatively small and that the batch-time may be reduced significantly.

Optimal Control of Greenhouse Climate: Computation of the Influence of Fast and Slow Dynamics

Abstract In case of optimal greenhouse climate control the fast greenhouse dynamics are generally ignored. Only the slow dynamics that describe the crop behaviour are considered. Through the computation of optimal climlate controls for growing lettuce in greenhouses, subjected to actual weather, it is demonstrated that the neglect of the greenhouse dynamics seriously affects the result (net profit).

Receding Horizon Optimal Control of a Solar Greenhouse

A solar greenhouse has been designed that maximizes solar energy use and minimizes fossil energy consumption. It is based on a conventional Venlo greenhouse extended with a heat pump, a heat exchanger, an aquifer and ventilation with heat recovery. The goal is to minimize fossil energy consumption, while maximizing crop dry weight, keeping temperature and humidity within certain limits and satisfying a temperature integral. To achieve this the aim is to implement a receding horizon optimal controller. This type of controller computes optimal closed loop controls based on a cost function and a greenhouse and crop model. In this paper simulations of a simplified version of this closed loop optimal control system are presented. It is found that the boiler use is reduced, thereby reducing fossil energy use. Gas use is decreased by 77% compared to a conventional greenhouse with optimal control.

Synthesis of digital optimal reduced-order compensators for asynchronously sampled systems

The synthesis of finite-horizon digital optimal reduced-order compensators is presented, for asynchronous and aperiodically sampled continuous-time systems. The dimensions of the compensator state are a priori fixed and may be time varying. Asynchronous and aperiodic sampling refers to a deterministic sampling scheme where an arbitrary, but a priori known, number of control variables is updated, and/or an arbitrary, but a priori known, number of outputs is sampled, at arbitrary, but a priori known, time instants. This sampling scheme generalizes most deterministic sampling schemes considered in the control literature. Through the use of an integral criterion the intersample behaviour is explicitly considered in the design. As a result, frequent, synchronous and periodic sampling is no longer necessary, which can be highly relevant in practice. Also the synthesis enables comparison of the optimal performance of reduced-order compensators as a function of their dimensions and the sampling scheme. The synthesis is illustrated with a numerical example

First order controllability and the time optimal control problem for rigid articulated arm robots with friction

For non-linear systems, linear in the control, a relationship between the singularity of the time optimal control problem and the differential controllability of the linearized dynamics along a time optimal solution that satisfies the minimum principle is established. Known results concerning the solution of the time optimal control problem for a two link planar articulated arm robot without friction are extended to a general rigid articulated arm robot with friction. Finally, these results are used to prove differential controllability of the linearized dynamics (called first order controllability) along any trajectory of rigid articulated arm robots with friction.

The equivalent discrete-time optimal control problem for time-varying continuous-time systems with white stochastic parameters

The transformation into discrete-time equivalents of digital optimal control problems, involving continuous-time linear systems with white stochastic parameters, and quadratic integral criteria, is considered. The system parameters have time-varying statistics. The observations available at the sampling instants are in general nonlinear and corrupted by discrete-time noise. The equivalent discrete-time system has white stochastic parameters. Expressions are derived for the first and second moment of these parameters and for the parameters of the equivalent discrete-time sum criterion, which are explicit in the parameters and statistics of the original digital optimal control problem. A numerical algorithm to compute these expressions is presented. For each sampling interval, the algorithm computes the expressions recursively, forward in time, using successive equidistant evaluations of the matrices which determine the original digital optimal control problem. The algorithm is illustrated with three examples. If the observations at the sampling instants are linear and corrupted by multiplicative and/or additive discrete-time white noise, then, using recent results, full and reduced-order controllers that solve the equivalent discrete-time optimal control problem can be computed.The transformation into discrete-time equivalents of digital optimal control problems, involving continuous-time linear systems with white stochastic parameters, and quadratic integral criteria, is considered. The system parameters have time-varying statistics. The observations available at the sampling instants are in general nonlinear and corrupted by discrete-time noise. The equivalent discrete-time system has white stochastic parameters. Expressions are derived for the first and second moment of these parameters and for the parameters of the equivalent discrete-time sum criterion, which are explicit in the parameters and statistics of the original digital optimal control problem. A numerical algorithm to compute these expressions is presented. For each sampling interval, the algorithm computes the expressions recursively, forward in time, using successive equidistant evaluations of the matrices which determine the original digital optimal control problem. The algorithm is illustrated with three exampl...

Comparison of Classical and Optimal Control of Greenhouse Tomato Crop Production

Abstract Through simulation, the optimal control of tomato crop production in a greenhouse based on an economic criterion, is compared with the result obtained with a conventional classical controller. The result is 6 % increase in profit and 43 % increase in energy efficiency over a characteristic autumn day. The solution of the optimal control problem is not at all straightforward. The greenhouse-tomato system is stiff. Singular perturbation theory is usually applied to cope with stiffness in optimal control problems, but in this case direct application is problematic due to the rapid external disturbances. In this paper the problem is solved by adapting a method proposed earlier by Van Henten (1994).

Connecting and unmasking relativity and quantum theory

The answer lies right in front of us, but we refuse to see it. Both relativity and quantum theory, the two pillars of fundamental physics, are modified in this paper to make them also explain the physical phenomena they describe. With this explanation, all current inconsistencies between the two vanish. The modifications relate to the presence of a medium, which is in fact potential energy, in three-dimensional space. This medium acts as a reference system, in accordance with Mach’s principle. The speed of light, therefore, is not absolute but relative to the medium and thus to the observer. It is also dependent on medium density. Quantum waves are real scalar waves occurring in the potential energy medium, not probabilities of particles being present. Real scalar quantum waves in three-dimensional space make up the whole of physics representing manifest energy. Particles therefore do not exist; they are local manifestations of real scalar quantum waves. As a result, the Doppler effect and wave interference play a central role in physics. Moreover, the dependence of quantum wave velocity (speed of light) on medium density provides the energy exchange mechanism that is central to physics because all physical phenomena, including observation, concern energy exchange, or interaction. The conceptual simplicity of the model of physics proposed in this paper is shown to clarify a series of paradoxes and ill-understood phenomena at the fundamental level of physics such as wave-particle duality, the twins paradox, and the double slit experiment. As to entanglement, superposition, and nonlocality, the model implies that only weak versions of these properties exist.

3.2 Control and Optimization

A wide range of various classical and modern control methods is classified from the point of view of required information and put in the context of optimization.