Multi‐objective robust fuzzy fractional order proportional–integral–derivative controller design for nonlinear hydraulic turbine governing system using evolutionary computation techniques

The present paper proposes a novel multi‐objective robust fuzzy fractional order proportional–integral–derivative (PID) controller design for nonlinear hydraulic turbine governing system (HTGS) by using evolutionary computation techniques. The fuzzy fractional order PID (FOPID) controller takes closed loop error and its fractional derivative as inputs and performs fuzzy logic operations. Then, it produces the output through the fractional order integrator. The predominant advantages of the proposed controller are its capability to handle complex nonlinear processes like HTGS in heuristic manner, due to fuzzy incorporation and extending an additional flexibility in tuning the order of fractional derivative/integral terms to enhance the closed loop performance. The present work formulates the optimal tuning problem of fuzzy FOPID controller for HTGS as a multi‐objective one instead of a traditional single‐objective one towards satisfying the conflicting criteria such as less settling time and minimum damped oscillations simultaneously to ensure the improved dynamic performance of HTGS. The multi‐objective evolutionary computation techniques such as non‐dominated sorting genetic algorithm‐II (NSGA‐II) and modified NSGA‐II have been utilized to find the optimal input/output scaling factors of the proposed controller along with the order of fractional derivative/integral terms for HTGS system under no load and load turbulence conditions. The performance of the proposed fuzzy FOPID controller is compared with PID and FOPID controllers. The simulations have been conducted to test the tracking capability and robust performance of HTGS during dynamic set point changes for a wide range of operating conditions and model parameter variations, respectively. The proposed robust fuzzy FOPID controller has ensured better fitness value and better time domain specifications than the PID and FOPID controllers, during optimization towards satisfying the conflicting objectives such as less settling time and minimum damped oscillations simultaneously, due to its special inheritance of fuzzy and FOPID properties.     

Sensorless Inverter‐Fed Compressor Drive System Using Back‐EMF Estimator with PIDNN Torque Observer

A saliency back‐EMF estimator with a proportional–integral–derivative neural network (PIDNN) torque observer is proposed in this study to improve the speed estimating performance of a sensorless interior permanent magnet synchronous motor (IPMSM) drive system for an inverter‐fed compressor. The PIDNN torque observer is proposed to replace the conventional proportional–integral–derivative (PID) torque observer in a saliency back‐EMF estimator to improve the estimating performance of the rotor flux angle and speed. The proposed sensorless control scheme use square‐wave type voltage injection method as the start‐up strategy to achieve sinusoidal starting. When the motor speed gradually increases to a preset speed, the sensorless drive will switch to the conventional saliency back‐EMF estimator using the PID observer or the proposed saliency back‐EMF estimator using the PIDNN observer for medium and high speed control. The theories of the proposed saliency back‐EMF rotor flux angle and speed estimation method are introduced in detail. Moreover, the network structure, the online learning algorithms and the convergence analyses of the PIDNN are discussed. Furthermore, a DSP‐based control system is developed to implement the sensorless inverter‐fed compressor drive system. Finally, some experimental results are given to verify the feasibility of the proposed estimator.     

非线性系统的模糊免疫PSD控制与仿真

针对模糊免疫PID控制算法中微分与积分增益不能根据系统特性自动调整的问题,提出了一种模糊免疫PSD(Proportional Summation Derivative)控制算法。该方法将自适应PSD算法与模糊免疫PID算法相结合,利用自适应PSD控制算法根据过程误差的几何特性建立的PSD控制规律,使得模糊免疫PID控制算法中的微分和积分增益可以随比例增益的变化而自适应调整,从而进一步提高控制算法的自适应性能。仿真实验表明,采用该算法可以提高非线性、时变系统的控制性能,并能减少参数调整的工作量。     

