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.     

Model reference robust adaptive control for a class of uncertain switched linear systems

In this paper, we proposed a model reference robust adaptive control approach for a class of uncertain switched linear systems, in which subsystems of the switched linear system are in control canonical form. The control architecture is composed of a switched reference system (SRS) and a switched adaptive controller (SAC). The SRS specifies the desired dynamics of the uncertain switched linear system, while the SAC makes the uncertain switched linear system dynamics track the SRS dynamics. By multiple Lyapunov functions method, we prove that the closed‐loop switched system is uniformly bounded under arbitrary switching laws, provided that a linear matrix inequality (LMI)‐based sufficient condition is satisfied. We apply the proposed approach to a typical servo‐hydraulic positioning system. The simulation results show that the proposed approach is fairly insensitive to disturbances, uncertainties and non‐smoothly varying dynamics, and performs better than a proportional‐derivative controller or a minimal controller synthesis controller. Copyright © 2011 John Wiley & Sons, Ltd.     

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     

Target point‐based path‐following controller for a car‐type vehicle using bounded controls

In this paper, we have studied the control problem of target point‐based path following for car‐type vehicles. This special path‐following task arises from the needs of vision‐based guidance systems, where a given target point located ahead of the vehicle, in the visual range of the camera, must follow a specified path. A solution to this problem is developed through a nonlinear transformation of the path‐following problem into a reference trajectory tracking problem, by modeling the target point as a virtual vehicle. The use of target point complicates the control problem, as the development produces a first‐order nonlinear nonglobally Lipschitz differential equation with finite escape time. This problem is solved by using small control signals. Bounded feedback laws are designed to control the real vehicle's angular acceleration and the virtual vehicle's velocity, to achieve stability. The resulting controller is globally asymptotically stable with respect to the origin, the proof of which is derived from Lyapunov‐based arguments and a bootstrap argument. It is also shown that the use of exponentially convergent observers/differentiators does not affect the stability of the closed‐loop system. The effectiveness of this controller has been illustrated through simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

optimization‐based fractional‐order PID controllers design

In this paper we propose a fractional‐order proportional‐integral‐derivative controller design based on the solution of an model matching problem for fractional first‐order‐plus‐dead‐time processes. Starting from the analytical solution of the problem, we show that a fractional proportional‐integral‐derivative suboptimal controller can be obtained. Guidelines for the tuning of the controller parameters are given in order to address the robust stability issue and to obtain the required performance. The main differences with respect to the integer‐order case are highlighted. Simulation results show that the design methodology is effective and allows the user to consider process with different dynamics in a unified framework. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Gpc‐Based Self‐Tuning PI Controller for Speed Servo System of PMSLM

In this paper, a generalized predictive control (GPC)‐based two degrees of freedom (2 DOF) proportional integral (PI) controller is proposed for the speed servo system of a permanent magnet synchronous linear motor (PMSLM). In this new approach, based on a dynamic model of a servo system, a simplified and high‐performance GPC supplies a 2 DOF PI controller with suitable control parameters, according to the varied operating conditions. In previous studies, GPC‐based proportional integral derivative (PID) controllers have been designed using a step‐type or ramp‐type reference input. In our work, however, the speed command for PMSLM usually is required to be a trapezium‐type signal because of the limited travel range. Hence, control performance of a speed servo system using a GPC‐based 2 DOF PI controller is enhanced for tracking a trapezium‐type command. The validity and usefulness of the proposed controller are verified through simulation and experiments.     

Robust saturation‐based control of bilateral teleoperation without velocity measurements

This paper addresses the control design problem under no velocity measurements for nonlinear teleoperation system in the presence of asymmetric time‐varying delays. Based on the proposed proportional‐derivative‐like controller and nonlinear‐proportional‐derivative‐like controller, which correspond, respectively, to the actuator non‐saturation and actuator saturation, the control objectives of boundedness of velocities and position tracking errors for the master robot and the slave robot are obtained. These designed controllers do not rely on the velocity signals. The effectiveness of the proposed controller are finally verified by two numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

A distributed leader‐following tracking controller using delayed control input information from neighbors

