H ∞ PID controller design for Lur’e systems and its application to a ball and wheel apparatus

In this paper, we consider the problem of synthesizing proportional-integral-derivative (PID) controllers for a given Lur’e system in the presence of exogenous energy-bounded disturbance. Based on the circle criterion, sufficient conditions for guaranteeing closed-loop absolute stability and achieving disturbance attenuation are given in terms of the multi-objective H _∞ specifications. The results from the earlier work are then used to solve the resulting multi-objective H _∞ PID design problem. It is shown that for a fixed proportional gain, and by sweeping over a variable, the set of admissible integral and derivative gain values can be determined constructively using linear-programming techniques. The proposed synthesis method is used to design a PID controller for the ball and wheel system and the experimental results are presented to show effectiveness of the proposed method.     

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。     

LMI‐Based Robust PID Controller Design for Voltage Control of Islanded Microgrid

This paper presents the design of a robust proportional integral derivative (PID) controller for the control of a single phase microgrid voltage. A microgrid consists of loads, distributed generation units and several power‐electronics interfaced LC filter and voltage source inverter. These loads are unknown and parameters are uncertain which produce unmodeled load dynamics. This unmodeled load dynamics reduces the voltage tracking performance of the microgrid. The proposed controller gives the robustness of the system with unmodeled load dynamics. Under different kinds of uncertainties, PID controller guarantees the stability and provides zero steady‐state error and fast transient response. The robustness and optimal performance of the controller is obtained by using linear matrix inequality approach. The performance of the controller under different uncertainties is studied. Results indicate the robustness and high voltage tracking performance of the microgrid system.     

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.     

Large angle attitude control of spacecraft with actuator saturation

This paper presents spacecraft large angle attitude control problem with actuator saturation limit. Traditional approach for control design for the spacecraft large angle maneuver is a fixed gain proportional plus integral plus derivative (PID) controller using quaternion attitude variables with stability guarantee. Unwanted external disturbance inputs may induce excessively large error by the PID control. Anti-windup control and intelligent integrator are effective in reducing the rapid build up of the control signal due to, in particular, integral control action. Application of the anti-windup and intelligent integrator which already have been studied extensively in other areas is made to the large angle feedback controller minimizing reaction wheel type actuator saturation. Conventional PID controller is modified by augmenting additional control actions for the purpose of performance improvement.     

A Novel Cascaded PID Controller for Automatic Generation Control Analysis With Renewable Sources

Present day power scenarios demand a high quality uninterrupted power supply and needs environmental issues to be addressed. Both concerns can be dealt with by the introduction of the renewable sources to the existing power system. Thus, automatic generation control (AGC) with diverse renewable sources and a modified-cascaded controller are presented in the paper. Also, a new hybrid scheme of the improved teaching learning based optimization-differential evolution (hITLBO-DE) algorithm is applied for providing optimization of controller parameters. A study of the system with a technique such as TLBO applied to a proportional integral derivative (PID), integral double derivative (IDD) and PIDD is compared to hITLBO-DE tuned cascaded controller with dynamic load change.The suggested methodology has been extensively applied to a 2-area system with a diverse source power system with various operation time non-linearities such as dead-band of, generation rate constraint and reheat thermal units. The multi-area system with reheat thermal plants, hydel plants and a unit of a wind-diesel combination is tested with the cascaded controller scheme with a different controller setting for each area. The variation of the load is taken within 1% to 5% of the connected load and robustness analysis is shown by modifying essential factors simultaneously by ± 30%. Finally, the proposed scheme of controller and optimization technique is also tested with a 5-equal area thermal system with non-linearities. The simulation results demonstrate the superiority of the proposed controller and algorithm under a dynamically changing load.      

Optimal design of fractional order PID controller for time-delay systems: an IWLQR technique

ABSTRACT

In this paper, an optimal design based state feedback gain of fractional order proportional integral derivative (PID) controller for time delay system is proposed. The proposed optimal design is called as IWLQR, which will be the joined execution of both the invasive weed optimization (IWO) and linear quadratic regulator (LQR). The proposed technique modifies a fractional order proportional integral derivative (FOPID) regulator among a high order time delay scheme that achieves an elevated performance for a wide area. In the proposed methodology, the gain of the FOPID controller is tuned to achieve the desired responses which are determined using the LQR theory and the weight matrices of the LQR is anticipated with the assistance of IWO technique. The uniqueness of the projected technique is to reduce the fault in a PID regulator among the higher order time delay scheme by the aid of the increase limits of the regulator. The objective of the proposed control method is chosen in view of the set point parameters and the accomplished parameters from the time delay system. The projected method is employed to achieve the avoidance of high order time delay and the dependability restrictions such as tiny overrun, resolving time and fixed condition defect. This technique is carried out in MATLAB/Simulink platform and the results are separated by the earlier regulator junction representation like Z-N system, Wang technique, curve fitting technique, regression technique which illustrates the superior presentation of the anticipated abstaining in the existing work.     

