Maximum sensitivity based fractional IMC–PID controller design for non-integer order system with time delay

A simple approach with a small number of tuning parameters is a key goal in fractional order controller design. Recently there have been a number of limited attempts to bring about improvements in these areas. In this paper, a new design method for a fractional order PID controller based on internal model control (IMC) is proposed to handle non-integer order systems with time delay. In order to reduce the number of tuning parameters and mitigate the impact of time delay, the fractional order internal model control scheme is used. Considering the robustness of the control system with respect to process variations and model uncertainty, maximum sensitivity is applied to the tuning of the parameters. The resulting controller has the structure of a fractional order PID which is cascaded with a filter. This is named a fractional IMC–PID controller. Numerical results are given to show the efficiency of the proposed controller.     

Control quality enhancement using fractional PIλDμ controller

The proportional–integral–derivative (PID) controllers have remained, by far, the most commonly and practically used in all industrial feedback control applications; therefore, there is a continuous effort to improve the system control quality performances. More recently Podlubny has proposed the fractional PI^λD^μ controller, a generalisation of the classical PID controller, involving an integration action of order λ and differentiation action of order μ. Since then, many researchers have been interested in the use and tuning of this type of controller. In this article, a new conception method of this fractional PI^λD^μ controller is considered. The basic ideas of this new tuning method are based, in the first place, on the classical Ziegler–Nichols tuning method for setting the parameters of the fractional PI^λD^μ controller for λ = μ = 1, which means setting the parameters of the classical PID controller, and on the minimum integral squared error criterion by using the Hall–Sartorius method for setting the fractional integration action order λ and the fractional differentiation action order μ. Illustrative examples and simulation results are presented to show the control quality enhancement of this proposed fractional PI^λD^μ controller conception method compared to the PID controller conception using Ziegler–Nichols tuning method.     

Adaptive explicit force control of position-controlled manipulators

This article presents a new adaptive outer-loop approach for explicit force regulation of position-controlled robot manipulators. The strategy is computationally simple and does not require knowledge of the manipulator dynamic model, the inner-loop position controller parameters, or the environment. It is shown that the control strategy guarantees global uniform boundedness of all signals and convergence of the position/force regulation errors to zero when applied to the full nonlinear robot dynamic model. If bounded external disturbances are present, a slight modification to the control scheme ensures that global uniform boundedness of all signals is retained and that arbitrarily accurate stabilization of the regulation errors can be achieved. Additionally, it is shown that the adaptive controller is also applicable to robotic systems with PID inner-loop position controllers. Computer simulation results are given for a Robotics Research Corporation (RRC) Model K-1207 redundant arm and demonstrate that accurate and robust force control is achievable with the proposed controller. Experimental results are presented for the RRC Model K-1207 robot and confirm that the control scheme provides a simple and effective means of obtaining high-performance force control. © 1996 John Wiley & Sons, Inc.     

基于分数阶内模控制的风力机叶片颤振研究

针对风力机叶片颤振系统,提出了一种结合分数阶(Fractional Order)控制与内模控制(Internal Model Control,IMC)的新型颤振控制方法.利用分数阶滤波器设计了分数阶内模控制器,基于闭环动态特性指标,如相位裕量和截止频率,实现对控制器参数的自整定.通过仿真实验对比证明,针对风力机叶片颤振控制,所设计的控制方法优于传统PID、内模PID控制方法,不仅减少了控制参数,而且提高了动态特性和鲁棒性.     

A Biologically Inspired Biped Locomotion Strategy for Humanoid Robots: Modulation of Sinusoidal Patterns by a Coupled Oscillator Model

Biological systems seem to have a simpler but more robust locomotion strategy than that of the existing biped walking controllers for humanoid robots. We show that a humanoid robot can step and walk using simple sinusoidal desired joint trajectories with their phase adjusted by a coupled oscillator model. We use the center-of-pressure location and velocity to detect the phase of the lateral robot dynamics. This phase information is used to modulate the desired joint trajectories. We do not explicitly use dynamical parameters of the humanoid robot. We hypothesize that a similar mechanism may exist in biological systems. We applied the proposed biologically inspired control strategy to our newly developed human-sized humanoid robot computational brain (CB) and a small size humanoid robot, enabling them to generate successful stepping and walking patterns.     

