CN112526889A - Optimization algorithm of PID-P temperature controller of sulfur-containing flue gas heat exchange system - Google Patents

Abstract

Translated fromChinese

本发明公开了一种含硫烟气换热系统PID‑P温度控制器优化算法，属于控制器参数整定策略及算法领域。其特征为在基本粒子群优化算法基础上引入了倒“S”型惯性权重递减策略来平衡算法的全局搜索和局部搜索能力；并且在PIF‑ITAE适应度函数的基础上提出PIF‑IITAE适应度函数来提高寻优算法的优良性。运用改进的粒子群优化算法整定相变烟气换热系统的PID‑P温度控制器参数，可以节省大量人力和时间资源，提高PID‑P温度控制器精度。

The invention discloses an optimization algorithm of a PID-P temperature controller of a sulfur-containing flue gas heat exchange system, and belongs to the field of controller parameter setting strategies and algorithms. It is characterized by introducing an inverted "S" type inertia weight decreasing strategy based on the basic particle swarm optimization algorithm to balance the global search and local search capabilities of the algorithm; and on the basis of the PIF-ITAE fitness function, the PIF-IITAE fitness is proposed. function to improve the goodness of the optimization algorithm. Using the improved particle swarm optimization algorithm to tune the PID-P temperature controller parameters of the phase change flue gas heat exchange system can save a lot of manpower and time resources and improve the accuracy of the PID-P temperature controller.

Description

Optimization algorithm of PID-P temperature controller of sulfur-containing flue gas heat exchange system

Technical Field

The invention belongs to the field of controller parameter setting strategies and algorithms, and particularly relates to a PID-P temperature controller optimization algorithm for a sulfur-containing flue gas heat exchange system.

Background

The controller parameter tuning is the core content of the control system design. The traditional parameter setting method of the cascade controller comprises a successive approximation method, a two-step setting method, a one-step setting method and the most common empirical trial and error method, wherein the methods are all based on manpower and have the defects of complex process and easiness in oscillation and overshoot, and particularly when the target is high-order and nonlinear. Meanwhile, the parameters of the manual setting controller can only be respectively set by different parameters, but the stability margin of each parameter also depends on other values, so that the optimal parameters are often difficult to set by a manual method.

In the 80 s of the 20 th century, a relay feedback technology is applied to the PID controller self-tuning of an industrial process, but the information of a critical point estimated by a standard relay feedback method is not accurate enough, so that a large error is generated when a high-order or large-time-lag object is met, and the response of a system is deteriorated; meanwhile, the relay feedback method also depends on a parameter setting formula.

At the end of the 20 th century, some intelligent PID controllers are newly developed, and the intelligent control technology is applied to the parameter setting process of the controllers, so that adverse factors such as large time lag, strong coupling and large disturbance in engineering are overcome.

The current more common controller parameter setting intelligent algorithms include a fuzzy algorithm, a neural network algorithm, a genetic algorithm, a particle swarm optimization algorithm and the like. The fuzzy algorithm completely depends on the establishment of an expert rule base; the particle swarm optimization algorithm and the genetic algorithm have many common points, both of which use fitness values to evaluate the individual goodness and the certain random search, but the particle swarm optimization algorithm determines the search according to the speed of the particle swarm optimization algorithm, has no obvious intersection and variation of the genetic algorithm, has a good mechanism to effectively balance the diversity and the directionality of the search process, and has simple principle, easy realization and less parameters needing to be adjusted, so the particle swarm optimization algorithm is widely applied to parameter optimization of a controller.

Disclosure of Invention

The invention aims to provide an optimization algorithm of a PID-P temperature controller of a sulfur-containing flue gas heat exchange system aiming at the problems in the prior art.

The technical scheme of the invention is as follows:

a PID-P temperature controller optimization algorithm of a sulfur-containing flue gas heat exchange system specifically comprises the following steps:

an inverse S-shaped inertial weight decreasing strategy and a PIF-IITAE fitness function are introduced on the basis of a basic particle swarm optimization algorithm to improve the advantages of the optimization algorithm.

The optimization algorithm process is as follows:

firstly, initializing the position and speed of each particle in a population, and respectively mapping the particle dimension to each parameter of a PID-P temperature controller in a phase change flue gas heat exchange system; secondly, updating the current optimal position of the ith particle in the jth dimension according to a fitness function, wherein i is a positive integer less than or equal to 50, and j is a positive integer less than or equal to 4; finally, when the fitness value accords with the convergence criterion, the PID-P temperature controller obtains the optimal parameter; otherwise, updating the position and the speed of the population according to the following formula, and simultaneously updating the current optimal position of each particle and the current optimal position of the population according to a fitness function respectively:

wherein v is_ijIs the velocity, x, of the ith particle in the jth dimension_ijIs the position of the ith particle in the jth dimension, r_1jAnd r_2jIs distributed in each dimension in [0,1 ]]Two independent random constants in between, c₁And c₂Is a learning factor, c₁Referred to as cognitive parameters, c₂Called the social parameter, k the current iteration number, w the inertial weight, p_ijIs the current optimal position of the ith particle in the jth dimension; p is a radical of_gjIs the current optimal position of all particles in the j-th dimension.

