Fuzzy control of a neutralization process

This paper studies the control of pH neutralization processes using fuzzy controllers. As the process to be controlled is highly nonlinear the usual PI-type fuzzy controller is not able to control these systems adequately. To solve this problem, based on prior knowledge of the process, the pH neutralization process is divided into several fuzzy regions such as high-gain, medium-gain and low-gain, with an auxiliary variable used to detect the process operation region. Then, a fuzzy logic controller can also be designed using this auxiliary variable as input, giving adequate performance in all regions. This controller has been tested in real-time on a laboratory plant. On-line results show that the designed control system operates the plant in a range of pH values, despite perturbations and variations of the plant parameters, obtaining good performance at the desired working points.     

基于跟踪误差调节的非线性自适应模糊预测控制

将模糊逻辑系统引入预测控制,对一类非线性离散系统提出了直接自适应模糊预测控制的方法,此方法首先建立被控对象的预测模型;然后基于此模型直接利用模糊逻辑系统设计预测控制器,并基于跟踪误差对控制器参数中的未知向量进行自适应调整;最后证明了此方法可使跟踪误差收敛到原点的一个小邻域内。     

Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems

A fuzzy logic controller equipped with a training algorithm is developed such that the H^∞ tracking performance should be satisfied for a model-free nonlinear multiple-input multiple-output (MIMO) system, with external disturbances. Due to universal approximation theorem, fuzzy control provides nonlinear controller, i.e., fuzzy logic controllers, to perform the unknown nonlinear control actions and the tracking error, because of the matching error and external disturbance is attenuated to arbitrary desired level by using H^∞ tracking design technique. In this paper, a new direct adaptive interval type-2 fuzzy controller is developed to handle the training data corrupted by noise or rule uncertainties for nonlinear MIMO systems involving external disturbances. Therefore, linguistic fuzzy control rules can be directly incorporated into the controller and combine the H^∞ attenuation technique. Simulation results show that the interval type-2 fuzzy logic system can handle unpredicted internal disturbance, data uncertainties, very well, but the adaptive type-1 fuzzy controller must spend more control effort in order to deal with noisy training data. Furthermore, the adaptive interval type-2 fuzzy controller can perform successful control and guarantee the global stability of the resulting closed-loop system and the tracking performance can be achieved.     

一类未知非线性离散系统的直接自适应模糊预测控制

将自适应模糊逻辑系统引入预测控制,对一类未知非线性离散系统提出了直接自适应 模糊预测控制方法.首先对被控对象提出了线性时变子模型加非线性子模型的预测模型,然后直 接利用模糊逻辑系统设计预测控制器,并基于广义误差估计值对控制器参数和广义误差估计值中 的未知向量进行自适应调整.文中证明了此方法可使广义误差估计值收敛到原点的小邻域内.     

高速公路非线性反馈模糊逻辑匝道控制器

入口匝道控制是高速公路交通控制和智能运输系统的重要组成部分,但现有的入口匝道控制效果尚不理想.为此,本文提出一种非线性反馈方法用模糊逻辑进行入口匝道控制.建立了高速公路交通流动态模型,在此基础上,结合模糊逻辑理论设计了非线性反馈匝道控制器,根据密度误差和误差变化用模糊控制决定匝道调节率,模糊变量选用三角形隶属度函数,并制定了包含56条模糊规则的规则库,最后用MATLAB软件进行系统仿真.结果表明该控制器具有优越的动态和稳态性能,它能使高速公路主线交通流密度保持为设定的期望密度,该方法用在高速公路入口匝道控制中效果良好.     

Steady-state error of a system with fuzzy controller

We consider the problem of control error of a fuzzy system with feedback. The system consists of a plant, linear or nonlinear, fuzzy controller, and feedback loop. As controller we use both PD and PI fuzzy type controllers. We apply different t-norm and co-norm: logic, algebraic, Yager, Hamacher, bounded, drastic, etc. in the process of fuzzy reasoning. Triangular shape of membership functions is supposed, but we generalize the results obtained. Steady-state error of a system is calculated. We have obtained very interesting results. The steady-state error is identical for pairs of triangular t- and co-norms.     