Integration of Derivative Control on SIPIC in Motor Speed Control

The proportional–integral–derivative (PID) controller is the most commonly used controller in control application due to its simplicity. However, the control output may exceed the plant input limit which eventually deteriorates the system performance. This is known as a windup phenomenon, which causes large overshoot, long settling time and instability in the control system. Various anti‐windup methods have been introduced to overcome the windup phenomenon such as the Steady‐State Integral Proportional‐Integral Controller (SIPIC). Due to the coupling of the proportional, integral and derivative tuning gains, it is difficult to tune for non‐overshoot and short settling time to coexist in a PID. With decoupling, a greater range of tuning gains can be applied to control the rising slope without disturbing the damping state. Currently, SIPIC with decoupling effect has only been studied for the proportional and integral tuning gains. This paper presents the effect of integrating derivative control on SIPIC in motor speed control. SIPIC+D shows better speed control on a direct current motor under no‐load and loading conditions compared with other existing anti‐windup added with derivative control.     

An Extended State Observer Based Fractional Order Sliding‐Mode Control for a Novel Electro‐Hydraulic Servo System with Iso‐Actuation Balancing and Positioning

An extended state observer based fractional order sliding‐mode control (ESO‐FOSMC) is proposed in this study, with consideration of the strong nonlinear characteristics of a new electro‐hydraulic servo system with iso‐actuation balancing and positioning. By adopting the fractional order calculus theory, a fractional order proportional–integral–derivative (PID)‐based sliding mode surface was designed, which has the ability to obtain an equivalent positioning control with fractional order kinetic characteristics. By introducing the integral term into the sliding mode surface, it was found to be beneficial in reducing the steady‐state errors, as well as improving the precision of the control system. Also, by using the fractional order calculus to replace the integral calculus, the form of the convergence is improved; the system transfer of energy is slowed down; and the chattering of the system is greatly weakened. The extended state observer was designed to observe the real‐time disturbances, and also to generate the compensation control commands which are added to the FOSMC to achieve the dynamic compensation. By means of numerical simulations, the dynamic and static characteristics of the sliding mode control system were compared with those of the FOSMC and ESO‐FOSMC. The experimental results show that the ESO‐FOSMC system could effectively restrain the external disturbances and achieve higher control precision, as well as better control quantity without chattering. The semi‐physical simulations based experimental tests also demonstrated that the proposed ESO‐FOSMC outperformed the FOSMC in terms of system robustness and control precision, which could have a stable control of the gun system quickly and accurately.     

Quasi sliding mode‐based single input fuzzy self‐tuning decoupled fuzzy PI control for robot manipulators with uncertainty

This paper presents a robust adaptive control strategy for robot manipulators, based on the coupling of the fuzzy logic control with the so‐called sliding mode control (SMC) approach. The motivation for using SMC in robotics mainly relies on its appreciable features. However, the drawbacks of the conventional SMC, such as chattering effect and required a priori knowledge of the bounds of uncertainties can be destructive. In this paper, these problems are suitably circumvented by adopting a reduced rule base single input fuzzy self tuning decoupled fuzzy proportional integral sliding mode control approach. In this new approach a decoupled fuzzy proportional integral control is used and a reduced rule base single input fuzzy self‐tuning controller as a supervisory fuzzy system is added to adaptively tune the output control gain of the decoupled fuzzy proportional integral control. Moreover, it is proved that the fuzzy control surface of the single‐input fuzzy rule base is very close to the input/output relation of a straight line. Therefore, a varying output gain decoupled fuzzy proportional integral sliding mode control approach using an approximate line equation is then proposed. The stability of the system is guaranteed in the sense of the Lyapunov theorem. Simulations using the dynamic model of a 3DOF planar manipulator with uncertainties show the effectiveness of the approach in high speed trajectory tracking problems. The simulation results that are compared with the results of conventional SMC indicate that the control performance of the robot system is satisfactory and the proposed approach can achieve favorable tracking performance, and it is robust with regard to uncertainties and disturbances. Copyright © 2011 John Wiley & Sons, Ltd.     

