CN108227494A - The fuzzy fault tolerant control method of the non-linear optimal constraints of batch process 2D - Google Patents

Abstract

The present invention seeks to improve the control performance and tracking performance of control method in non-linear batch process, a kind of fuzzy fault controller method of the optimal constraints of 2D of non-linear batch process is proposed.The non-linear and two-dimensional characteristics that the present invention passes through batch process, establish 2D T S fringe spatial models, further combined with system mode error and output error, the dynamic model of original system is converted into a closed loop failure fuzzy system model represented in the form of prediction with Roesser models, design constraint is obscured iterative learning faults-tolerant control rule is converted into determining constraint more new law；According to designed infinite optimality criterion and 2D system Lyapunov Theory of Stability, with linear matrix inequality（LMI）Constraint type provides the fuzzy fault-tolerant more new law real-time online design for ensuring closed-loop system robust asymptotically stabilization.The present invention solves the problems, such as that non-linear lower system model is more intractable very well, ensure that system in worst case still can even running, and with optimal tracking performance.

Description

Nonlinear batch process 2D optimal constraint fuzzy fault-tolerant control method

Technical Field

The invention belongs to the field of advanced control of industrial processes, and relates to a nonlinear batch process 2D optimal constraint fuzzy fault-tolerant control method.

Background

As a batch process, which is one of the production methods, there are roughly two types of system descriptions, one is linear and the other is nonlinear. The early control of the intermittent process is mostly directly aimed at the linear model, however, in the actual industrial process, the intermittent process has strong nonlinear characteristics, and the linear model and the actual process have a large mismatch problem. Making it difficult to achieve optimal control in practical applications. Direct processing of non-linear systems presents certain difficulties. For this purpose, a new model is used to approximate the nonlinear system.

Along with the increase of the production scale and the increase of the complexity of the production steps, the uncertainty existing in the actual production is increasingly prominent, so that the high-efficiency and smooth operation of the system is influenced, and even the quality of the product is threatened. These complex operating conditions, in turn, increase the probability of system failure. Among them, actuator failure is a common failure, which affects the operation of the process and reduces the control performance, even endangers the personal safety. Although control methods such as iterative learning reliable fault-tolerant control and the like appear in the batch processing process, the control problem that the system still stably runs when an actuator fails can be well solved. However, for equipment with high precision, the possibility of failure occurrence is extremely low, if no failure occurs, the equipment is reliably controlled to use, so that resource waste is caused, the cost is increased in the past, and the environment-friendly concept of energy conservation and emission reduction is obviously not met. In the event of a serious fault, the reliable control law may completely lose control, which may lead to system breakdown, resulting in significant property loss and casualties.

In addition, although the robust iterative learning reliable control strategy adopted at the present stage can effectively resist the influence caused by uncertainty and faults in the production link, ensure the stability of the system and maintain the control performance of the system, the control law is obtained by solving based on the whole production process and belongs to global-covering optimization control in the control effect, namely the same control law is used all the time. However, in actual operation, under the influence of interference and faults, the system state cannot change completely according to the obtained control law action; if the system state at the current moment deviates from the set value to a certain extent, the same control law is still continuously adopted, the deviation of the system state is increased gradually along with the lapse of time, and the existing robust iterative learning reliable control method cannot solve the problem of the deviation of the system state, which inevitably has adverse effects on the stable operation and the control performance of the system. In addition, the existing literature does not consider the constraint problem for control law design and system output, and the constraint must be considered in the actual production process.

The Model Predictive Control (MPC) can well meet the requirement of real-time update and correction of the control law, and the optimal control law at each moment is obtained through rolling optimization and feedback correction, so that the system state can be ensured to run along the set track as much as possible. However, in the prior art, a one-dimensional infinite time domain control law is mostly adopted, a learning process is lacked among batches, and the control effect is not improved along with the increment of the batches; there is also a process that only considers batch-to-batch "learning" and this approach does not achieve the control problem of an intermittent process where the initial value is uncertain. It is clear that the discussion of the infinite time domain constraint optimization problem for systems with uncertainty and faults is left to be further. Therefore, a new control method is urgently needed to make up the defects of the existing method so as to achieve the aims of saving energy, reducing consumption, reducing cost, even reducing the occurrence of accidents which harm human safety and the like in the batch production process.

