Moving horizon approach

FIG. 8-44 The moving horizon approach of model predictive control. 

Scheduling Under Uncertainty Using a Moving Horizon Approach 187 9.2... 

A key feature of MPC is that future process behavior is predicted using a dynamic model and the available measurements. The controller outputs are calculated so as to minimize the difference between the predicted process response and the desired response. At each sampling instant the control calculations are repeated and the predictions updated based on current measurements, which is a moving horizon approach. Garcia et al. (1989), Richalet (1993), and Qin and Badgwell (1997) have provided surveys of the MPC approach. 

FIG. 8-43 The moving horizon approach of model predictive control. (Seborg, Edgar, and Melliehamp, Process Dynamics and Control, 2d ed., Wiley, New York, 2004.)... 

A receding horizon approach is employed. At each sampling instant, only the first control move (of the m moves that were calculated) is actually implemented. Then the predictions and control calculations are repeated at the next sampling instant. 

In the first part of this chapter (Section 9.2), we present an uncertainty conscious scheduling approach that combines reactive scheduling and stochastic scheduling by using a moving horizon scheme with an uncertainty conscious model. In this approach, it is assumed that decisions are made sequentially and that the effect of the revealed uncertainties can be partially compensated by later decisions. The sequence of decisions and observations is modeled by a sequence of two-stage stochastic programs. 

An uncertainty conscious scheduling approach for real-time scheduling was presented in this chapter. The approach is based on a moving horizon scheme where in each time period a two-stage stochastic program is solved. For the investigated example it was found that the stochastic scheduler improved the objective on average by 10% compared to a deterministic scheduler. 

Robertson, D. J. H. Lee and J. B. Rawlings. A Moving Horizon-based Approach for Least Squares State Estimation. AIChE J 42(8) 2209-2224 (1996). 

Thereafter, the experimental data were fitted to the above model equation by a graphical superposition technique. The data and model curve were plotted separately as fraction adsorbed or desorbed against the log of the square root of time. The experimental curve was moved horizonally until the best fit was obtained, thereby determining the appropriate value at Dc/a. This method uses all of the data, as opposed to some approaches based on the values at early times which have been used by others (1, 2, 5). It was applied easily in this work because of the excellent agreement of the model with the data obtained. 

Expected Performance Approach. Zhang and Henson [347] have proposed an on-line comparison between expected and actual process performance. The expected performance is obtained by implementing controller actions on the process model. The expected performance incorporates estimates of state noise, but no output disturbances. The actual and expected performance are compared on-line over a moving horizon Pc of past data using the ratio [347] ... 

An(A ), is actually implemented. Then at the next sampling instant, new data are acquired and a new set of control moves is calculated. Once again, only the first control move is implemented. These activities are repeated at each sampling instant, and the strategy is referred to as a receding horizon approach. The first control move, u k), can be calculated from Eqs. 20-53 and 20-56,... 

It may seem strange to calculate an M-step control policy and then only implement the first move. The important advantage of this receding horizon approach is that new information in the form of the most recent measurement y k) is utilized immediately instead of being ignored for the next M sampling instants. Otherwise, the multistep predictions and control moves would be based on old information and thus be adversely affected by unmeasured disturbances, as demonstrated in Example 20.4. 

The two extra problems, the partly unknown demand and the moving horizon, will be approached in the following way. In our algorithm we do not consider the demand distribution, but we will replace the unknown future demands by their expected value, still assuming that we can not produced expected orders before their arrival date. The second problem is known as the effect of terminal conditions in the rolling schedule. Baker (1981) studies this problem in a special quadratic production-inventory model. In his solution the terminal conditions are based on the profile of states that occurs in a deterministic finite horizon model. Implemented in a situation with uncertain demand, this solution achieves a near-optimal performance. Although we do not have this quadratic production-inventory model, we will also consider terminal conditions. Therefore we assume some simple production mle to be used after the horizon to measure the effect of an action sequence on later periods. 

The power of directed evolution is now well documented. These methods are robust and are able to improve industrial enzymes in reasonably short times. The first laboratory-evolved enzymes are now used commercially in laundry detergents12011 other commercial applications are on the horizon. Directed evolution may well help move biocatalysis from an enabling tool to a lowest cost approach . It also offers new opportunities to engineer multi-enzyme pathways and even whole microbes [69- 224> 2251, which will lead to straightforward single-pot, multi-enzyme bioconversions and new fermentation processes based on green resources such as glucose or inexpensive waste materials. 

This final chapter aims to summarise a number of the themes which regularly crop up within the book. A second aim of this chapter is to offer some speculations regarding the likely directions the field of Patient Safety Culture (PSC) will take in the coming years, as well as potential areas for future exploration. A key argument is that the field of PSC needs to move beyond ciurent concerns and expand its theoretical and methodological horizons. Part of this will involve improving the way in which we develop and test PSC surveys, tools and instruments. A second element is the need to take a closer look at some of the key lessons from other industries and work towards an improved application of a wider systems approach to future PSC research and practice (Wilson 2014). 

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