Gradient‐based back‐propagation dynamical iterative learning scheme for the neuro‐fuzzy inference system

In this paper, a gradient‐based back propagation dynamical iterative learning algorithm is proposed for structure optimization and parameter tuning of the neuro‐fuzzy system. Premise and consequent parameters of the neuro‐fuzzy model are initialized randomly and then tuned by the proposed iterative algorithm. The learning algorithm is based on the first order partial derivative of the output with respect to the structure parameters. The first order derivative of the model output with respect to the structure parameters determines the sensitivity of the model to structure parameters. The sensitivity values are then used to set the tuning factors and parameters updating step sizes. Therefore, an adaptive dynamical iterative scheme is achieved which adapts the learning procedure to the current state of the performance during the optimization process. Larger tuning step sizes make the convergence speed higher and vice versa. In this regard, this parameter is treated according to the calculated sensitivity of the model to the parameter. The proposed learning algorithm is compared with the least square back propagation method, genetic algorithm and chaotic genetic algorithm in the neuro‐fuzzy model structure optimization. Smaller mean square error and shorter learning time are sought in this paper, and the performance of the proposed learning algorithm is versified regarding these criteria.     

Developments of fuzzy PID controllers

Abstract: This paper describes the development and tuning methods for a novel self-organizing fuzzy proportional integral derivative (PID) controller. Before applying fuzzy logic, the PID gains are tuned using a conventional tuning method. At supervisory level, fuzzy logic readjusts the PID gains online. In the first tuning method, fuzzy logic at the supervisory level readjusts the three PID gains during the system operation. In the second tuning method, fuzzy logic only readjusts the proportional PID gain, and the corresponding integral and derivative gains are readjusted using the Ziegler–Nichols tuning method while the system is in operation. For the compositional rule of inferences in the fuzzy PID and the self-organizing fuzzy PID schemes two new approaches are introduced: the min implication function with the mean of maxima defuzzification method, and the max-product implication function with the centre of gravity defuzzification method. The fuzzy PID controller, the self-organizing fuzzy PID controller and the PID controller are all applied to a non-linear revolute-joint robot arm for step input and path tracking experiments using computer simulation. For the step input and path tracking experiments, the novel self-organizing fuzzy PID controller produces a better output response than the fuzzy PID controller; and in turn both controllers exhibit better process output than the PID controller.     

Improved adaptive fault‐tolerant control design for hypersonic vehicle based on interval type‐2 T‐S model

This study proposes an improved adaptive fault estimation and accommodation algorithm for a hypersonic flight vehicle that uses an interval type‐2 Takagi‐Sugeno fuzzy model and a quantum switching module. First, an interval type‐2 Takagi‐Sugeno fuzzy model for the hypersonic flight vehicle system with elevator faults is developed to process the nonlinearity and parameter uncertainties. An improved adaptive fault estimation algorithm is then constructed by adding an adjustable parameter. The quantum switching module is also applied to the estimation part to select an appropriate algorithm in different fault cases. The estimation results from the given fuzzy observer are used to design a type‐2 fuzzy fault accommodation controller to stabilize the fuzzy system. The stability of the proposed scheme is analyzed using the Lyapunov stability theory. Finally, the validity and availability of the method are verified by a series of comparisons on numerical simulation results.     

Adaptive Control of the Electro‐Hydraulic Servo‐System with External Disturbances

The paper deals with the structure of the adaptive control electro‐hydraulic servo‐system (EHSS) with external load disturbances, practical verification of the identification, and control algorithms. The electro‐hydraulic servo system composed of a servo‐cylinder controlled with a servo‐valve is discussed. It is a strongly nonlinear object with parameters changing over time. Adaptive adjuster parameters were determined by means of current identification resulting in the parametric model. Identification was conducted on the basis of measurement of the controlling size and regulated size objects. The identified model of the object was applied to carry out the on‐line synthesis of the proportional–integral–derivative (PID) controller. The selected problems connected with obtaining the algorithm of adaptive control are presented. The computer program for implementing the algorithm with numerical simulation and identification of the control physical model object were calculated. The aim of the research was to examine the effectiveness of the adaptive control method in an electro‐hydraulic servo system, both theoretically and experimentally.     

