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

2D Optimal Constraint Fuzzy Fault Tolerant Control Method for Nonlinear Batch Process

technical field

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

Background technique

As one of the production methods, there are roughly two types of system descriptions for the batch process, one is linear and the other is nonlinear. Most of the control of batch process in the early stage was directly based on the linear model. However, in the actual industrial process, the batch process itself has strong nonlinear characteristics, and there is a large mismatch between the linear model and the actual process. It is difficult to achieve the best control effect in practical application. There are certain difficulties in dealing with nonlinear systems directly. To this end, it is necessary to use new models to approximate nonlinear systems.

With the increase of production scale and the complexity of production steps, the uncertainty in actual production has become increasingly prominent, which not only affects the efficient and stable operation of the system, but even threatens the quality of products. Moreover, these complex operating conditions correspondingly increase the probability of system failure. Among them, actuator failure is a common failure, which will affect the operation of the process and reduce the control performance, and even endanger personal safety. Although control methods such as iterative learning reliable fault-tolerant control have appeared in the batch processing process, they can well solve the control problem that the system can still run stably when actuator failure occurs. However, for high-precision equipment, the possibility of failure is extremely low. If reliable control is used regardless of whether there is a failure or not, it will cause a waste of resources. Environmental protection concept. Reliable control law may completely lose its control function in the event of a serious failure, which is very likely to lead to system collapse, resulting in heavy property losses and casualties.

In addition, although the robust iterative learning reliable control strategy adopted at this stage can effectively resist the influence of uncertainties and faults in the production process, ensure the stability of the system, and maintain the control performance of the system, but the control law is Based on the solution of the entire production process, the control effect belongs to the optimal control covering the whole world, that is, the same control law is used from beginning to end. However, in actual operation, under the influence of disturbances and faults, the system state cannot completely change according to the obtained control law; if the current system state deviates from the set value to a certain extent, the same control law, as time goes by, the deviation of the system state will increase, and the current robust iterative learning reliable control method cannot solve the problem of system state deviation, which will inevitably have adverse effects on the stable operation and control performance of the system Impact. In addition, for the control law design and system output, the existing literature does not consider the constraints, but in the actual production process, constraints must be considered.

Model Predictive Control (MPC) can well meet the needs of real-time update and correction of control law. The optimal control law at each moment is obtained through "rolling optimization" and "feedback correction" to ensure that the system state can follow the The set trajectory runs. However, most of the existing technologies use a one-dimensional infinite time-domain control law, which lacks a "learning" process between batches, and the control effect does not improve with the increase in batches; there is another method that only considers batches The process of "learning" between times, this method cannot realize the control problem of the batch process with uncertain initial value. Obviously, the discussion on the optimization problem of infinite time-domain constraints for systems with uncertainties and faults needs to be further deepened. Therefore, it is urgent to propose a new control method to make up for the shortcomings of the existing methods, so as to achieve the goals of energy saving, cost reduction, and even reduction of personal safety accidents in the batch production process.

Most of the current predictive control technologies design the control law in the one-dimensional direction, only considering the time direction or batch direction, and only considering the time direction makes each batch just a simple repetition, and the control performance cannot be improved with the increment of batches ; Only considering the batch direction can not realize the control problem of batch process with uncertain initial value. Although there are a few results considering time and batch direction, there are no good research results for nonlinearity and actuator failure.

Therefore, in order to solve the above-mentioned problems, respond to the call for energy saving and emission reduction in the production process, and ensure the control performance of the system, it is extremely necessary to propose a 2D fuzzy-constrained fault-tolerant control method for infinite time-domain optimization of nonlinear batch processes.

Contents of the invention

In order to solve the above-mentioned existing technical problems, the present invention provides a 2D optimal fuzzy-constrained fault-tolerant control method for a nonlinear batch process. A 2D fuzzy iterative learning control law for nonlinear infinite time-domain optimization is designed for batch process models with nonlinear disturbances and actuator failures. Using this design method to design the control law can not only ensure the smooth operation of the system when a fault occurs, so as to achieve the goals of energy saving, consumption reduction and cost reduction, but also the goal of reducing the occurrence of accidents that endanger personal safety.

