A novel variable universe fuzzy controller based on cat swarm optimization (CSO-VUFC) is proposed to regulate the temperature of the reactor system, which is characterized by nonlinearity, large time delay, and uncertainty. In CSO-VUFC, firstly, corresponding contraction-expansion factors with the function form were, respectively, introduced for the input and output fuzzy universes of the controller. Then, cat swarm optimization was used to optimize the relevant parameter values in the contraction-expansion factor function to achieve the intelligence optimization of the contraction-expansion factors, based on the system performance test function as an evaluation index; the contradiction between the universe adjustment and control accuracy of the fuzzy controller will be effectively solved to achieve the online self-adjustment of the universe. The simulation results indicate that the variable universe adaptive fuzzy control method based on the cat swarm optimization has the features of high precision adjustment, short transient time, and hard real-time.
A fuzzy controller, which is designed based on experts’ experiences and is independent of the mathematical model of the controlled object, can be used to effectively control the objects with characteristics of nonlinearity, large time delay, and uncertainty. However, a fuzzy controller is essentially a differential controller and the contradiction between the number of control rules and accuracy leads to the deficiencies of low steady-state accuracy and poor adaptability [
In order to solve the above-mentioned problems, [
In the past, many optimization algorithms in the computational intelligence area such as the genetic algorithm (GA), simulated annealing (SA), and particle swarm optimization (PSO) have been used to tune the control parameters in order to find an optimal performance [
On the basis of the previous researchers, in this paper, a new variable universe fuzzy controller based on the cat swarm optimization (CSO-VUFC) is proposed and the temperature of a reactor is the controlled object, with the large time delay characteristics. Firstly, with analyzing and deciding the structure of contraction-expansion factor
Denote that If then
By letting
Illustration of variable universe.
Based on (
It is easy to find that
Generally speaking, a function Duality: Zero kept: Monotonicity: Normality: Compatibility:
At present, the contraction-expansion factors of universes have no unified form. The following equation is chosen as the contraction-expansion factor in this paper:
It is easy to verify that (
Generally, for a dual-input single-output fuzzy control system, the error
Based on (
Based on (
Cat swarm optimization (CSO) was proposed by Tsai et al. [
In the seeking mode, cats do not move, but just stay in a certain position and sense for the next best move, thus having only state and no velocity [ seeking memory pool (SMP): the seeking memory size for each cat to consider the candidate coordinates, seeking range of the selected dimension (SRD): the range to be varied for a selected dimension, counts of dimension to change (CDC): the index of dimensions to be mutated.
The steps involved in the seeking mode are as follows.
Generate
Execute the mutation operator on the replicated copies based on SRD and CDC, which could make each copy reach a new location.
Calculate the fitness values of all the copies in seeking memory pool.
Select the position relating to the best fitness value and move the cat to this location.
The tracing mode is a model established under the condition that cat is tracking a target, which uses a speed-displacement model to change the value in every dimension.
The steps involved in this mode are described as follows.
Every cat employs the following to update its velocity:
If so, it needs to be reset to a given boundary value.
According to the following, cat’s location is updated:
The structure of CSO-VUFC is illustrated in Figure
The structure of the CSO-VUFC.
The universes of The controller employed triangle membership function, as in Figure
Fuzzy membership function.
The design idea of CSO-VUFC can be summarized as follows: firstly, determine the universes of error, error rate, and control variable; then, initialize the fuzzy queries; finally, apply the cat swarm optimization algorithm to optimize the parameters of contraction-expansion factors to make the system output close to the setting value.
Implementation steps of CSO-VUFC are described as follows.
Separately identify the fuzzy universe of
Optimize Initialize the parameters of CSO; the population size of the cat group is 100; dimension of cat is 4 and the mixture ratio of two modes is 0.3; the seeking range of the selected dimension is 0.2; and the memory pool size is 20. Update the position and velocity of the cat group and calculate the fitness value of each cat; according to ( Separately calculate the fitness value of each cat Update the global optimal solution
Determine if the current output is desired. If so, terminate the process and return the global optimal solutions; otherwise, return to Step 2.
In this work, the experiments of optimizing relevant parameters of fuzzy controller by cat swarm optimization (CSO) were carried out based on MATLAB software. The temperature of the reactor, approximately a first-order lag process with dead time described in (
On the platform of the MATLAB software, from simulation of the CSO-VUFC controller, an optimal set of parameters is obtained and the evolution tracks of
Evolution track of
Evolution track of ITAE.
These optimized parameters are then applied in the design of the CSO-VUFC controller, and the controller is used to control the temperature of the reactor; the output is compared with the results of PID controller and traditional fuzzy controller (T-Fuzzy).
When the system is set with a step signal at 90°C, the simulation results of three methods are shown in Figure
Compared results of three controllers.
Rise time (S) | Overshoot (°C) | Regulation time (S) | |
---|---|---|---|
PID | 56 | 16 | 1323 |
T-Fuzzy | 214 | 9 | 1146 |
CSO-VUFC | 278 | 0.2 | 784 |
The curves of the temperature of three controllers.
From Figure
In this paper, as to the questions that the fuzzy universe for the conventional fuzzy controller cannot be adjusted in time at the time of the system operation, the variable universe fuzzy control method based on the cat swarm optimization is proposed. By, respectively, introducing the corresponding contraction-expansion factors with the function form in the input and output fuzzy universes of the controller. Then, cat swarm optimization was used to optimize the relevant parameter values in the contraction-expansion factor function to achieve the intelligence optimization of the contraction-expansion factors, based on the system performance test function as an evaluation index; the contradiction between the universe adjustment and control accuracy of the fuzzy controller will be effectively solved to achieve the online self-adjustment of the universe. The simulation results indicate that the variable universe adaptive fuzzy control method based on the cat swarm optimization has the features of high precision adjustment, short transient time, and hard real-time.
The authors declare that they have no competing interests.
This paper is supported by Zhejiang Provincial Natural Science Foundation of China (Grant no. LZ15F030005). Thanks are due to Dr. Keyu Pan, for his contribution to the paper by text sorting, proofreading, and modifying icons.