The velocity control of an electro‐hydraulic displacement‐controlled system using adaptive fuzzy controller with self‐tuning fuzzy sliding mode compensation

Hydraulic servo control systems have been used widely in industry. Within the realm of hydraulic control systems, conventional hydraulic valve‐controlled systems have higher response and lower energy efficiency, whereas hydraulic displacement‐controlled servo systems have higher energy efficiency. This paper aims to investigate the velocity control performance of an electro‐hydraulic displacement‐controlled system (EHDCS), where the controlled hydraulic cylinder is altered by a variable displacement axial piston pump to achieve velocity control. For that, a novel adaptive fuzzy controller with self‐tuning fuzzy sliding‐mode compensation (AFC‐STFSMC) is proposed for velocity control in EHDCS. The AFC‐STFSMC approach combining adaptive fuzzy control and the self‐tuning fuzzy sliding‐mode control scheme, has the advantages of the capability of automatically adjusting the fuzzy rules and of reducing the fuzzy rules. The proposed AFC‐STFSMC scheme can design the sliding‐mode controller with no requirement on the system dynamic model, and it can be free of chattering, thereby providing stable tracking control performance and robustness against uncertainties. Moreover, the stability of the proposed scheme via the Lyapunov method is proven. Therefore, the velocity control of EHDCS controlled by AFC‐STFSMC is implemented and verified experimentally in different velocity targets and loading conditions. The experimental results show that the proposed AFC‐STFSMC method can achieve good velocity control performance and robustness in EHDCS with regard to parameter variations and external disturbance. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A new anti‐windup strategy for PID controllers with derivative filters

This paper presents a new strategy for suppressing the windup effect caused by actuator saturation in proportional–integral–derivative (PID) controlled systems. In the proposed approach, the windup effect is modeled as an external disturbance imported to the PID controller and an observer‐based auxiliary controller is designed to minimize the difference between the controller output signal and the system input signal in accordance with an H‐infinite optimization criterion. It is shown that the proposed anti‐windup (AW) scheme renders the performance of the controlled system more robust toward the effects of windup than conventional PID AW schemes and provides a better noise rejection capability. In addition, the proposed PID AW scheme is system independent and is an explicit function of the parameters of the original PID controller. As a result, the controller is easily implemented using either digital or analog circuits and facilitates a rapid, on‐line tuning of the controller parameters as required in order to prevent the windup effect. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Sensor runout compensation in active magnetic bearings via an integral adaptive observer

Sensor runout is one of the main sources of harmonic disturbances in active magnetic bearing systems. This type of the disturbance not only causes harmonic vibrations in the system but also changes the steady-state position of the axis of rotation from the geometric center of the AMB. In this paper, an integral adaptive observer is proposed to identify the dc and harmonic content of the sensor runout and to estimate the states of the system at the same time. The Lyapunov method is used to prove asymptotic stability of the proposed observer. Unlike the proportional observer which amplifies the measurement error, the sensor runout can be completely compensated when the states of the integral adaptive observer are used for feedback stabilization. It is shown that the proposed technique can also attenuate rotor displacements, when both sensor runout and mass unbalance disturbances are applied to the system. Simulation results have been presented for both cases to demonstrate the performance of the integral adaptive observer. Experimental results are also obtained by an AMB test rig, which confirm the effectiveness of the proposed method.     

Robust PID‐PSD Controller Design: BMI Approach

A new robust proportional‐integral‐derivative (PID)–proportional‐sum‐derivative (PSD) controller design method based on linear (bilinear) matrix inequalities (LMI, BMI) is proposed for uncertain affine linear system. The design procedure guarantees the parameter dependent quadratic stability, and guaranteed cost control with a new quadratic cost function (LQRS) including the derivative term for the state vector as a tool to influence the overshoot and response rate. The second approach to the PSD controller design procedure is based on a Lyapunov function with a special term corresponding to the time‐delay part of the control algorithm. The results obtained are illustrated on three examples to show the robust PID, PSD control design procedure and the influence of the choice of matrix S in the extended cost function.     