In this paper, we propose a simple, continuous, and distributed controller for the second‐order multiagent system to achieve leader‐following trajectory tracking, by exploiting the control input information of neighbors (CIIN) and using proportional‐derivative (PD) control in terms of local neighborhood synchronization error. A constant time delay is introduced in the CIIN as a design parameter to avoid the algebraic loop issue arising from the control input coupling. We develop an easily testable condition on the PD gains to ensure that the resulting neutral‐type error system is input‐to‐state stable for an arbitrary bounded delay, and prove that when the leader's acceleration is a Lipschitz continuous function with respect to time, the ultimate bound of tracking errors is strictly increasing with respect to the introduced time delay. Moreover, we analyze the robustness of the controller with respect to model uncertainties and show its potential advantages over two existing controllers in balancing the steady‐state tracking precision, the communication cost, and the continuity of controller signal. Finally, extensive simulations are conducted to show the effect of the delay on system stability, to verify the condition on PD gains, to confirm the robustness of the controller, and to demonstrate the detailed advantages.     

IMC–PID Design: Analytical Optimization for Performance/Robustness Tradeoff Tuning for Servo/Regulation Mode

This paper addresses the analytical design of a one‐degree‐of‐freedom (1‐DoF) robust proportional–integral–derivative (PID) controller for the servo/regulation mode in line with the enhanced internal model control (IMC) principle based on a first order plus dead time (FOPDT) model. The proposed enhanced IMC–PID can provide acceptable performance both for set‐point tracking and for load disturbance rejection. The design procedure is formulated as a constrained optimization problem, in which the robustness of the system is adequately considered. Therefore, the resulting PID controller gives optimal performance with an exact selected robustness degree. Illustrative examples are given to show the effectiveness and merits of the analytical tuning rules for a wide range of plants.     

A STABLE ON‐LINE SELF‐TUNING OPTIMAL PID CONTROLLER FOR A CLASS OF UNKNOWN SYSTEMS

In this paper, a novel self‐tuning method of optimal PID control laws is proposed for both continuous‐time systems and discrete‐time systems. The controlled plant is assumed to be unknown except the system order (or system delay) and the direction of transmitting control input. Through the minimization of PID gains subject to the Lyapunov stability based reaching condition, the tuning of the three PID control gains is transformed to solve the inequality constraint optimization problem. An unknown SISO nonlinear system subject to a unit step input, and the tracking control problem of the piezoelectric actuator (PZA) with unknown dynamics are simulated. The simulation results show that the excellent tracking performance can be achieved.     

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 Output Feedback Stabilization of Switched Nonlinear Systems with Average Dwell Time

For some switched nonlinear systems, stabilization can be achieved under arbitrary switching with state feedback control. Due to switching zero dynamics, output feedback stabilization for some switched nonlinear systems needs dwell time between switching to guarantee system stability. In this paper, we consider a class of switched nonlinear systems with unknown parameters and unknown switching signals. We design a robust output feedback controller that stabilizes the system under a class of switching signals with average dwell time (ADT) where the value of ADT can be reduced by adjusting the control gain. For some special cases, common quadratic Lyapunov functions of the closed‐loop systems can be found and the value of ADT is further relaxed. Some examples and simulations are provided to validate the results.     

Model and robust gain‐scheduled PID control of a bio‐inspired morphing UAV based on LPV method

In this paper, a linear parameter‐varying (LPV)‐based model and robust gain‐scheduled structural proportion integral and derivative (PID) control design solution are proposed and applied on a bio‐inspired morphing wing unmanned aerial vehicle (UAV) for the morphing process. In the LPV model method, the authors propose an improved modeling method for LPV systems. The method combines partial linearization and function substitution. Using the proposed method, we can choose the varying parameters simply, thus creating a model that is more flexible and applicable. Then, a robust gain‐scheduled structural PID control design method is given by introducing a structural matrix to design a structural PID controller, which is more consistent with the structure of the PID controller used in practice and has a simpler structure than representative ones in the existing literature. The simulation results show that the developed LPV morphing UAV model is able to catch the response of the original nonlinear model with a smaller error than the existing Jacobian linearization method and the designed controller can maintain stable flights in practice with satisfactory robustness and performance.     

