| CPC C02F 3/006 (2013.01) [C02F 3/02 (2013.01); G05B 13/048 (2013.01); C02F 2209/006 (2013.01); C02F 2209/10 (2013.01); C02F 2209/14 (2013.01); C02F 2209/15 (2013.01); C02F 2209/22 (2013.01); Y02W 10/10 (2015.05)] | 1 Claim |
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1. A method of designing a cooperative optimal control system for WWTP, comprising the steps:
(1) providing an optimal control system that contains a center control unit, a blower, an internal flow recycle pump, sensor unit that includes a SO sensor, two SNO sensors, a SS sensor, a SNH sensor, two MLSS sensors;
the center control unit is configured to receive measured data from the sensor unit, calculate optimal set-points of control variables based on the measured data, and generate control commands to optimize operation of the WWTP;
the blower and the internal flow recycle pump are applied to perform the control commands transmitted by the center control unit;
the sensor unit is used to measure data of process variables, the SO sensor, located in the aerobic tank, is configured to measure values of SO; the two SNO sensors, located in the anoxic and secondary sedimentation tanks, are configured to measure values of SNO; the SS sensor, located in the aerobic tank, is configured to measure values of SS; the SNH sensor, located in the secondary sedimentation tank, is configured to measure values of SNH; the two MLSS sensors, located in the anoxic and secondary sedimentation tank, are configured to measure values of MLSS;
(2) adaptive calculation of the optimal set-points of control variables, rather than the fixed values by expert experience, the steps are:
1) select related process variables of PE: SNO, MLSS, and choose related process variables of AE and EQ: SO, SS, SNH, SNO;
2) formulate two-level models based on different time scales, an upper-level model is for PE, and lower-level models are for AE and EQ:
 where F1(t1) is the upper-level model for PE at time t1, l1(xu(t1)) is a mapping function of PE model, f1(t2) is the lower-level model for AE at time t2, l2(xl(t2), x*u(t1)) is a mapping function of AE model, x*u(t1) is optimal set-points of nitrate nitrogen SNO*, f2(t2) is the lower-level model for EQ at time t2, l3(xl(t2), x*u(t1)) is a mapping function of EQ model, xu(t1)=[SNO(t1), MLSS(t1)] is input variables vector of PE at time t1, SNO(t1) is concentration of SNO at time t1, MLSS(t1) is concentration of MLSS at time t1, and initial values of the two variables are [0.85, 1.56], xl(t2)=[SO(t2), SS(t2), SNH(t2)], SO(t2) is concentration of SO at time t2, SS(t2) is concentration of SS at time t2, SNH(t2) is concentration of SNH at time t2, [SO(t2), SS(t2), SNH(t2), SNO*(t1)] is input variables vector of AE and EQ at time t2, and initial values of [SO(t2), SS(t2), SNH(t2), SNO*(t1)] are [1.9, 11.6, 3.8, 0.95];
3) design a cooperative optimization algorithm to optimize the upper-level and lower-level optimization problems for obtaining the optimal set-points of the control variables, where the optimization period in the upper level is 1-3 hours dedicated to the slower process dynamics, in the lower level is 10-50 minutes dedicated to the faster process dynamics, the steps are:
1 formulate the upper-level and lower-level problems:
 where Min F1(SNO(t1), MLSS(t1)) is the upper-level optimization problem, Min [f1(SO(t2), SNH(t2), SS(t2), SNO*(t1)), f2(SO(t2), SNH(t2), SS(t2), SNO*(t1))] is the lower-level optimization problem;
2 set the number of the particle population in the upper level optimization I1, the number of the particle population in the lower level optimization I2, the maximum number of iterations in the upper level optimization N1, and the maximum number of iterations in the lower level optimization N2, where I1=50, I2=50, N1=20, N2=50;
3 introduce the single particle swarm optimization (SPSO) algorithm to optimize the upper-level optimization problem, the position and the velocity of the ith particle can be shown as:
 si(t1) is the position of the ith particle at time t1, si,1(t1) is the value of SNO at time t1, si,2(t1) is the value of MLSS at time t1, vi(t1) is the velocity of the ith particle at time t1, i is the number of particles, 1=1, 2, . . . , 50, the update process of si(t1) and vi(t1) are
