Hardware-in-the-loop experimental study on a fractional order networked control system testbed

Networked Control Systems (NCS) are of great interest in many industries because of their convenience in data sharing and manipulation remotely. However, there are several problems along with NCS itself due to the uncertainties in network communication. One issue inherent to NCS is the network-induced delays which may deteriorate the performance and may even cause instability of the system. Therefore a controller which can make the plant stable at large values of delay is always desirable in NCS systems. Our past work on Optimal Fractional Order Proportional Integral (OFOPI) controller showed that fractional order PI controllers have larger jitter margin (maximum value of delay for which system is stable) for lag-dominated systems when compared to traditional Proportional Integral Derivative (PID) controllers, whereas integer order PID controllers have larger jitter margin for delay-dominated systems. This paper aims at the design process of a tele-presence controller based on OFOPI tuning rules. To illustrate this, an extensive experimental study on the real-time Smart Wheel networked speed control system is performed using hardware-in-the-loop control. The real-time random delay in the world wide network is collected by pinging different locations, and is considered as the delay in our simulation and experimental systems. Comparisons are made with existing integer order PID controller. It is found that the proposed OFOPI controller is a promising controller and has faster response time than the traditional integer order PID controllers. Since the plant into consideration viz. the Smart Wheel is a delay-dominated system, it is verified that PID achieves larger jitter margin as compared to OFOPI tuning rules. Simulation results and real-time experiments showing comparisons between OFOPI and OPID tuning rules prove the significance of this method in NCS.     

Real-coded Genetic Algorithm for system identification and tuning of a modified Model Reference Adaptive Controller for a hybrid tank system

Modeling and controlling of level process is one of the most common problems in the process industry. As the level process is nonlinear, Model Reference Adaptive Control (MRAC) strategy is employed in this paper. To design an MRAC with equally good transient and steady state performance is a challenging task. The main objective of this paper is to design an MRAC with very good steady-state and transient performance for a nonlinear process such as the hybrid tank process. A modification to the MRAC scheme is proposed in this study. Real-coded Genetic Algorithm (RGA) is used to tune off-line the controller parameters. Three different versions of MRAC and also a Proportional Integral Derivative (PID) controller are employed, and their performances are compared by using MATLAB. Input–output data of a coupled tank setup of the hybrid tank process are obtained by using Lab VIEW and a system identification procedure is carried out. The accuracy of the resultant model is further improved by parameter tuning using RGA. The simulation results shows that the proposed controller gives better transient performance than the well-designed PID controller or the MRAC does; while giving equally good steady-state performance. It is concluded that the proposed controllers can be used to achieve very good transient and steady state performance during the control of any nonlinear process.     

Digital PID controller design for multivariable analogue systems with computational input-delay

This paper presents a new methodology to design MIMO digitalPID controllers for multivariable analogue systems with computationalinput time-delay. The preliminarily designed analogue PID controlleris refined using a newly developed state-feedback and state-feedforwardLQR approach. The optimally designed closed-loop system withthe refined MIMO analogue PID controller has pre-assigned closed-loopeigenvalues. A prediction-based digital redesign technique isdeveloped to discretize the cascaded MIMO analogue PID controller,such that the states of the digitally redesigned closed-loopsampled-data system with the MIMO digital PID controller areclose to those of the analogously designed closed-loop systemwith the refined MIMO analogue PID controller. The aforementioneddigital redesign technique is further modified based on thepredictive control method to cope with MIMO analogue systemswith input delay.     

Hardware Implementation of Fuzzy PID Controllers

For traditional hardware implementation of fuzzy PID controllers, it is large at computation and bad in real-time performance, so, a kind of PID control algorithm, whose gain parameters could be tuned by their fuzzy system, was selected as studying example for a novel idea of hardware implementation. In this paper, authors presented hardware network of memory address mapping to implement fuzzy PID control algorithm, and designed the corresponding hardware system. The idea actually realizes fusion of hardware and intelligent algorithm. The implementation effectively simplified hardware circuits, the whole controller is very simple without CPU. Meanwhile, it is very easy to use, only connecting the sensor/transducer, the driver and the actuator is OK. The controller is very rapid in response, it need only two A/D conversion periods for outputting a required control signal. So the implementation could meet real-time performance effectively.     