Fuzzy logic based attitude control of the spacecraft X-38 along a nominal re-entry trajectory

Fuzzy logic control techniques are investigated for applications in the intelligent re-entry flight control of the ESA–NASA crew return vehicle. Three PD-Mamdani fuzzy controllers are constructed to control the inner-loop attitude dynamics, simulated by a fully nonlinear 3 degree-of-freedom simulator of the CRV. Each controller uses an angle tracking error and its derivative to calculate a commanded control surface deflection of the simulator. The input-domains are partitioned with 5 membership functions, resulting in 25 fuzzy rules for each rule-base. The output-domains are partitioned with 9 membership functions. The Mamdani controllers use a standard max–min inference process and a fast center of area method to calculate the crisp control signals. Simulation results show the ability to track a reference trajectory with acceptable performance, though the real strength of a nonlinear fuzzy logic controller is yet to be proven with more demanding benchmark trajectories.     

A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices

A novel fractional order (FO) fuzzy Proportional-Integral-Derivative (PID) controller has been proposed in this paper which works on the closed loop error and its fractional derivative as the input and has a fractional integrator in its output. The fractional order differ-integrations in the proposed fuzzy logic controller (FLC) are kept as design variables along with the input–output scaling factors (SF) and are optimized with Genetic Algorithm (GA) while minimizing several integral error indices along with the control signal as the objective function. Simulations studies are carried out to control a delayed nonlinear process and an open loop unstable process with time delay. The closed loop performances and controller efforts in each case are compared with conventional PID, fuzzy PID and PI^λD^μ controller subjected to different integral performance indices. Simulation results show that the proposed fractional order fuzzy PID controller outperforms the others in most cases.     

Interval type-2 fuzzy inverse controller design in nonlinear IMC structure

In the recent years it has been demonstrated that type-2 fuzzy logic systems are more effective in modeling and control of complex nonlinear systems compared to type-1 fuzzy logic systems. An inverse controller based on type-2 fuzzy model can be proposed since inverse model controllers provide an efficient way to control nonlinear processes. Even though various fuzzy inversion methods have been devised for type-1 fuzzy logic systems up to now, there does not exist any method for type-2 fuzzy logic systems. In this study, a systematic method has been proposed to form the inverse of the interval type-2 Takagi-Sugeno fuzzy model based on a pure analytical method. The calculation of inverse model is done based on simple manipulations of the antecedent and consequence parts of the fuzzy model. Moreover, the type-2 fuzzy model and its inverse as the primary controller are embedded into a nonlinear internal model control structure to provide an effective and robust control performance. Finally, the proposed control scheme has been implemented on an experimental pH neutralization process where the beneficial sides are shown clearly.     

不需持续激励条件的非线性离散时间系统的自适应模糊逻辑控制

针对一类非线性离散时间系统，根据模糊逻辑系统的逼近性质，给出了一种自适应模糊逻辑控制器的设计方法。利用李亚普诺夫稳定性理论，证明了控制算法是全局稳定的，跟踪误差收敛于零的某一领域中。该设计方法克服了要求模糊基函数向量满足持续激励（PE）条件这一难以验证和满足的假设条件。     

未知多变量非线性系统自适应模糊预测控制

对一类未知多变量非线性系统提出了直接自适应模糊预测控制方法,此方法首先对被控对象提出了线性时变子模型加非线性子模型的预测模型,然后直接用模糊逻辑系统组成的向量来设计预测控制器,并基于时变死区函数对控制器中的未知向量和广义误差估计值中的未知矩阵进行自适应调整．文中证明了此方法可使广义误差向量估计值收敛到原点的一个邻域内．     

间歇精馏过程的模糊逻辑与增益自调整PID混合控制

针对间歇精馏过程的强非线性和非平稳时变特性,结合模糊逻辑控制和增益自调整PID控制的优点,提出了一种模糊逻辑和增益自调整PID混合控制的先进控制策略,详细推导了其控制算法,设计了相应的控制器,并在EuroBEEB工控机上用实时BASIC语言编程实现,对一套甲醇/水二元间歇精馏塔的塔顶浓度进行了推断控制实验,获得了比单独采用模糊逻辑控制时更好的控制结果。这说明,模糊逻辑和增益自调整PID混合控制是强非线性和非平稳时变过程的一种有效控制策略。     

Design and analysis of a fuzzy logic controller

The fuzzy logic controller (FLC) presented by Siler and Ying (1989) is discussed here and is proved to be equivalent to a non-fuzzy, nonlinear, proportional-integral (PI) controller. Some characteristic properties of this fuzzy logic controller are then investigated. The achievable performance of such a specific fuzzy controller is examined and found to be not necessarily better than that of the conventional, linear, non-fuzzy PI controller. Various extended designs of the basic FLC, including the FLC with dual control laws and the three-piece FLC, are then presented to enhance control performance. These extensions can provide servo-control performance. These extensions can provide servo-control performance superior to that of the basic FLC design, as illustrated by simulation results. Finally a highly nonlinear neutralization process is advanced to demonstrate the applicability of the various FLCs to industrial process control.     