Further, an inverse S-type inertial weight decreasing strategy, namely an IWS-ISF-type inertial weight decreasing strategy, is adopted, and is mainly used for balancing the global search capability and the local search capability of the algorithm. The IWS-ISF type inertia weight decreasing strategy adopts the following formula:

wherein, w_startRepresenting the upper value of the inertial weight, w_endRepresents the lower limit of the inertial weight, Iter is the number of iterations, Iter_maxK is a proportionality coefficient for the maximum number of iterations.

The unit step response of the PID-P temperature controller parameters is set based on different inertia weight decreasing strategies and particle swarm optimization algorithms, specific performance index parameters are shown in the table 1, performance index values of the three inertia weight decreasing strategies are close to each other, and when the inertia weights are in an inverted S-shaped decreasing strategy, the fitness value can approach to 1096.67 only by iterating for 10 times. The inertial weight is in an inverted S-shaped descending strategy, so that the algorithm can keep a longer-time maximum value at the initial stage, the global search capability of the algorithm is enhanced, a longer-time minimum value is kept at the later stage of iteration, the local search capability of the algorithm is enhanced, the global optimal position in a population is reserved, and the convergence speed of the algorithm is accelerated.

Further, a PIF-IITAE fitness function is adopted, the PIF-IITAE fitness function is based on the PIF-ITAE fitness function, an improved IITAE performance index is provided according to an ITAE performance index, and an overshoot sigma item is introduced into the ITAE performance index; meanwhile, in order to keep the original good process quality of ITAE, a weight coefficient f is introduced₁And f₂To control the relative importance of the original ITAE term and the overshoot term in the ITAE performance index. Wherein f is₁Is 1;

，

is expressed by taking f_ITAEThe order of magnitude of the value; f. of_cIs constant, take 1.5; PIF is Performance index functionThe abbreviation of n; I. t, A and E represent integration, time, absolute value, and error, respectively. The PIF-IITAE fitness function is shown as follows:

wherein T represents the integration duration of the fitness function, T_1setIs a set value T of the temperature of the flue gas outlet of the flue gas heat exchanger₁And (t) is the outlet temperature value of the flue gas heat exchanger at t time, and t represents the running time of the controller.

Based on the unit step response of the system under different fitness function conditions, the specific performance index parameters are shown in table 2, and it can be seen that the IITAE index has a rapid and stable transition process and a small overshoot, and the IITAE index is a control system performance evaluation index with good engineering practicability and selectivity.

The invention has the following advantages:

the particle swarm algorithm determines searching according to own speed, obvious intersection and variation do not exist, the particle swarm algorithm has a good mechanism to effectively balance diversity and directionality of a searching process, and meanwhile, the particle swarm algorithm is simple in principle, easy to implement and less in parameters needing to be adjusted.

The PID-P temperature controller parameters of the phase change flue gas heat exchange system are optimized by using the particle swarm algorithm, so that a large amount of manpower and time resources can be saved, and the precision of the PID-P temperature controller is improved.

The PID-P temperature controller of the phase change flue gas heat exchange system is optimized by adopting a particle swarm algorithm based on an IWS-ISF type inertia weight decreasing strategy, the strategy strengthens the global search capability at the initial stage of the algorithm and the local search capability at the later stage of the algorithm, and the convergence speed is higher.

The particle swarm optimization algorithm based on the PIF-IITAE fitness function is adopted to set the PID-P temperature controller parameters of the phase change flue gas heat exchange system, so that the system has better dynamic and steady-state performance, the method is a control parameter optimization method with good engineering practicability and robustness, and design basis is provided for controlling the temperature of the flue gas at the outlet of the heat exchanger of the phase change flue gas heat exchange system.

Drawings

FIG. 1 is a system diagram of a PID-P temperature controller of a phase change flue gas heat exchange system of a specific embodiment;

FIG. 2 is a flow chart of a PID-P temperature controller particle swarm optimization algorithm of a specific embodiment;

FIG. 3 is a graph of unit step response of a PID-P temperature controller according to an embodiment.