Delay‐ and Packet‐Disordering‐Dependent H∞ Output Tracking Control for Networked Control Systems

This paper is concerned with the problem of H_∞ output tracking control for networked control systems (NCSs) with network‐induced delay and packet disordering. Different from the results in existing literature, the controller design in this paper is both delay‐ and packet‐disordering‐dependent. Based on the different cases of consecutive predictions, the networked output tracking system is modeled into a switched system. Moreover, by the corresponding switching‐based Lyapunov functional approach, a linear matrix inequality (LMI)‐based procedure is proposed for designing state‐feedback controllers, which guarantees that the output of the closed‐loop NCSs tracks the output of a given reference model well in the H_∞ sense. In addition, the proposed method can be applied variously due to all kinds of prediction numbers of the consecutive disordering packet have been considered, and the designed controller is based on the prediction case in the last transmission interval, which brings about less conservatism. Finally numerical examples and simulations are used to illustrate the effectiveness and validity of the proposed switching‐based method and the delay‐ and packet‐disordering‐dependent H_∞ output tracking controller design.     

ROBUST FAULT‐TOLERANT CONTROL FOR A CLASS OF SWITCHED NONLINEAR SYSTEMS IN LOWER TRIANGULAR FORM

This paper investigates the problem of robust fault‐tolerant control for a class of uncertain switched nonlinear systems in lower triangular form. A system of this class involves parameter uncertainties and unknown nonlinear disturbances. A sufficient condition for the problem to be solvable under arbitrary switching is given in terms of linear matrix inequalities (LMIs). State feedback controllers of subsystems are designed by using the solutions to the matrix inequalities to guarantee global asymptotic stability of the closed‐loop systems in presence of actuator failures and under arbitrary switching. A practical system of hybrid haptic display is analyzed to demonstrate the proposed design method.     

Guaranteed cost PID control for uncertain discrete‐time stochastic systems with additive gain perturbations

This paper investigates a novel design method for robust nonfragile proportional‐integral‐derivative (PID) control that is based on the guaranteed cost control (GCC) problem for a class of uncertain discrete‐time stochastic systems with additive gain perturbations. On the basis of linear matrix inequality (LMI), a class of fixed PID controller parameters is obtained, and some sufficient conditions for the existence of the GCC are derived. Although the additive gain perturbations are included in the feedback systems, both the stability of closed‐loop systems and adequate cost bound are attained. As a sequel, decentralized GCC PID for a class of discrete‐time uncertain large‐scale stochastic systems is also considered. Finally, the numerical results demonstrate the efficiency of the proposed controller synthesis. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

NON‐PDC Observer‐Based T‐S Fuzzy Tracking Controller Design and its Application in CHAOS Control

In many mechanical devices with chaotic behavior, stabilizing unstable periodic orbits (UPOs) of the system has positive effects in the lifetime and effectiveness of these devices. In this study, a new non‐parallel distributed compensation (non‐PDC) observer‐based tracking controller is presented for Takagi–Sugeno fuzzy systems to control the chaotic behavior of such systems. Asymptotic stability synthesis of the closed‐loop system is investigated using a fuzzy Lyapunov function to derive less conservative conditions than common quadratic Lyapunov function‐based approaches. To tackle the main drawback of the fuzzy Lyapunov‐based approaches, which assume some upper bounds on the derivatives of the fuzzy grade functions, we propose a new procedure by considering a constraint on the control signal. The new design conditions are given in the form of linear matrix inequalities (LMIs). The proposed control structure is applied to spinning disks in which chaos phenomena appear in lateral vibration. Simulation results are given to show the applicability of the proposed tracker to the UPO problem.     

Distributed event‐triggered feedback consensus control with state‐dependent threshold for general linear multi‐agent systems

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under undirected graphs. Based on state feedback, we propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus, without continuous communication in either controller update or triggering condition monitoring. Each agent only needs to monitor its own state continuously to determine if the event is triggered. It is proved that there is no Zeno behavior under the proposed consensus control algorithm. To relax the requirement of the state measurement of each agent, we further propose a novel distributed observer‐based event‐triggered consensus controller to solve the consensus problem in the case with output feedback and prove that there is no Zeno behavior exhibited. Finally, simulation results are given to illustrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Finite‐time angular velocity observers for rigid‐body attitude tracking with bounded inputs

The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite‐time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion‐based nonlinear proportional‐derivative controller using full‐state feedback is designed first, yielding uniformly almost globally finite‐time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional‐derivative controller ensures finite‐time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high‐gain injection, as opposed to the semi‐global results, but also overcome the unwinding problem associated with some quaternion‐based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.