The purpose of the invention is to improve the control performance and tracking performance of the control method in the nonlinear batch process, and propose a 2D optimal constraint fuzzy fault-tolerant controller design method for the nonlinear batch process. The present invention establishes a 2D T-S fuzzy state space model through the nonlinear and two-dimensional characteristics of the batch process, further combines the system state error and output error, and uses the Roesser model to convert the dynamic model of the original system into a closed-loop fault expressed in a predictive form The system model transforms the design-constrained iterative learning fault-tolerant control law into a definite constraint update law; according to the designed infinite optimization performance index and 2D system Lyapunov stability theory, it is given in the form of linear matrix inequality (LMI) constraints to ensure the robustness of the closed-loop system Real-time online design of asymptotically stable fuzzy fault-tolerant update law. The invention is dedicated to the design of fuzzy optimal fault-tolerant controller under the condition that actuator of nonlinear batch process fails. Firstly, it solves the problem that the system model is difficult to deal with under nonlinear conditions, and secondly, it solves the design of constrained fault-tolerant control law under the condition of failure. This control algorithm can finally achieve the goals of energy saving, cost reduction, and personal safety accidents.

The present invention is achieved through the following technical solutions:

A 2D optimal constraint fuzzy fault-tolerant control method for a nonlinear batch process, the specific steps of which are:

Step 1. Establish a nonlinear batch process equivalent 2D-Rosser error augmentation model:

Step 1.1 Considering the actuator gain fault, according to the nonlinear and two-dimensional characteristics of the batch process, a 2D T-S fuzzy fault state space model is established, expressed by formula (1):

And its input and output constraints satisfy:

Among them, 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; are the upper bound constraint values of input and actual output respectively, t and k respectively represent the running time and batch in the batch; T _p represents the total running time of a batch; p is the number of premise variables; r is the number of fuzzy rules ; A _i , B _i , C _i are the system state matrix, system input matrix, and system output matrix under the corresponding fuzzy rule i; x(0,k) is the initial state of the kth batch; M _ij is the fuzzy set, M _ij (x _j (t,k)) is the membership degree of x _j (t,k) belonging to M _ij ; Depend on Available

Different α values are defined to indicate different fault types of actuators. When α>0, it means a partial failure; when α=0, it means a complete failure, which does not involve the problem of optimal controller;

For the partial failure of the actuator, α>0 needs to satisfy the following form:

In the formula, and is a known constant;

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

It can be seen that to design u(t,k), it is only necessary to design k batches of update laws r(t,k) at time t, so as to realize the system output y(t,k) tracking 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)

make Then formula (1) is transformed into an equivalent error model as formula (5):

in, 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 the dimension-appropriate identity matrix; and let Then the above model is expressed as:

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

Step 2. Design an iterative learning control law for the batch process model with disturbance and actuator failure:

Step 2.1 Design a 2D predictive fault-tolerant controller for the above model (5) to achieve the minimum optimal control under the maximum disturbance and maximum fault, even if the model (5) reaches a steady state and satisfies the following robust performance index at each moment:

limit:

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

Step 2.2 defines the state feedback control law to make the system achieve quadratic stability, and the selected update law is:

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

in, Then its closed-loop prediction model is expressed as:

Step 2.3 uses the 2D Lyapunov function to prove the stability of the system, and defines the Lyapunov function as:

Among them, M>0

Step 2.4 Model (8c) can still run smoothly within the allowable range of faults, it must meet:

(1) 2D Lyapunov function inequality constraints:

(2) For a given positive semi-definite symmetric matrix R, Q, there is a positive-definite symmetric matrix M=diag{M ^h , M ^v }, a positive semi-definite symmetric matrix Matrix Y _i , Y _j (i=1,2,...r,), scalar ε _i ,ε _j ,γ,θ>0, 0<α<1, 0<μ<1, can make the following matrix The inequality holds:

and

and

in,

The robust update law gain is:

Therefore, the further update law is expressed as: Putting it into u(t,k)=u(t,k-1)+r(t,k), the 2D constrained iterative learning control law design u(t,k) can be obtained, and at the next moment, repeat Step 2.4, continue to solve the new control quantity u(t,k), and loop in turn.

Compared with prior art, the beneficial effect of the present invention is:

This method designs a fuzzy fault-tolerant iterative learning control law based on the control system model with nonlinearity, disturbance and fault, introduces the state error and output error, and uses the Roesser model to convert the dynamic model of the original system into a predictive form. The closed-loop system model converts the designed fuzzy fault-tolerant iterative learning control law into a definite update law; according to the designed infinite optimization performance index and 2D system Lyapunov stability theory, it is given in the form of linear matrix inequality (LMI) constraints to ensure the robustness of the closed-loop system The asymptotically stable update law is designed on-line in real time, which effectively solves the problem that the system model is difficult to deal with under nonlinear conditions and the problem of constrained fuzzy optimal fault-tolerant control law design in the event of a fault. It effectively solves the problem that the control performance of the nonlinear batch process cannot be improved with the increase of the batch, realizes that the system can be optimized in real time within the variable constraint range regardless of whether there is a fault, improves the system control performance, and ensures the system in It can still run smoothly and have the best tracking performance in the worst case. Ultimately, energy saving, consumption reduction, cost reduction, and accidents endangering personal safety are reduced.