Design of model-based unbalance compensator with fuzzy gain tuning mechanism for an active magnetic bearing system

This paper deals with the unbalanced vibration problem of a stabilized active magnetic bearing (AMB) system. First, a model-based integral-type observer is proposed to evaluate the shaft displacement and the unbalancing forces of the rotor of an AMB system controlled by a proportional-integral-derivative (PID) controller. A fuzzy gain tuning mechanism is added to adjust the output of the PID controller in order to overcome the disturbances and suppress the unbalancing vibration. We have shown via simulation that the addition of the integral-type force observer improves the rotating accuracy in the device operating range. The experimental results demonstrate an efficient reduction of the shaft displacement of the rotor. Thus, the proposed scheme allows for a remarkable improvement in the unbalanced vibration of an AMB system over conventional PID controls without fuzzy gain tuning mechanism.     

Identification Recurrent Type 2 Fuzzy Wavelet Neural Network and L2‐Gain Adaptive Variable Sliding Mode Robust Control of Electro‐Hydraulic Servo System (EHSS)

An electro‐hydraulic servo system (EHSS) is a kind of system with the characteristics of time‐variant, serious nonlinearity, parameter and structural uncertainty, and uncertain load disturbance in most cases. These characteristics make it very difficult to realize highly accurate control by conventional methods. In order to solve the above problems, this paper introduces a recurrent type 2 fuzzy wavelet neural network to approximate the unknown nonlinear functions of the dynamic systems through tuning by the desired adaptive law. Based on the identification by recurrent type 2 fuzzy wavelet neural network, a L2 gain design method, combining gain adaptive variable sliding mode control with H infinity control, is proposed for load disturbance, thereby accommodating uncertainties that are the main factors affecting system stability and accuracy in EHSS. In this algorithm, a recurrent type 2 fuzzy wavelet neural network is employed to evaluate the unknown dynamic characteristics of the system and gain adaptive variable sliding mode control to compensate for evaluating errors, and H infinity control to suppress the effect on system by load disturbance. The experiment results show that the proposed system L2 gain design method can make the system exhibit strong robustness to parameter variation and load disturbance.     

Neural‐Adaptive Control and Nonlinear Observer for Waste‐To‐Energy Boilers

This paper looks at the problem of controlling an incinerator that burns waste gas to generate power. The system is modelled as a standard utility boiler using one known and one unknown (waste) fuel input. Standard linear controls have trouble dealing with large variations in the waste input, and in practice boiler shutdowns can occur. In this work, a nonlinear adaptive control design accounts for uncertainty in the plant parameters, and an adaptive neural‐network estimates the effect of the waste input. Since a linear observer design cannot guarantee convergence away from a set point, a novel nonlinear observer design provides estimates of the states. The observer design uses fictitious states to estimate nonlinear terms in the observer dynamics. The analysis guarantees Lyapunov stability, thus the observer bounds depend on the accuracy of the observer initial conditions. Simulation results show the proposed method can obtain accurate performance and stability, improving over results obtained withproportional–integral control.     

Decentralized PID neural network control for five degree-of-freedom active magneticbearing

A decentralized proportional–integral–derivative neural network (PIDNN) control scheme is proposed to regulate and stabilize a fully suspended five degree-of-freedom (DOF) active magnetic bearing (AMB) system which is composed of two radial AMBs (RAMBs) and one thrust AMB (TAMB). First, the structure and operating principles of the five-DOF AMB system are introduced. Then, the adopted differential driving mode (DDM) for the drive system of the AMB is analyzed. Moreover, due to the exact dynamic model of the five-DOF AMB system is vague, a decentralized PIDNN controller is proposed to control the five-axes of the rotor simultaneously in order to confront the uncertainties including inherent nonlinearities and external disturbances effectively. Furthermore, the connective weights of the PIDNN are trained on-line and the convergence analysis of the regulating error is provided using a discrete-type Lyapunov function. Based on the decentralized concepts, the computational burden is reduced and the controller design is simplified. Finally, the experimental results show that the proposed control scheme provides good control performances and robustness for controlling the fully suspended five-DOF AMB system in different operating conditions.