Most of the existing prediction control technologies design a control law in a one-dimensional direction, only the time direction or the batch direction is considered, only the time direction is considered, so that each batch is only simply repeated, and the control performance cannot be improved along with the increment of the batch; the control problem of the intermittent process with uncertain initial values cannot be realized only by considering the batch direction. Although there are few results considering time and batch direction, there is no good research result for the situations of nonlinearity, actuator failure and the like.

Therefore, in order to solve the problems, respond to calls for energy conservation, emission reduction and the like in the production process and ensure the control performance of the system, it is necessary to provide a 2D fuzzy constraint fault-tolerant control method for infinite time domain optimization in a nonlinear batch process.

Disclosure of Invention

In order to solve the technical problems, the invention provides a nonlinear batch process 2D optimal fuzzy constraint fault-tolerant control method. And designing a nonlinear infinite time domain optimized 2D fuzzy iterative learning control law for batch process models with nonlinear interference and actuator faults. The control law is designed by the design method, so that the system can be ensured to stably run when a fault occurs, the aims of saving energy, reducing consumption, reducing cost and the like are fulfilled, and the aims of reducing the occurrence of personal safety hazard and the like can be fulfilled.

The invention aims to improve the control performance and the tracking performance of a control method in a nonlinear batch process, and provides a 2D optimal constraint fuzzy fault-tolerant controller design method for the nonlinear batch process. According to the method, a 2D T-S fuzzy state space model is established through the nonlinear and two-dimensional characteristics of a batch process, a system state error and an output error are further combined, a dynamic model of an original system is converted into a closed-loop fault system model represented in a prediction mode through a Roesser model, and a design constraint iterative learning fault-tolerant control law is converted into a determination constraint updating law; according to designed infinite optimization performance indexes and a 2D system Lyapunov stability theory, a fuzzy fault-tolerant update law real-time online design for ensuring the stability of the robustness asymptotic of a closed-loop system is given in a Linear Matrix Inequality (LMI) constraint form. The invention is directed to the design of a fuzzy optimal fault-tolerant controller under the condition that an actuator of a nonlinear batch process fails. The control algorithm can achieve the aims of saving energy, reducing consumption, reducing cost, reducing the occurrence of personal safety hazards and the like.

The invention is realized by the following technical scheme:

the nonlinear batch process 2D optimal constraint fuzzy fault-tolerant control method comprises the following specific steps:

step 1, establishing an equivalent 2D-Rosser error augmentation model of a nonlinear batch process:

step 1.1, considering actuator gain faults, and establishing a 2D T-S fuzzy fault state space model according to the nonlinear and two-dimensional characteristics of the batch process, wherein the model is represented by formula (1):

and the input and output constraints thereof meet:

wherein x (t, k), y (t, k), u (t, k), ω (t, k) respectively represent the state of the system, the output of the system, the control input of the system, and the unknown disturbance;the upper bound constraint values of input and actual output are respectively, and t and k respectively represent the running time and the batch in the batch; t is_pRepresents the total time of a batch run; p is the number of preconditions; r is the number of fuzzy rules; a. the_i,B_i,C_iA system state matrix, a system input matrix and a system output matrix under the corresponding fuzzy rule i are obtained; x (0, k) is the initial state of the kth batch; m_ijFor fuzzy sets, M_ij(x_j(t, k)) is x_j(t, k) is M_ijDegree of membership of;byCan obtain the product

Defining different α values to indicate different fault types of the actuator, indicating partial failure fault when α is more than 0, indicating complete failure fault when α is equal to 0, and not relating to the problem of the optimal controller;

for partial actuator failure, α > 0 should satisfy the following form:

in the formula,andis a known constant;

step 1.2, designing a 2D iterative learning controller u (t, k), as shown in formula (3):

therefore, u (t, k) is designed, and only k batches of the updating law r (t, k) at t moment are designed to realize that the system output y (t, k) tracks the given expected output y_d(t,k)；

Step 1.3 defines the state error and output error in the batch direction as follows:

δ(x(t,k))＝x(t,k)-x(t,k-1) (4a)

order toThen the equation (1) is converted into an equivalent error model which is equation (5):

wherein,δ(ω(t,k))＝ω(t,k)-ω(t,k-1)，

δ(h_i(x(t,k)))＝h_i(x(t,k))-h_i(x(t,k-1))， i is an adaptive identity matrix; and is provided with The above model is then expressed as:

wherein,the horizontal and vertical state components of the adaptive vector, respectively, and Z (t, k) is the controlled output of the system;

step 2, designing an iterative learning control law for batch process models with interference and actuator faults:

step 2.1, a 2D predictive fault-tolerant controller is designed for the model (5) to achieve minimum optimal control under the maximum interference and the maximum fault, even if the model (5) achieves a steady state and meets the following robust performance indexes at each moment:

and (3) limiting:

and Q (Q > 0) and R (R > 0) are weighting matrices of appropriate dimensions, R (t + i | t, k) is the predicted value input at time t to t + i, and R (t, k) ═ R (t | t, k),represents an input increment;

step 2.2, defining a state feedback control law to enable the system to achieve secondary stability, wherein the selected updating law is as follows:

the closed-loop model of (5) is expressed as:

wherein,its closed-loop prediction model is represented as:

step 2.3, the stability of the system is proved by using a 2D Lyapunov function, wherein the Lyapunov function is defined as follows:

wherein M > 0

Step 2.4 the model (8c) can still run stably within the fault tolerance range, and the following requirements must be met:

(1) the 2D lyapunov function is inequality constrained:

(2) for a given semi-positive definite symmetric matrix R, Q, there is a positive definite symmetric matrix M ═ diag { M^h,M^v}, semi-positive definite symmetric matrixMatrix Y_i,Y_j(i ═ 1, 2.. r.,), scalar epsilon_i,ε_jγ, θ > 0, 0 < α < 1,0 < μ < 1, such that the following matrix inequality holds:

and is

And is

Wherein,

the robust update law gain is:

therefore, the further update law is represented as:and (3) the value is substituted into u (t, k) ═ u (t, k-1) + r (t, k), so that a 2D constraint iterative learning control law design u (t, k) can be obtained, the step 2.4 is continuously repeated at the next moment, the new controlled variable u (t, k) is continuously solved, and the steps are sequentially circulated.

Compared with the prior art, the invention has the beneficial effects that:

designing a fuzzy fault-tolerant iterative learning control law on the basis of a control system model with nonlinearity, interference and faults, introducing a state error and an output error, converting a dynamic model of an original system into a closed-loop system model represented in a prediction form by using a Roesser model, and converting the designed fuzzy fault-tolerant iterative learning control law into a determined updating law; according to designed infinite optimization performance indexes and a 2D system Lyapunov stability theory, an update law real-time online design for ensuring asymptotic stability of a closed-loop system robustness is given in a Linear Matrix Inequality (LMI) constraint form, and the problems that a system model is difficult to process under nonlinearity and a fuzzy optimal fault-tolerant control law is constrained under a fault condition are effectively solved. The method effectively solves the problem that the control performance of the nonlinear batch process cannot be improved along with the increment of the batch, realizes the real-time optimization of the system in a variable constraint range regardless of the existence of faults, improves the control performance of the system, ensures that the system can still run stably under the worst condition and has the optimal tracking performance. Finally, the purposes of saving energy, reducing consumption, reducing cost and reducing the occurrence of accidents damaging personal safety are achieved.

Detailed Description

The present invention will be further described with reference to the following specific examples.

The nonlinear batch process 2D optimal constraint fuzzy fault-tolerant control method comprises the following specific steps:

step 1, establishing an equivalent 2D-Rosser error augmentation model of a nonlinear batch process:

step 1.1, considering actuator gain faults, and establishing a 2D T-S fuzzy fault state space model according to the nonlinear and two-dimensional characteristics of the batch process, wherein the model is represented by formula (1):

and the input and output constraints thereof meet:

wherein x (t, k), y (t, k), u (t, k), ω (t, k) respectively represent the state of the system, the output of the system, the control input of the system, and the unknown disturbance;the upper bound constraint values of input and actual output are respectively, and t and k respectively represent the running time and the batch in the batch; t is_pRepresents the total time of a batch run; p is the number of preconditions; r is the number of fuzzy rules; a. the_i,B_i,C_iA system state matrix, a system input matrix and a system output matrix under the corresponding fuzzy rule i are obtained; x (0, k) is the initial state of the kth batch; m_ijFor fuzzy sets, M_ij(x_j(t, k)) is x_j(t, k) is M_ijDegree of membership of;byCan obtain the product