Detailed ways

The present invention will be further described below in conjunction with specific embodiments.

A 2D optimal constraint fuzzy fault-tolerant control method for a nonlinear batch process, the specific steps of which are:

Step 1. Establish a nonlinear batch process equivalent 2D-Rosser error augmentation model:

Step 1.1 Considering the actuator gain fault, according to the nonlinear and two-dimensional characteristics of the batch process, a 2D T-S fuzzy fault state space model is established, expressed by formula (1):

And its input and output constraints satisfy:

Among them, 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; are the upper bound constraint values of input and actual output respectively, t and k respectively represent the running time and batch in the batch; T _p represents the total running time of a batch; p is the number of premise variables; r is the number of fuzzy rules ; A _i , B _i , C _i are the system state matrix, system input matrix, and system output matrix under the corresponding fuzzy rule i; x(0,k) is the initial state of the kth batch; M _ij is the fuzzy set, M _ij (x _j (t,k)) is the membership degree of x _j (t,k) belonging to M _ij ; Depend on Available

Different α values are defined to indicate different fault types of actuators. When α>0, it means a partial failure; when α=0, it means a complete failure, which does not involve the problem of optimal controller;

For the partial failure of the actuator, α>0 needs to satisfy the following form:

where α ( α ≤1) and is a known constant;

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

It can be seen that to design u(t,k), it is only necessary to design k batches of update laws r(t,k) at time t, so as to realize the system output y(t,k) tracking 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)

make Then formula (1) is transformed into an equivalent error model as formula (5):

in, 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 the dimension-appropriate identity matrix; and let Then the above model is expressed as:

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

Step 2. Design an iterative learning control law for the batch process model with disturbance and actuator failure:

Step 2.1 Design a 2D predictive fault-tolerant controller for the above model (5) to achieve the minimum optimal control under the maximum disturbance and maximum fault, even if the model (5) reaches a steady state and satisfies the following robust performance index at each moment:

limit:

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

Step 2.2 defines the state feedback control law to make the system achieve quadratic stability, and the selected update law is:

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

in, Then its closed-loop prediction model is expressed as:

Step 2.3 uses the 2D Lyapunov function to prove the stability of the system, and defines the Lyapunov function as:

Among them, M>0

Step 2.4 Model (8c) can still run smoothly within the allowable range of faults, it must meet:

(1) 2D Lyapunov function inequality constraint:

(2) For a given positive semi-definite symmetric matrix R, Q, there is a positive-definite symmetric matrix M=diag{M ^h , M ^v }, a positive semi-definite symmetric matrix Matrix Y _i , Y _j (i=1,2,...r,), scalar ε _i ,ε _j ,γ,θ>0, 0<α<1, 0<μ<1, can make the following matrix The inequality holds:

and

and

in,

The robust update law gain is:

Therefore, the further update law is expressed as: Putting it into u(t,k)=u(t,k-1)+r(t,k), the 2D constrained iterative learning control law design u(t,k) can be obtained, and at the next moment, repeat Step 2.4, continue to solve the new control quantity u(t,k), and loop in turn.

Example

Consider a nonlinear continuous stirred tank:

Wherein, C _A is the concentration of A in the irreversible reaction (A → B) process; T is the reactor temperature; T _C is the cooling flow temperature, as the manipulated variable q=100 (L/min), V=100 (L) , C _Af ＝1(mol/L), T _f ＝400(K), ρ＝1000(g/L), C _P ＝1(J/gK), k ₀ ＝4.71×10 ⁸ (min ^-1 ) , E/R=8000(K), ΔH=-2×10 ⁵ (J/mol), UA=1×10 ⁵ (J/minK). The variable range is limited to 200≤T _C ≤450(K), 0.01≤C _A ≤1(mol/L), 250≤T≤500(K); y(t,k)=Cx(t,k) is the output . The above nonlinear model is transformed into:

in,

C=[1 0]

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

The simulation was run in 50 batches, each run for 600 steps. The evaluation index uses root sum of square error (RSSE) to evaluate the control effect.

The calculated initial stage controller gain 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].

This method designs a fuzzy iterative learning control law for the nonlinear batch process with disturbances and faults, which effectively solves the problem that the system model is difficult to deal with under nonlinear conditions and the problem of constrained fuzzy optimal fault-tolerant control method design in the case of faults. It effectively solves the problem that the control performance of the nonlinear batch process cannot be improved with the increase of the batch, realizes that the system can be optimized in real time within the variable constraint range regardless of whether there is a fault, improves the system control performance, and ensures the system in It can still run smoothly and have the best tracking performance in the worst case. Ultimately, energy saving, consumption reduction, cost reduction, and accidents endangering personal safety are reduced.

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.