Optimal control and operation of drum granulation processes

Process optimisation and optimal control of batch and continuous drum granulation processes are studied in this paper. The main focus of the current research has been: (i) construction of optimisation and control relevant, population balance models through the incorporation of moisture content, drum rotation rate and bed depth into the coalescence kernels; (ii) investigation of optimal operational conditions using constrained optimisation techniques; (iii) development of optimal control algorithms based on discretized population balance equations; and (iv) comprehensive simulation studies on optimal control of both batch and continuous granulation processes. The objective of steady state optimisation is to minimise the recycle rate with minimum cost for continuous processes. It has been identified that the drum rotation-rate, bed depth (material charge), and moisture content of solids are practical decision (design) parameters for system optimisation. The objective for the optimal control of batch granulation processes is to maximize the mass of product-sized particles with minimum time and binder consumption. The objective for the optimal control of the continuous process is to drive the process from one steady state to another in a minimum time with minimum binder consumption, which is also known as the state-driving problem. It has been known for some time that the binder spray-rate is the most effective control (manipulative) variable. Although other possible manipulative variables, such as feed flow-rate and additional powder flow-rate have been investigated in the complete research project, only the single input problem with the binder spray rate as the manipulative variable is addressed in the paper to demonstrate the methodology. It can be shown from simulation results that the proposed models are suitable for control and optimisation studies, and the optimisation algorithms connected with either steady state or dynamic models are successful for the determination of optimal operational conditions and dynamic trajectories with good convergence properties. (c) 2005 Elsevier Ltd. All rights reserved.

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.

Degrees of freedom and motor planning in purposive movement

This paper presents empirical evidence suggesting that healthy humans can perform a two degree of freedom visuo-motor pursuit tracking task with the same response time delay as a one degree of freedom task. In contrast, the time delay of the response is influenced markedly by the nature of the motor synergy required to produce it. We suggest a conceptual account of this evidence based on adaptive model theory, which combines theories of intermittency from psychology and adaptive optimal control from engineering. The intermittent response planning stage has a fixed period. It possesses multiple optimal trajectory generators such that multiple degrees of freedom can be planned concurrently, without requiring an increase in the planning period. In tasks which require unfamiliar motor synergies, or are deemed to be incompatible, internal adaptive models representing movement dynamics are inaccurate. This means that the actual response which is produced will deviate from the one which is planned. For a given target-response discrepancy, corrective response trajectories of longer duration are planned, consistent with the principle of speed-accuracy trade-off. Compared to familiar or compatible tasks, this results in a longer response time delay and reduced accuracy. From the standpoint of the intermittency approach, the findings of this study help make possible a more integral and predictive account of purposive action. (c) 2005 Elsevier B.V. All rights reserved.

Effect of knee joint angle on motor unit synchronization

Activity of the vasti has been argued to vary through knee range of movement due to changes in passive support of the patellofemoral joint and the relative contribution of these muscles to knee extension. Efficient function of the knee is dependent on optimal control of the patellofemoral joint, largely through coordinated activity of the medial and lateral quadriceps. Motor unit synchronization may provide a mechanism to coordinate the activity of vastus medialis (VMO) and vastus lateralis (VL), and may be more critical in positions of reduced passive support for the patellofemoral joint (i.e., full extension). Therefore, the aim of this study was to determine whether the degree of motor unit synchronization between the vasti muscles is dependent on joint angle. Electromyographic (EMG) recordings of single motor unit action potentials (MUAPs) were made from VMO and multiunit recordings from VL during isometric contractions of the quadriceps at 0 degrees, 30 degrees, and 60 degrees of knee flexion. The degree of synchronization between motor unit firing was evaluated by identification of peaks in the rectified EMG averages of VL, triggered from MUA-Ps in VMO. The proportion of cases in which there was a significant peak in the triggered averages was calculated. There was no significant difference in the degree of synchronization between the vasti at different knee angles (p = 0.57). These data suggest that this basic coordinative mechanism between the vasti muscles is controlled consistently throughout knee range of motion, and is not augmented at specific angles where the requirement for dynamic control of stability is increased. (D 2006 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

Optimal unravellings for feedback control in linear quantum systems

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case: Given a fixed interaction between the system and the environment what is the optimal measurement on the environment for a particular control problem? We show that for a broad class of optimal (state- based) control problems ( the stationary linear-quadratic-Gaussian class), this question is a semidefinite program. Moreover, the answer also applies to Markovian (current-based) feedback.

Practicality of time-optimal two-qubit Hamiltonian simulation

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer, and Cirac [Phys. Rev. Lett. 88, 237902 (2002)] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.

Optimally distributed actuator placement and control for a slewing single-link flexible manipulator

A method is proposed for determining the optimal placement and controller design for multiple distributed actuators to reduce the vibrations of flexible structures. In particular, application of piezoceramic patches to a horizontally-slewing single-link flexible manipulator modeled using the assumed modes method is investigated. The optimization method uses simulated annealing and allows placement of any number of distributed actuators of unequal length, although piezoceramics of fixed equal lengths are used in the example. It also designs an linear-quadratic-regulator controller as part of the optimization procedure. The measures of performance used in the investigation to determine optimality are the total mass of the system and the time integral of the absolute value of the hub and tip position error. This study also varies the relative weightings for each of these performance measures to observe the effects on the controller designs and piezoceramic patch positions in the optimized solutions.

Optimal strategies in political elections

In the Majoritarian Parliamentary System, the government has a constitutional right to call an early election. This right provides the government a control to achieve its objective to remain in power for as long as possible. We model the early election problem mathematically using opinion polls data as a stochastic process to proxy the government's probability of re-election. These data measure the difference in popularity between the government and the opposition. We fit a mean reverting Stochastic Differential Equation to describe the behaviour of the process and consider the possibility for the government to use other control tools, which are termed 'boosts' to induce shocks to the opinion polls by making timely policy announcements or economic actions. These actions improve the government's popularity and have some impact upon the early-election exercise boundary. © Austral. Mathematical Soc. 2005.

Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.