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.     

Feedback QoS control scheme for wireless network applications

Wireless LAN networking is an indispensable technology in an All-IP network architecture to satisfy the “anytime and anywhere” communication requirement of end users. This investigation proposes feedback controllers designing based on dynamic quality-of-service requirement for wireless LAN multimedia services. During the controllers design process, the time-domain is replaced by the s-domain, simplifying the calculation. This work presents three controllers namely proportional integral (PI), proportional derivative (PD) and proportional integral derivative (PID). Experimental results show that systems that employ the proposed controllers can quickly achieve the required system performance. Additionally, the PID controller has the best performance, and can improve delay performance by a rate 11.44% that without the feedback controller. The PI controller is superior to the PD controller. The delay when using the PD is 6.2% less than that achieved without the feedback controller.     

Reliable computation of PID gain space for general second-order time-delay systems

This paper addresses the problem of determining the stability gain space of a PID controller for general second-order time-delay systems. First, a review of existing results and the associated drawbacks is presented. Subsequently, a new algorithm to compute the entire PID stability gain space is developed. The new algorithm is based upon existing results on the relationship between the stability of a quasi-polynomial and its derivatives, an extended version of the Hermit–Biehler theorem, and also the Nyquist criterion. The algorithm entails extraction of an admissible range for the PID parameter K_p, and then based on this range, a stability region in the (K_i ? K_d) plane is computed. Well-known examples are studied to demonstrate the reliability and accuracy of the results.     

First application of symbiotic organisms search algorithm to off-line optimization of PI parameters for DSP-based DC motor drives

To enhance the performance and dynamics of a direct current (DC) motor drive, this paper proposes a new alternative based on recently introduced powerful symbiotic organisms search (SOS) algorithm for tuning proportional integral parameters. While imitating the symbiotic behavior that is seen among organisms in an ecosystem, SOS has important features such that it does not require tuning parameters, and its implementation is very easy with efficient three phases. After obtaining the optimized values of K _p  − K _i pair within the accurately prepared simulation software, they are used in real time. By managing the DC motor speed-controlled system with DSP of TMS320F28335, several simulations and experimental results confirming the performance of our proposal are presented along with comparisons against those of particle swarm optimization (PSO), genetic algorithm (GA), and Ziegler–Nichols (Z–N) tuning method. Results explicitly show that SOS is the pioneer in yielding better tracking performance and load disturbance rejection capability of the concerned drive system, which is followed by PSO, GA, and Z–N method, respectively. This has been achieved due to the fact that the gains obtained by SOS are more performant than those obtained by other applied methods.

     

Design and Robust Performance Evaluation of a Fractional Order PID Controller Applied to a DC Motor

This paper proposes a methodology for the quantitative robustness evaluation of PID controllers employed in a DC motor. The robustness analysis is performed employing a 23 factorial experimental design for a fractional order proportional integral and derivative controller (FOPID), integer order proportional integral and derivative controller (IOPID) and the Skogestad internal model control controller (SIMC). The factors assumed in experiment are the presence of random noise, external disturbances in the system input and variable load. As output variables, the experimental design employs the system step response and the controller action. Practical implementation of FOPID and IOPID controllers uses the MATLAB stateflow toolbox and a NI data acquisition system. Results of the robustness analysis show that the FOPID controller has a better performance and robust stability against the experiment factors.      

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.     

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.     

Novel bacterial foraging-based ANFIS for speed control of matrix converter-fed industrial BLDC motors operated under low speed and high torque

In this paper, a novel adaptive neuro-fuzzy inference system (ANFIS)-based control technique optimized by Bacterial Foraging Optimization Algorithm for speed control of matrix converter (MC)-fed brushless direct current (BLDC) motor is presented. ANFIS is considered to be one of the most promising technologies for control of electrical drives fed by MC. Optimizing the training parameters of ANFIS, to improve its performance, is still being considered by several researchers recently. Parameters of the online ANFIS controller such as learning rate (η), forgetting factor (λ) and steepest descent momentum constant (α) are optimized by using the proposed algorithm. For the purpose of comparison, proportional integral derivative controller, fuzzy logic controller, PSO-ANFIS and BAT-ANFIS are considered. Set point tracking performances of the proposed system are carried out at various operating points for an industrial BLDC motor operating at a maximum rated speed of 380 rpm and torque of 6.4 N m. Time domain specifications such as rise time, settling time, peak time, steady-state error and peak overshoot in the presence and absence of load torque disturbances are presented. Time integral performance measures such as integral square error, integral absolute error, and integral time multiplied absolute error are analyzed for various operating conditions. Speed fluctuation in the output of BLDC motor is dependent on the source current harmonics of the inverter/converter. To illustrate this, total harmonic distortion (THD) analysis is carried out for the existing PWM inverter and the proposed MC, and it is proved that MC results in reduced THD, as compared to PWM inverter. Simulation results confirm that the proposed controller outperforms the other existing control techniques under various set speed and torque conditions. Statistical analysis is effectively carried out to prove the effectiveness of the proposed controller. Experimental analysis is performed to validate the performance of the proposed control scheme.