 where d is the space dimension, d=1, 2, vi,d(t1) is the velocity of the ith particle in the dth dimension at time t1, pi,d(t1) is the individual optimal solution of the ith particle in the dth dimension at time t1, gd(t1) is the global optimal solutions of the ith particle at time t1;
4 if SPSO reaches the preset maximum number of evolutions N1, stop the iterative evolution process, transfer the value of SNO* to the lower level; if SPSO does not reach the preset maximum number of evolutions N1, return to step 3;
5 introduce the multiobjective particle swarm optimization (MOPSO) algorithm to optimize the lower-level optimization problem, the position of the jth particle aj(t2) and the velocity of the jth particle bj(t2) can be represented as aj(t2)=[aj,1(t2), aj,2(t2), aj,3(t2), aj,4(t2)], ai,1(t2) represents the value of SO at time t2, ai,2(t2) represents the value of SNH at time t2, ai,3(t2) represents the value of SS at time t2, ai,4(t2) represents the value of SNO* at time t2, bj(t2)=[bj,1(t2), bj,2(t2), bj,3(t2), bj,4(t2)], j is the number of particles, j=1, 2, . . . , 50; during the iterative evolution process, the obtained non-dominated solutions are conserved in the external archive Z(t2), Z(t2)=[z1(t2), z2(t2), . . . , zj(t2), . . . , z50(t2)], the update rule of the external archive is:
 where zj(t2) is the jth non-dominated solution at time t2 before the archive is updated, žj(t2) is the jth non-dominated solution at time t2 after the archive is updated, zj(t2)=[zj,1(t2), zj,2(t2)], žj(t2)=[žj,1(t2), žj,2(t2)], zj,1(t2) and žj,1(t2) are the values of SO before and after the archive is updated, zj,2(t2) and žj,2(t2) are the values of SNO before and after the archive is updated, ∇D is the gradient descent direction;
6 establish the multi-input-multi-output radial basis assisted model (RBSM) based on the non-dominated solutions in Z(t2):
 where Bj(t2) is the output vector of RBSM, Bj(t2)=[Bj,1(t2), Bj,2(t2)]T, Bj,1(t2) is the predicted value of the aeration energy at time t2, Bj,2(t2) is the predicted value of the effluent quality at time t2, oj(t2)=[oj,1(t2), oj,2(t2), . . . , oj,8(t2)]T are the connection weights, θj(t2)=[θj,1(t2), θj,2(t2), . . . , θj,8(t2)]T is the output vector of the neurons in hidden layer, the sum of the squared errors between the output of RBSM and the actual system is expressed as
 where e(zn(t2)) is the sum of the squared errors between the outputs of nth non-dominated solution Bn(t2) and the actual system Q(t2), n∈[1, 50], Q(t2)=[Q1(t2), Q2(t2)] is the real outputs of AE and EQ in the actual system, select the solution corresponding to the minimal sum of the squared error as the global optimal solution;
7 if MOPSO reaches the preset maximum number of evolutions N2, stop the iterative evolution process and output the optimal set-points of dissolved oxygen SO*; if MOPSO does not reach the preset maximum number of evolutions N2, return to step 5; then the optimal set-points of SNO*and SO* can be obtained;
(3) perform the control commands: if the measured value of SNO is lower or higher than SNO*, it is noted that the internal recycle flow should be adjusted to satisfy the operating requirement by manipulating the electromagnetic valve of internal flow recycle pump; if the measured value of SO is lower or higher than SO*, it is noted that the supplied oxygen should be adjusted by manipulating the fan frequency of blower; the detailed adjusting strategy is realized by the predictive control; the steps are:
1 define the cost functions in the predictive control strategy:
 where z1(t) and z2(t) are the optimal set-points of SO* and SNO*, y1(t) and y2(t) are the predicted values of SO and SNO;
2 update the control laws based on the predictive control strategy, the updated rule is:
 where u(t) is the control law at time t, Δu(t) are the control variations, whose expressions are shown as:
 where Δu(t) are the variations of the manipulated variables electromagnetic valve of internal flow recycle pump and the fan frequency of blower, Δu(t)=[Δu1(t), Δu2(t)]; the values of SO and SNO will be changed accordingly, and then transmitted to the center control unit to realize the optimal control; the effects of the proposed optimal control results are reflected by the daily average of PE value, the daily average of AE value, the daily average of EQ value, and the tracking control results of SO and SNO.
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