Detailed Description

In order to more fully express the technical scheme provided by the invention, the following further description is carried out through specific examples:

a phase change recovery system for flue gas waste heat in front of a desulfurizing tower comprises two subsystems which are respectively defined as a phase change air heat exchange system and a phase change flue gas heat exchange system.

In the flue gas waste heat phase change recovery system, the lithium bromide dilute solution vaporizes liquid water in the phase change flue gas heat exchanger, and two-phase media containing steam and a lithium bromide concentrated solution enter a wall temperature regulator for gas-liquid separation; the steam directly enters the phase change air heat exchanger, is cooled by air into condensed water and is stored in a condensed water tank; the condensed water enters the wall temperature regulator through the electric regulating valve, is mixed with the lithium bromide concentrated solution to become dilute solution, and flows into the phase-change flue gas heat exchanger again.

The cascade PID-P temperature controller system diagram of the phase change flue gas heat exchange system is shown in figure 1, under the condition of constant pressure, the concentration of the lithium bromide aqueous solution directly influences the phase change temperature of the lithium bromide aqueous solution in the heat transfer process, the flow of condensed water from a condensed water tank is controlled by adjusting the opening of an actuator, namely an electric adjusting valve, and the concentration of the lithium bromide aqueous solution in a wall temperature regulator is indirectly controlled by a liquid level controller. When the acid dew point temperature of the sulfur-containing flue gas fluctuates greatly, the liquid level controller assists the temperature controller to adjust the wall temperature of the flue gas heat exchanger. In the figure, T₁₀Indicating the flue gas inlet temperature, T, of the flue gas heat exchanger₂₀Indicating wall temperature regulator or flue gas heat exchanger inletThe temperature of lithium bromide solution at the opening, h represents the liquid level of the wall temperature regulator, l represents the opening degree of the electric regulating valve, and q₁Expressing the volume flow of the solution at the outlet of the electric regulating valve or the volume flow of the solution at the inlet of the wall temperature regulator, K_DRepresenting the differential coefficient, K, of a PID controller_IIndicating the integral coefficient, K, of the PID controller_PIndicating the proportionality coefficient, K, of the PID controller_P0Representing the scaling factor of the cascaded controller.

And (3) setting parameters of a PID-P temperature controller of the sulfur-containing flue gas heat exchange system by adopting an inverse S-shaped inertia weight decreasing strategy and a particle swarm optimization algorithm improved by a PIF-IITAE fitness function.

The flow chart of the particle swarm optimization algorithm of the PID-P temperature controller of the sulfur-containing flue gas heat exchange system is shown in FIG. 2, wherein P is_ijIs the current optimal position of the ith particle in the jth dimension; p is a radical of_gjIs the current optimal position of all particles in the j-th dimension. Firstly, initializing the position and speed of each particle in the population, and respectively mapping the particle dimension to each parameter of a PID-P temperature controller in the phase change flue gas heat exchange system. Secondly, comparing the fitness value of the ith particle at the jth dimension position with the current optimal position of the particle, and updating according to a fitness function; then, the fitness values of the ith particle at the current optimal position of the jth dimension and all the particles at the current optimal position of the jth dimension are compared, and updating is carried out according to a fitness function; finally, when the iteration times are larger than the set maximum iteration times or the adaptability value is smaller than the set minimum adaptability value, the PID-P temperature controller obtains the optimal parameter K_D，K_I，K_P，K_P0(ii) a Otherwise, the positions and the speeds of the particles are updated according to a formula, and simultaneously the current optimal position of each particle and the current optimal position of the population are respectively updated according to a fitness function.

In order to verify the reliability of the new and improved particle swarm optimization algorithm, a unit step response graph of the PID-P temperature controller based on the particle swarm optimization algorithm is shown in FIG. 3, and it can be seen from the graph that the rise time difference between the original optimization algorithm and the improved optimization algorithm is not large, the adjustment time difference between the original optimization algorithm and the improved optimization algorithm is not large, but the overshoot of the improved optimization algorithm is obviously reduced compared with that of the original optimization algorithm. Obviously, the improved particle swarm optimization is effective for optimizing the parameters of the PID-P temperature controller of the sulfur-containing flue gas heat exchange system.

