Model predictive control (MPC) schemes such as MOCCA, DMC, MAC, MPHC, and IMC use discrete step (or impulse) response data rather than a parametric model. They predict the future output trajectory of the process &(k + I], i = 1, . . . , PI, then the controller calculates the required control action {Au(k + I], i = 0, 1, . . . , M -i } so that the difference between the predicted trajectory and user-specified (setpoint) trajectory is minimized. This paper shows how the step (impulse) response model can be put into state space form thus reducing computation time and permitting the use of state space theorems and techniques with any of the above-mentioned MPC schemes. A series of experimental runs on a simple pilot plant shows that a Kalman filter based on the proposed state space model gives better performance that direct use of the step response data for prediction. IntroductionIn this paper, the generic term "model predictive control" (MPC) is used to define the class of control techniques which include: MPHC (model predictive heuristic control) (Richalet et al., 1978); DMC (dynamic matrix control) (Cutler and Ramaker, 1980); MAC (model algorithmic control) (Rouhani and Mehra, 1982); IMC (internal model control) (Garcia and Morari, 1982); and MOCCA (multivariable, optimal, constrained control algorithm) (Sripada and Fisher, 1985). Each of these control schemes differs in detail but includes the following key features as illustrated in Figure 1: 1. The future outputs Y i ( k ) = ( y i ( k + i l k ) , i -0, 1, . . . , P } are predicted using a set of discrete step or impulse response coefficients rather than a typical state space or transfer function model. 2. A "correction term" for each element of the predicted output is usually calculated to account for the difference between the estimated value and the measured plant output. This correction can be calculated using known disturbance response data, by identifying parameters on-line to permit forecasting of future values or by estimation techniques such as a Kalman filter. The model based value, Y ; ( k ) , and the correction term, R ( k ) , are combined to produce the estimated trajectory p ( k ) = { j ( k + i l k ) , i = 1,. . . , P}. 3. A predictive control strategy is used to calculate the control action (Ahu(k + i). i = 0, 1, . . . , M -1; M s P ) which minimizes a user-specified performance index, e.g., which minimizes the square of the difference between the desired trajectory Y,,(k) and predicted trajectory p ( k ) that would result if no further control action were taken. S. Li is on leave from4. The control calculation is usually formulated as an optimization problem: linear or nonlinear; weighted or unweighted; constrained or unconstrained. Depending on the characteristics of the optimization problem, the solution may require anything from simple off-line calculations to on-line, constrained, nonlinear optimization.MPC is popular in industry and academia because it: Uses step response data which is relatively easy to obtain Is multivariable Handles tim...

Chinese sprangletop [Leptochloa chinensis (L.) Nees] is one grass weed severely affecting rice (Oryza sativa L.) growth in paddies in China. Cyhalofop-butyl is the main herbicide used to control grass weeds in Chinese paddy fields, especially for controlling L. chinensis; however, L. chinensis has evolved resistance to cyhalofop-butyl due to continuous and extensive application. To investigate cyhalofop-butyl resistance levels and mechanisms in L. chinensis in some of the Chinese rice areas, 66 field populations were collected and treated with cyhalofop-butyl. Of these tested populations, 10 showed a high level of resistance to cyhalofop-butyl; the 50% effective dose ranged within 108.4 to 1,443.5 g ai ha−1 with resistance index values of 9.1 to 121.8 when compared with the susceptible population. Acetyl-coenzyme A carboxylase genes (ACCase) of susceptible and all 10 resistant populations were amplified and sequenced. Among them, Ile-1781-Leu, Trp-2027-Cys, Trp-2027-Ser, and Ile-2041-Asn mutations were found in five resistant populations. No known resistance-related mutations were found in the other five resistant populations, indicating that resistance to cyhalofop-butyl in these populations was likely to be endowed by non–target site resistance mechanisms. Notably, the Ile-1781-Leu and Trp-2027-Cys substitutions have previously been reported, but this is the first report of Trp-2027-Ser and Ile-2041-Asn mutations in L. chinensis. Furthermore, three derived cleaved amplified polymorphic sequence methods were developed to rapidly detect these mutations in L. chinensis.

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