Defining different α values to indicate different fault types of the actuator, indicating partial failure fault when α is more than 0, indicating complete failure fault when α is equal to 0, and not relating to the problem of the optimal controller;

for partial actuator failure, α > 0 should satisfy the following form:

in the formula,α(α1) andis a known constant;

step 1.2, designing a 2D iterative learning controller u (t, k), as shown in formula (3):

therefore, u (t, k) is designed, and only k batches of the updating law r (t, k) at t moment are designed to realize that the system output y (t, k) tracks the given expected output y_d(t,k)；

Step 1.3 defines the state error and output error in the batch direction as follows:

δ(x(t,k))＝x(t,k)-x(t,k-1) (4a)

order toThen the equation (1) is converted into an equivalent error model which is equation (5):

wherein,δ(ω(t,k))＝ω(t,k)-ω(t,k-1)，

δ(h_i(x(t,k)))＝h_i(x(t,k))-h_i(x(t,k-1))，is an adaptive identity matrix; and is provided withThe above model is then expressed as:

wherein,the horizontal and vertical state components of the adaptive vector, respectively, and Z (t, k) is the controlled output of the system;

step 2, designing an iterative learning control law for batch process models with interference and actuator faults:

step 2.1, a 2D predictive fault-tolerant controller is designed for the model (5) to achieve minimum optimal control under the maximum interference and the maximum fault, even if the model (5) achieves a steady state and meets the following robust performance indexes at each moment:

and (3) limiting:

and Q (Q > 0) and R (R > 0) are weighting matrices of appropriate dimensions, R (t + i | t, k) is the predicted value input at time t to t + i, and R (t, k) ═ R (t | t, k),represents an input increment;

step 2.2, defining a state feedback control law to enable the system to achieve secondary stability, wherein the selected updating law is as follows:

the closed-loop model of (5) is expressed as:

wherein,its closed-loop prediction model is represented as:

step 2.3, the stability of the system is proved by using a 2D Lyapunov function, wherein the Lyapunov function is defined as follows:

wherein M > 0

Step 2.4 the model (8c) can still run stably within the fault tolerance range, and the following requirements must be met:

(1) the 2D lyapunov function is inequality constrained:

(2) for a given semi-positive definite symmetric matrix R, Q, there is a positive definite symmetric matrix M ═ diag { M^h,M^v}, semi-positive definite symmetric matrixMatrix Y_i,Y_j(i ═ 1, 2.. r.,), scalar epsilon_i,ε_jγ, θ > 0, 0 < α < 1,0 < μ < 1, such that the following matrix inequality holds:

and is

And is

Wherein,

the robust update law gain is:

therefore, the further update law is represented as:and (3) the value is substituted into u (t, k) ═ u (t, k-1) + r (t, k), so that a 2D constraint iterative learning control law design u (t, k) can be obtained, the step 2.4 is continuously repeated at the next moment, the new controlled variable u (t, k) is continuously solved, and the steps are sequentially circulated.

Examples

Consider a non-linear continuous stirred tank:

wherein, C_AConcentration of A during irreversible reaction (A → B); t is the temperature of the reaction kettle; t is_CFor the cooling stream temperature, the manipulated variables q are 100(L/min), V100 (L), C_Af＝1(mol/L)，T_f＝400(K)，ρ＝1000(g/L)，C_P＝1(J/gK)，k₀＝4.71×10⁸(min^-1)，E/R＝8000(K)，ΔH＝-2×10⁵(J/mol)，UA＝1×10⁵(J/minK). The variable range is limited to 200 ≦ T_C≤450(K)，0.01≤C_AT is more than or equal to 1(mol/L) and more than or equal to 250 and less than or equal to 500 (K); y (t, k) ═ Cx (t, k) is the output. The above nonlinear model translates into:

wherein,

C＝[1 0]

the control objective is to let the reactor temperature follow a given curve:

the simulation was performed for 50 batches, each run for 600 steps. The evaluation index uses a sum of squares root error (RSSE) for evaluating the control effect.

The initial phase controller gain calculated is:

K1＝[-0.0905 0.0041 0.5031]；

K2＝[0.1120 0.0021 0.5799]；

K3＝[0.1344 -0.0078 0.2622]；

K4＝[0.0260 0.0042 0.4630]。

the method designs a fuzzy iterative learning control law under the condition of interference and faults in the nonlinear batch process, and effectively solves the problems that a system model is difficult to process under the nonlinear condition and the design problem of a constraint fuzzy optimal fault-tolerant control method under the condition of faults. The method effectively solves the problem that the control performance of the nonlinear batch process cannot be improved along with the increment of the batch, realizes the real-time optimization of the system in a variable constraint range regardless of the existence of faults, improves the control performance of the system, ensures that the system can still run stably under the worst condition and has the optimal tracking performance. Finally, the purposes of saving energy, reducing consumption, reducing cost and reducing the occurrence of accidents damaging personal safety are achieved.