Development,design and experimental testing of fuzzy-based controllers for a laboratory scale sun-tracking heliostat

The objective of this study is to develop and design fuzzy-based controllers for experimental examination and application to a laboratory scale sun tracking heliostat with dynamic movement about azimuth and elevation axes. The experimental approach accounts for unknown parameters such as, nonlinear static and dynamic frictions, nonlinear and variant effect of gravity on system, magnetic saturation of motors, limitations of power source in supplying rush and steady current and variation in heliostat dynamics due to different spacial and time passing conditions. To meet the objective, a classical PI and PID as well as Fuzzy-PI (F-PI) and Fuzzy-PID (F-PID) controllers are designed and experimentally implemented. The performance of each controller is measured by means of evaluating a cost function that is based on the integral of absolute value of error signal. The results show that for azimuth-axis angle, the cost of F-PI controller for deviation from set point is 67% lower as compared with that of PI controller. Also, it is shown that the application of F-PI controller results in lower cost for elevation-axis angle by 36%, 40%, and 50%, when compared with PI, PID, and F-PID controllers, respectively.     

Robust control of a spatial robot using fuzzy sliding modes

In order to improve the performance of the sliding mode controller, fuzzy logic sliding mode controller is proposed in this study. The control gain of the conventional sliding mode controller is tuned by a fuzzy logic rule base and, also dynamic sliding surfaces are obtained by changing their slopes using the error states of the system in another fuzzy logic algorithm. These controllers are then combined in order to enhance the performance. Afterwards, proposed controllers were used in trajectory control of a three degrees of freedom spatial robot, which is subjected to noise and parameter variations. Finally, the controllers introduced are compared with a PID controller which is commonly used for control of robotic manipulators in industry. The results indicate the superior performance of the proposed controller.     

A conformal mapping based fractional order approach for sub-optimal tuning of PID controllers with guaranteed dominant pole placement

A novel conformal mapping based fractional order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PI^λD^μ) controller have been approximated in this paper vis-à-vis a LQR tuned conventional integer order PID controller, to achieve equivalent integer order PID control system. This approach eases the implementation of analog/digital realization of a FOPID controller with its integer order counterpart along with the advantages of fractional order controller preserved. It is shown here in the paper that decrease in the integro-differential operators of the FOPID/PI^λD^μ controller pushes the open loop zeros of the equivalent PID controller towards greater damping regions which gives a trajectory of the controller zeros and dominant closed loop poles. This trajectory is termed as “M-curve”. This phenomena is used to design a two-stage tuning algorithm which reduces the existing PID controller’s effort in a significant manner compared to that with a single stage LQR based pole placement method at a desired closed loop damping and frequency.     

Feedback control of combustion oscillations in combustion chambers

Model-based algorithms are generally employed in active control of combustion oscillations. Since practical combustion processes consist of complex thermal and acoustic couplings, their accurate models and parameters may not be obtained in advance economically, a model free controller is necessary for the control of thermoacoustic instabilities. Active compensation based control algorithm is applied in the suppression of combustion instabilities. Tuning the controller parameters on line, the amplitudes of the acoustic waves can be modulated to desired values. Simulations performed on a control oriented, typical longitudinal oscillations combustor model illustrate the controllers’ capability to attenuate combustion oscillations.     

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the controller effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective optimal state-feedback regulator design while minimizing another time domain integral performance index, comprising of a weighted sum of Integral of Time multiplied Squared Error (ITSE) and the controller effort. The proposed methodology is extended for a new kind of fractional order (FO) integral performance indices. The impact of fractional order (as any arbitrary real order) cost function on the LQR tuned PID control loops is highlighted in the present work, along with the achievable cost of control. Guidelines for the choice of integral order of the performance index are given depending on the characteristics of the process, to be controlled.     

Robust continuous-time and discrete-time flow control of a dam–river system. (II) Controller design

The paper presents robust design methods for the automatic control of a dam–river system, where the action variable is the upstream flow rate and the controlled variable the downstream flow rate. The system is modeled with a linear model derived analytically from simplified partial derivative equations describing open-channel flow dynamics. Two control methods (pole placement and Smith predictor) are compared in terms of performance and robustness. The pole placement is done on the sampled model, whereas the Smith predictor is based on the continuous model. Robustness is estimated with the use of margins and also with the use of a bound on multiplicative uncertainty taking into account the model errors, due to the nonlinear dynamics of the system. Simulations are carried out on a nonlinear model of the river and performance and robustness of both controllers are compared to the ones of a continuous-time PID controller.     