Pitch Loop Control of a VTOL UAV Using Fractional Order Controller

Pitch loop control is the fundamental tuning step for vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs), and has significant impact on the flight. In this paper, a fractional order strategy is designed to control the pitch loop of a VTOL UAV. First, an auto-regressive with exogenous input (ARX) model is acquired and converted to a first-order plus time delay (FOPTD) model. Next, based on the FOPTD model, a fractional order [proportional integral] (FO[PI]) controller is designed. Then, an integer order PI controller based on the modified Ziegler-Nichols (MZNs) tuning rule and a general integer order proportional integral derivative (PID) controller are also designed for comparison following three design specifications. Simulation results have shown that the proposed fractional order controller outperforms both the MZNs PI controller and the integer order PID controller in terms of robustness and disturbance rejection. At last, ARX model based system identification of AggieAir VTOL platform is achieved with experimental flight data.     

分数阶系统的分数阶PID控制器设计

对于一些复杂的实际系统,用分数阶微积分方程建模要比整数阶模型更简洁准确.分数阶微积分也为描述动态过程提供了一个很好的工具.对于分数阶模型需要提出相应的分数阶控制器来提高控制效果.本文针对分数阶受控对象,提出了一种分数阶PID控制器的设计方法.并用具体实例演示了对于分数阶系统模型,采用分数阶控制器比采用古典的PID控制器取得更好的效果.     

Online Balance Controllers for a Hopping and Running Humanoid Robot

This paper describes online balance controllers for running in a humanoid robot and verifies the validity of the proposed controllers via experiments. To realize running in the humanoid robot, the overall control structure is composed of an offline controller and an online controller. The main purpose of the online controller is to maintain dynamic stability while the humanoid robot hops or runs. The online controller is composed of the posture balance control in the sagittal plane, the transient balance control in the frontal plane and the swing ankle pitch compensator in the sagittal plane. The posture balance controller makes the robot maintain balance using an inertial measurement unit sensor in the sagittal plane. The transient balance controller makes the robot keep its balance in the frontal plane using gyros attached to each upper leg. The swing ankle pitch compensator prevents the swing foot from hitting the ground at unexpected times while the robot runs forward. HUBO2 was used for the running experiment. It was designed for the running experiment, and is lighter and more powerful than the previous walking robot platform, HUBO. With the proposed controllers, HUBO2 ran forward stably at a maximum speed of 3.24 km/h and this result verified the effectiveness of the proposed algorithm. In addition, in order to show the contribution of the stability, the running performance according to the existence of each controller was described by experiment.     

PID auto-tuning using new model reduction method and explicit PID tuning rule for a fractional order plus time delay model

In this paper, a new model reduction method and an explicit PID tuning rule for the purpose of PID auto-tuning on the basis of a fractional order plus time delay model are proposed. The model reduction method directly fits the fractional order plus time delay model to frequency response data by solving a simple single-variable optimization problem. In addition, the optimal tuning parameters of the PID controller are obtained by solving the Integral of the Time weighted Absolute Error (ITAE) minimization problem and then, the proposed PID tuning rule in the form of an explicit formula is developed by fitting the parameters of the formula to the obtained optimal tuning parameters. The proposed tuning method provides almost the same performance as the optimal tuning parameters. Simulation study confirms that the auto-tuning strategy based on the proposed model reduction method and the PID tuning rule can successfully incorporate various types of process dynamics.     