     

Teaching–learning based optimization algorithm based fuzzy-PID controller for automatic generation control of multi-area power system

This paper deals with the design of a novel fuzzy proportional–integral–derivative (PID) controller for automatic generation control (AGC) of a two unequal area interconnected thermal system. For the first time teaching–learning based optimization (TLBO) algorithm is applied in this area to obtain the parameters of the proposed fuzzy-PID controller. The design problem is formulated as an optimization problem and TLBO is employed to optimize the parameters of the fuzzy-PID controller. The superiority of proposed approach is demonstrated by comparing the results with some of the recently published approaches such as Lozi map based chaotic optimization algorithm (LCOA), genetic algorithm (GA), pattern search (PS) and simulated algorithm (SA) based PID controller for the same system under study employing the same objective function. It is observed that TLBO optimized fuzzy-PID controller gives better dynamic performance in terms of settling time, overshoot and undershoot in frequency and tie-line power deviation as compared to LCOA, GA, PS and SA based PID controllers. Further, robustness of the system is studied by varying all the system parameters from −50% to +50% in step of 25%. Analysis also reveals that TLBO optimized fuzzy-PID controller gains are quite robust and need not be reset for wide variation in system parameters.     

An intelligent coordinator design for GCSC and AGC in a two-area hybrid power system

This study addresses the design procedure of an optimized fuzzy fine-tuning (OFFT) approach as an intelligent coordinator for gate controlled series capacitors (GCSC) and automatic generation control (AGC) in hybrid multi-area power system. To do so, a detailed mathematical formulation for the participation of GCSC in tie-line power flow exchange is presented. The proposed OFFT approach is intended for valid adjustment of proportional–integral controller gains in GCSC structure and integral gain of secondary control loop in the AGC structure. Unlike the conventional classic controllers with constant gains that are generally designed for fixed operating conditions, the outlined approach demonstrates robust performance in load disturbances with adapting the gains of classic controllers. The parameters are adjusted in an online manner via the fuzzy logic method in which the sine cosine algorithm subjoined to optimize the fuzzy logic. To prove the scalability of the proposed approach, the design has also been implemented on a hybrid interconnected two-area power system with nonlinearity effect of governor dead band and generation rate constraint. Success of the proposed OFFT approach is established in three scenarios by comparing the dynamic performance of concerned power system with several optimization algorithms including artificial bee colony algorithm, genetic algorithm, improved particle swarm optimization algorithm, ant colony optimization algorithm and sine cosine algorithm.     

Fractional Control of a Humanoid Robot Reduced Model with Model Disturbances

There is an open discussion between those who defend mass-distributed models for humanoid robots and those in favor of simple concentrated models. Even though each of them has its advantages and disadvantages, little research has been conducted analyzing the control performance due to the mismatch between the model and the real robot, and how the simplifications affect the controller’s output. In this article we address this problem by combining a reduced model of the humanoid robot, which has an easier mathematical formulation and implementation, with a fractional order controller, which is robust to changes in the model parameters. This controller is a generalization of the well-known proportional–integral–derivative (PID) structure obtained from the application of Fractional Calculus for control, as will be discussed in this article. This control strategy guarantees the robustness of the system, minimizing the effects from the assumption that the robot has a simple mass distribution. The humanoid robot is modeled and identified as a triple inverted pendulum and, using a gain scheduling strategy, the performances of a classical PID controller and a fractional order PID controller are compared, tuning the controller parameters with a genetic algorithm.     

Some investigations on fuzzy P + fuzzy I + fuzzy D controller for non-stationary process

The paper addresses the adaptive behaviour of parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP+FI+FD) controller. The parallel FP+FI+FD controller is actually a non-linear adaptive controller whose gain changes continuously with output of the process under control. Two non-stationary processes, whose characteristics change with time, are considered for simulation study. Simulation is performed using software LabVIEW TM . The set-point tracking response of parallel FP+FI+FD is compared with conventional parallel proportional plus integral plus derivative (PID) controller, tuned with the Ziegler-Nichols (Z-N) tuning technique. Simulation results show that conventional PID controller fails to track the set-point and becomes unstable as the process changes its characteristic with time. But the parallel FP+FI+FD controller shows considerably much better set-point tracking response and does not deviate from steady state. Also, a huge spike is observed in the output of PID controller as the reference set-point and process parameters are changed, while the FP+FI+FD controller gives spike free control signal.     

基于PID神经元网络和内模控制的拥塞控制算法*

针对网络系统的大时滞和非线性特性,设计了一种新的拥塞控制算法,将PID神经元网络与内模控制相结合应用于主动队列管理中,并使用Lyapunov理论证明了此算法的稳定性。NS仿真结果表明,这种算法的稳态和瞬态性能都优于PID算法,并且在参数变化和负载扰动时具有很强的鲁棒性。