Advanced Optimal Feedback Control for Tracking of Real-Life Applications

Calculating the open–loop solution of an optimal control problem is just the first step to cope with the practical realization of real life applications. Feedback controllers, like the classical Linear Quadratic Regulator (LQR), are needed to compensate pertubations appearing in reality. Although these controllers have proven to be a powerful tool in many applications and to be robust enough to countervail most differences between simulation and practice, they are not optimal if disturbances in the system data occur. If these controllers are applied in a real process, the possibility of data disturbances force recomputing the feedback control law in real–time to preserve stability and optimality, at least approximately. For this purpose, variations of the classical closed–loop controller with the extention to a trackingtype controller are analysed by means of an industrial application of container cranes. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal PID controller of robots under stochastic uncertainty

In practice often it is not possible to specify exact model parameters. Hence, precomputed controller based on some parameter estimates can produce bad results. In this presentation the aim is to combine classical PID control theory and stochastic optimisation methods in order to obtain robust optimal feedback control. The method works with cost functions being minimized and takes into account stochastic parameter varations. After Taylor expansion to calculate expected cost functions and a few transformations an approximate deterministic substitute PID control problem follows. Here, retaining only linear terms, approximation of expectations and variances of the expected cost functions can be calculated explicitly. By means of splines, numerical approximations of the objective function and the differential equations are obtained then. Using stochastic optimization methods, random parameter variations are incorporated into the optimal control process. Hence, robust optimal feedback controls are obtained. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simple, robust, selftuning controller

This paper proposes a robust method for automatic tuning of parameters of a discrete PID controller. The tuning rules for SISO and MIMO systems are based on automatic determination of critical gain and critical frequency from the estimated model parameters. The plant model can be expressed by a transfer function in continuous and/or discrete form or by differential and/or difference equation. A simple control law using Takahashi discrete form is proposed. Simulations results prove that it is easy to use being able to handle minimum and nonminimum phase plant as well.     

A new hybrid algorithm based on optimal fuzzy controller in multimachine power system

In this article, a new methodology based on fuzzy proportional‐integral‐derivative (PID) controller is proposed to damp low frequency oscillation in multimachine power system where the parameters of proposed controller are optimized offline automatically by hybrid genetic algorithm (GA) and particle swarm optimization (PSO) techniques. This newly proposed method is more efficient because it cope with oscillations and different operating points. In this strategy, the controller is tuned online from the knowledge base and fuzzy interference. In the proposed method, for achieving the desired level of robust performance exact tuning of rule base and membership functions (MF) are very important. The motivation for using the GA and PSO as a hybrid method are to reduce fuzzy effort and take large parametric uncertainties in to account. This newly developed control strategy mixed the advantage of GA and PSO techniques to optimally tune the rule base and MF parameters of fuzzy controller that leads to a flexible controller with simple structure while is easy to implement. The proposed method is tested on three machine nine buses and 16 machine power systems with different operating conditions in present of disturbance and nonlinearity. The effectiveness of proposed controller is compared with robust PSS that tune using PSO and the fuzzy controller which is optimized rule base by GA through figure of demerit and integral of the time multiplied absolute value of the error performance indices. The results evaluation shows that the proposed method achieves good robust performance for a wide range of load change in the presents of disturbance and system nonlinearities and is superior to the other controllers. © 2014 Wiley Periodicals, Inc. Complexity 21: 78–93, 2015     

An indirect adaptive pole place for MIMO systems based on multirate sampling of the plant output

The use of multirate-output controllers in order to achieveadaptive pole placement in linear multiple-input multiple-outputsystems with unknown parameters is investigated for the firsttime. Multirate-output controllers contain a multirate samplingmechanism with different sampling period at each system output.Such {acute} control allows us to assign the poles of the sampledclosed-loop system arbitrarily in desired locations, and doesnot make assumptions on the plant other than controllability,observability, and the knowledge of two sets of structural indices,namely the controllability and the observability indices. Anindirect adaptive control scheme based on these sampled-datacontrollers is proposed, which estimates the controller parameterson line. Using the proposed adaptive algorithm, the problemof adaptive pole placement is reduced to the determination ofa fictitious static state-feedback controller, due to the meritsof dynamic multirate-output controllers. Known techniques resortto the direct computation of dynamic controllers. The controllerdeterminations here is based on the transformation of the discreteanalogue of the systems under control to a phase-variable canonicalform prior to the applications of the control design procedure.The solution of the problem can be obtained by a quite simpleutilization of the concept of state similarity transformation,whereas known techniques usually require the solution of matrixpolynomial Diophantine equations. Moreover, persistent excitationof the continuous-time plant is provided without assuming anyspecial richness of the reference signals.     

