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Model Predictive Control Part 8

Tham khảo tài liệu 'model predictive control part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Model predictive control of nonlinear processes 133 where J is defined by Eq. 64 . At any instant the current control signal uk and the prediction output based on this control input y k Ĩ are used to compute the objective function f x in Eq. 68 as the energy function E k i . The E k i and the previously evaluated E k provides the AE as AE k E k i - E k 69 The comparison of the AE with the random numbers generated between 0 and 1 determines the probability of acceptance of u k . If AE 0 all u k are accepted. If AE 0 u k are accepted with a probability of exp -AE TA . If nm be the number of variables nk be the number of function evaluations and nT be the number of temperature reductions then the total number of function evaluations required for every sampling condition are nT x nk x nm . Further details of NMPC based on stochastic optimization can be referred elsewhere Venkateswarlu and Damodar Reddy 2008 . Implementation procedure The implementation of NMPC based on SA proceeds with the following steps. 1. Set Ta as a sufficiently high value and let nk be the number of function evaluations to be performed at a particular Ta. Specify the termination criterion s. Choose the initial control vector u and obtain the process output predictions using Eq. 63 . Evaluate the objective function Eq. 68 as the energy function E k . 2. Compute the incremental input vector Auk stochastically and update the control vector as u k i u k Au k 70 Calculate the objective function E k i as the energy function based on this vector. 3. Accept u k i unconditionally if the energy function satisfies the condition E k i E k 71 Otherwise accept u k i with the probability according to the Metropolis criterion i E k i - E k Y exp - ----------p-----y E r 72 where TA is the current annealing temperature and r represents random number. This step proceeds until the specified function evaluations nk are completed. 4. Carry out the temperature reduction in the outer loop according to the decrement .