控制方向未知的SISO非仿射系统间接自适应模糊输出反馈控制

针对一类单输入单输出(SISO)非仿射非线性系统控制方向未知时出现的控制器奇异问题,提出了一种间接自适应模糊控制方案.利用中值定理将非仿射系统转化为仿射系统,通过模糊逻辑系统逼近该仿射系统中的未知函数,并构造模糊控制器,同时利用Lyapunov稳定性定理设计自适应律,最终克服了控制器的奇异问题;在此基础上,通过构造观测器估计跟踪误差,设计输出反馈自适应模糊控制器,解决了状态不可测时系统控制器设计难题,采用Lyapunov稳定性定理证明控制器能使得跟踪误差收敛同时闭环系统所有信号均有界.仿真结果验证了所设计控制方案的可行性与有效性.     

基于模糊逼近的一类不确定非线性系统的容错控制

针对一类不确定非线性系统,提出了一种模糊容错控制方案.采用模糊T-S模型来逼近非线性系统,由线性矩阵不等式设计模糊模型的控制律.构建了模糊逻辑系统作为补偿器来抵消对非线性系统的建模误差和因故障引起的不确定性,并证明了闭环系统能够满足期望的跟踪性能.仿真实例表明了所提出容错控制方案的有效性.     

Controlling spillway gates of dams by using fuzzy logic controller with optimum rule number

Reservoir operation of dams during floods is a complex, nonlinear, nonstationary control process and is significantly affected by hydrological conditions which are not predictable beforehand. In this paper, an operation method based on fuzzy logic control is presented for the operation of spillway gates of reservoirs during floods. The rule base of fuzzy logic controller is optimally determined by using tabu search algorithm which is a modern popular heuristic algorithm. Simulation results demonstrate that the proposed approach based on fuzzy logic controller designed by using tabu search produces an accurate and efficient solution for the reservoir operation of dams.     

Fuzzy PI control design for an industrial weigh belt feeder

An industrial weigh belt feeder is used to transport solid materials into a manufacturing process at a constant feedrate. It exhibits nonlinear behavior because of motor friction, saturation, and quantization noise in the sensors, which makes standard autotuning methods difficult to implement. The paper proposes and experimentally demonstrates two types of fuzzy logic controllers for an industrial weigh belt feeder. The first type is a PI-like fuzzy logic controller (FLC). A gain scheduled PI-like FLC and a self-tuning PI-like FLC are presented. For the gain scheduled PI-like FLC the output scaling factor of the controller is gain scheduled with the change of setpoint. For the self-tuning PI-like FLC, the output scaling factor of the controller is modified online by an updating factor whose value is determined by a rule base with the error and change of error of the controlled variable as the inputs. A fuzzy PI controller is also presented, where the proportional and integral gains are tuned online based on fuzzy inference rules. Experimental results show the effectiveness of the proposed fuzzy logic controllers. A performance comparison of the three controllers is also given.     

Self-organizing fuzzy control of active suspension systems

A self-organizing fuzzy controller (SOFC) is proposed to control an active suspension system and evaluate its control performance. In complicated nonlinear system control, the SOFC continually updates the learning strategy in the form of fuzzy rules during the control process. The learning rate and the weighting distribution value of the controller are hard to regulate, so its fuzzy control rules may be excessively modified such that the system response generally causes an oscillatory phenomenon. Two fuzzy-logic controllers were designed according to the system output error and the error change, and introduced to the SOFC to determine the appropriate parameters of the learning rate and the weighting distribution, to eliminate this oscillation. This new modifying self-organizing fuzzy-control approach can effectively improve the control performance of the system, reduce the time consumed to establish a suitable fuzzy rule table, and support practically convenient fuzzy-controller applications in an active suspension control system, as verified experimentally.     

FLC design for bounded separable functions with linear input-outputrelations as a special case

A systematic procedure is presented for designing a knowledge base which exactly implements a specified bounded separable function in fuzzy logic. The design of a fuzzy logic control (FLC) for local linear control is a special case of the result. Examples, including controller design for a nonlinear process control application, are presented