Minimizing the number of variable parameters for optimizing the fuzzy-controller

In the case of a few input and output variables fuzzy systems have a large number of variable parameters which make the practical design and optimization of fuzzy controllers more difficult. It is necessary to reduce the number of variable parameters to simplify the design of fuzzy controllers and to make it accessible to automated design methods. In this paper, the response characteristics and the quality of fuzzy controllers were analysed by using different variable parameters. The quality of a controller is evaluated by the deformation of the characteristic field under consideration of a similarity criterion and the Fourier analysis. It is shown that the reduction in the number of variable parameters does not necessarily result in a restriction of the quality of the fuzzy controller.     

PI controller design using artificial bee colony algorithm for MPPT of photovoltaic system supplied DC motor‐pump load

Maximum Power Point Tracking (MPPT) is used in Photovoltaic (PV) systems to maximize its output power. A new MPPT system has been suggested for PV‐DC motor pump system by designing two PI controllers. The first one is used to reach MPPT by monitoring the voltage and current of the PV array and adjusting the duty cycle of the DC/DC converter. The second PI controller is designed for speed control of DC series motor by setting the voltage fed to the DC series motor through another DC/DC converter. The suggested design problem of MPPT and speed controller is formulated as an optimization task which is solved by Artificial Bee Colony (ABC) to search for optimal parameters of PI controllers. Simulation results have shown the validity of the developed technique in delivering MPPT to DC series motor pump system under atmospheric conditions and tracking the reference speed of motor. Moreover, the performance of the ABC algorithm is compared with Genetic Algorithm for various disturbances to prove its robustness. © 2015 Wiley Periodicals, Inc. Complexity 21: 99–111, 2016     

Optimal PID control in case of random initial conditions

The aim of this presentation is to construct a robust optimal PID feedback controller, taking into account stochastic uncertainties in the initial conditions. Usually, a precomputed feedback control is based on exactly known model parameters. However, in practice, often exact information about model parameters and initial values is not given. Hence, having an inital point, which differs from the nominal values, a standard precomputed controller may produce bad results. Supposing now that the probability distribution of the random parameter variations is known, in the following stochastic optimisation methods will be applied in order to obtain robust optimal feedback controls. Taking into account stochastic parameter variations at the initial point, the method works with expected total costs arising from the primary control expenses and the tracking error. Furthermore, the free regulator parameters are selected then such that the expected total costs are minimized. After Taylor expansion to calculate expected cost functions and a few transformations an approximate deterministic substitute control problem follows. Here, retaining only linear terms, approximation of expectations and variances of the expected cost functions can be calculated explicitly. By means of splines, numerical approximations of the objective function and the differential equations are obtained then. Using stochastic optimization methods, random parameter variations are incorporated into the optimal control process. Hence, robust optimal feedback controls are obtained. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

孵化控制系统的模糊免疫PID控制算法研究

家禽孵化是一个复杂的生物学过程,实现其自动控制水平有着重大意义.针对孵化系统是一个多变量、强耦合、大滞后的复杂动态系统,提出一种模糊免疫P ID控制方法,该方法根据模糊控制原理对P ID参数进行在线修改,利用生物免疫机理调整非线性函数,然后用免疫修正进一步调整P ID系统参数,使被控对象具有良好的性能,实现了家禽孵化设备中温度、湿度和含氧量的智能控制.系统投入运行表明,动态响应好,控制精度高,鲁棒性高,易于各种孵化的实现,从而提高了孵化率.     

Model based fuzzy control

Fuzzy controllers can be made to adapt to changing process and environment dynamics. This paper presents one methodology to adapt the initial knowledge base to changing operating conditions. The membership functions associated with the process controller output are adjusted in response to future or past performance of the feedback control system. A linearized process model is identified on line and is used to predict the future performance to the controller. This performance index is used to adapt the controller as long as the identified process model is statistically reliable. If the process model is considered unreliable, then an index related to the past performance of the controller is used to make the adjustments.