Claims (3)

Translated fromChinese

1.含硫烟气换热系统PID-P温度控制器优化算法，其特征在于：1. PID-P temperature controller optimization algorithm of sulfur-containing flue gas heat exchange system, is characterized in that:在基本粒子群优化算法基础上引入了倒“S”型惯性权重递减策略和PIF-IITAE适应度函数来提高寻优算法的优良性；On the basis of the basic particle swarm optimization algorithm, the inverted "S" type inertia weight decreasing strategy and the PIF-IITAE fitness function are introduced to improve the fineness of the optimization algorithm;所述优化算法过程是：The optimization algorithm process is:首先，初始化种群中每个粒子的位置和速度，粒子的维度分别映射到相变烟气换热系统中PID-P温度控制器的每个参数；其次，第i个粒子在第j维的当前最优位置将根据适应度函数更新，i为小于等于50的正整数，j为小于等于4的正整数；最后，当适应度值符合收敛准则时，PID-P温度控制器将获得最优参数；否则，根据如下公式更新种群的位置和速度，同时每个粒子的当前最优位置和种群的当前最优位置根据适应度函数分别更新：First, the position and velocity of each particle in the population are initialized, and the dimension of the particle is mapped to each parameter of the PID-P temperature controller in the phase change flue gas heat exchange system; secondly, the current value of the i-th particle in the j-th dimension The optimal position will be updated according to the fitness function, i is a positive integer less than or equal to 50, j is a positive integer less than or equal to 4; finally, when the fitness value meets the convergence criterion, the PID-P temperature controller will obtain the optimal parameters ; otherwise, the position and velocity of the population are updated according to the following formulas, and the current optimal position of each particle and the current optimal position of the population are updated respectively according to the fitness function:

其中v_ij为第i个粒子在第j维的速度，x_ij为第i个粒子在第j维的位置，r_1j和r_2j是在每个维度上分布在[0,1]之间的两个独立随机常数，c₁和c₂是学习因子，c₁称为认知参数，c₂称为社会参数，k是当前迭代次数，w是惯性权重，p_ij是第i个粒子在第j维上的当前最优位置；p_gj是所有粒子在第j维上的当前最优位置。where v_ij is the velocity of the ith particle in the jth dimension, x_ij is the position of the ith particle in the jth dimension, and r_1j and r_2j are distributed between [0, 1] in each dimension Two independent random constants, c₁ and c₂ are learning factors, c₁ is called a cognitive parameter, c₂ is called a social parameter, k is the current iteration number, w is the inertia weight, and p_ij is the ith particle in the The current optimal position in the j dimension; p_gj is the current optimal position of all particles in the jth dimension.2.根据权利要求1所述含硫烟气换热系统PID-P温度控制器优化算法，其特征在于，采用倒“S”型惯性权重递减策略，即IWS-ISF型惯性权重递减策略，来平衡算法的全局搜索和局部搜索能力， IWS-ISF型惯性权重递减策略采用如下公式：2. according to the described sulfur-containing flue gas heat exchange system PID-P temperature controller optimization algorithm of claim 1, it is characterized in that, adopt inverted "S" type inertia weight decreasing strategy, namely IWS-ISF type inertia weight decreasing strategy, come To balance the global search and local search capabilities of the algorithm, the IWS-ISF inertia weight decreasing strategy adopts the following formula:

其中，w_start代表惯性权重的上限值，w_end代表惯性权重的下限值，Iter为迭代次数，Iter_max为最大迭代次数，k为比例系数。Among them, w_start represents the upper limit of the inertia weight, w_end represents the lower limit of the inertia weight, Iter is the number of iterations, Iter_max is the maximum number of iterations, and k is the proportional coefficient.3.根据权利要求1所述含硫烟气换热系统PID-P温度控制器优化算法，其特征在于，采用的PIF-IITAE适应度函数是在PIF-ITAE适应度函数的基础上改进的，根据ITAE性能指标提出的改进IITAE性能指标，在ITAE性能指标中引入超调量σ项；同时为了保持ITAE原有的良好过程品质，引入权重系数f₁和f₂来控制原ITAE项和超调量项在IITAE性能指标中的相对重要性，PIF-IITAE适应度函数如下式所示：3. according to the described sulfur-containing flue gas heat exchange system PID-P temperature controller optimization algorithm of claim 1, it is characterized in that, the PIF-IITAE fitness function that adopts is improved on the basis of PIF-ITAE fitness function, According to the improved IITAE performance index proposed by the ITAE performance index, the overshoot σ term is introduced into the ITAE performance index; at the same time, in order to maintain the original good process quality of ITAE, weight coefficients f₁ and f₂ are introduced to control the original ITAE term and overshoot The relative importance of the quantity item in the IITAE performance index, the PIF-IITAE fitness function is as follows:

其中，T代表适应度函数的积分时长，T_1set为烟气换热器烟气出口温度设定值，T₁（t）为烟气换热器烟气在t时间的出口温度值，t代表控制器运行时间。Among them, T represents the integration time of the fitness function, T_1set is the set value of the flue gas outlet temperature of the flue gas heat exchanger, T₁ (t) is the outlet temperature value of the flue gas of the flue gas heat exchanger at time t, and t represents Controller runtime.

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