Claims (1)

1. The nonlinear batch process 2D optimal constraint fuzzy fault-tolerant control method is characterized by comprising the following steps: the method comprises the following specific steps:

step 1, establishing an equivalent 2D-Rosser error augmentation model of a nonlinear batch process:

step 1.1, considering actuator gain faults, and establishing a 2D T-S fuzzy fault state space model according to the nonlinear and two-dimensional characteristics of the batch process, wherein the model is represented by formula (1):

and the input and output constraints thereof meet:

wherein x (t, k), y (t, k), u (t, k), ω (t, k) respectively represent the state of the system, the output of the system, the control input of the system, and the unknown disturbance;the upper bound constraint values of input and actual output are respectively, and t and k respectively represent the running time and the batch in the batch; t is_pRepresents the total time of a batch run; p is the number of preconditions; r is the number of fuzzy rules; a. the_i,B_i,C_iA system state matrix, a system input matrix and a system output matrix under the corresponding fuzzy rule i are obtained; x (0, k) is the initial state of the kth batch; m_ijFor fuzzy sets, M_ij(x_j(t, k)) is x_j(t, k) is M_ijDegree of membership of;byCan obtain the product

Defining different α values to indicate different fault types of the actuator, indicating partial failure fault when α is more than 0, indicating complete failure fault when α is equal to 0, and not relating to the problem of the optimal controller;

for partial actuator failure, α > 0 should satisfy the following form:

in the formula,α(α1) andis a known constant;

step 1.2, designing a 2D iterative learning controller u (t, k), as shown in formula (3):

therefore, u (t, k) is designed, and only k batches of the updating law r (t, k) at t moment are designed to realize that the system output y (t, k) tracks the given expected output y_d(t,k)；

Step 1.3 defines the state error and output error in the batch direction as follows:

δ(x(t,k))＝x(t,k)-x(t,k-1) (4a)

order toThen the equation (1) is converted into an equivalent error model which is equation (5):

wherein,δ(ω(t,k))＝ω(t,k)-ω(t,k-1)，

δ(h_i(x(t,k)))＝h_i(x(t,k))-h_i(x(t,k-1))， i is an adaptive identity matrix; and is provided with The above model is then expressed as:

wherein,the horizontal and vertical state components of the adaptive vector, respectively, and Z (t, k) is the controlled output of the system;

step 2, designing an iterative learning control law for batch process models with interference and actuator faults:

step 2.1, a 2D predictive fault-tolerant controller is designed for the model (5) to achieve minimum optimal control under the maximum interference and the maximum fault, even if the model (5) achieves a steady state and meets the following robust performance indexes at each moment:

and (3) limiting:

and Q (Q > 0) and R (R > 0) are weighting matrices of appropriate dimensions, R (t + i | t, k) is the predicted value input at time t to t + i, and R (t, k) ═ R (t | t, k),represents an input increment;

step 2.2, defining a state feedback control law to enable the system to achieve secondary stability, wherein the selected updating law is as follows:

the closed-loop model of (5) is expressed as:

wherein,its closed-loop prediction model is represented as:

step 2.3, the stability of the system is proved by using a 2D Lyapunov function, wherein the Lyapunov function is defined as follows:

wherein,

step 2.4 the model (8c) can still run stably within the fault tolerance range, and the following requirements must be met:

(1) the 2D lyapunov function is inequality constrained:

(2) for a given semi-positive definite symmetric matrix R, Q, there is a positive definite symmetric matrix M ═ diag { M^h,M^v}, semi-positive definite symmetric matrixMatrix Y_i,Y_j(i ═ 1, 2.., r), scalar epsilon_i,ε_jγ, θ > 0, 0 < α < 1,0 < μ < 1, such that the following matrix inequality holds:

and is

And is

Wherein,the robust update law gain is:

therefore, the further update law is represented as:and (3) the value is substituted into u (t, k) ═ u (t, k-1) + r (t, k), so that a 2D constraint iterative learning control law design u (t, k) can be obtained, the step 2.4 is continuously repeated at the next moment, the new controlled variable u (t, k) is continuously solved, and the steps are sequentially circulated.