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

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

Fuzzy sliding mode control of a finger of a humanoid robot hand

Abstract: The motion control problem for the finger of a humanoid robot hand is investigated. First, the index finger of the human hand is dynamically modelled as a kinematic chain of cylindrical links. During construction of the model, special attention is given to determining bone dimensions and masses that are similar to the real human hand. After the kinematic and dynamic analysis of the model, in order to ensure that the finger model tracks its desired trajectory during a closing motion, a fuzzy sliding mode controller is applied to the finger model. In this controller, a fuzzy logic algorithm is used in order to tune the control gain of the sliding mode controller; thus, an adaptive controller is obtained. Finally, numerical results, which include a performance comparison of the proposed fuzzy sliding mode controller and a conventional sliding mode controller, are presented. The results demonstrate that the proposed control method can be used to perform the desired motion task for humanoid robot hands efficiently.     

Model predictive control for fast reaching in clutter

A key challenge for haptically reaching in dense clutter is the frequent contact that can occur between the robot’s arm and the environment. We have previously used single-time-step model predictive control (MPC) to enable a robot to slowly reach into dense clutter using a quasistatic mechanical model. Rapid reaching in clutter would be desirable, but entails additional challenges due to dynamic phenomena that can lead to higher forces from impacts and other types of contact. In this paper, we present a multi-time-step MPC formulation that enables a robot to rapidly reach a target position in dense clutter, while regulating whole-body contact forces to be below a given threshold. Our controller models the dynamics of the arm in contact with the environment in order to predict how contact forces will change and how the robot’s end effector will move. It also models how joint velocities will influence potential impact forces. At each time step, our controller uses linear models to generate a convex optimization problem that it can solve efficiently. Through tens of thousands of trials in simulation, we show that with our dynamic MPC a simulated robot can, on average, reach goals 1.4 to 2 times faster than our previous controller, while attaining comparable success rates and fewer occurrences of high forces. We also conducted trials using a real 7 degree-of-freedom (DoF) humanoid robot arm with whole-arm tactile sensing. Our controller enabled the robot to rapidly reach target positions in dense artificial foliage while keeping contact forces low.     

Design of a fractional order PID controller for an AVR using particle swarm optimization

Application of fractional order PID (FOPID) controller to an automatic voltage regulator (AVR) is presented and studied in this paper. An FOPID is a PID whose derivative and integral orders are fractional numbers rather than integers. Design stage of such a controller consists of determining five parameters. This paper employs particle swarm optimization (PSO) algorithm to carry out the aforementioned design procedure. PSO is an advanced search procedure that has proved to have very high efficiency. A novel cost function is defined to facilitate the control strategy over both the time-domain and the frequency-domain specifications. Comparisons are made with a PID controller and it is shown that the proposed FOPID controller can highly improve the system robustness with respect to model uncertainties.     

A multivariable control scheme for robot manipulators

The article puts forward a simple scheme for multivariable control of robot manipulators to achieve trajectory tracking. The scheme is composed of an inner loop stabilizing controller and an outer loop tracking controller. The inner loop utilizes a multivariable PD controller to stabilize the robot by placing the poles of the linearized robot model at some desired locations. The outer loop employs a multivariable PID controller to achieve input-output decoupling and trajectory tracking. The gains of the PD and PID controllers are related directly to the linearized robot model by simple closed-form expressions. The controller gains are updated on-line to cope with variations in the robot model during gross motion and for payload change. Alternatively, the use of high gain controllers for gross motion and payload change is discussed. Computer simulation results are given for illustration.     

计及温控负荷响应的二维云模型分布式频率控制

为改善电力系统频率稳定性,充分调用需求侧可控负荷资源,本文提出一种计及温控负荷响应的二维云模型分布式频率控制方法。建立了多区域互联电力系统负荷频率控制模型,设计了基于福克普朗克方程的温控负荷分布式控制策略,同时采用云模型算法与分数阶微积分理论,设计了二维云模型分数阶PID分布式频率控制器。最后通过控制仿真比较与分析,验证了在不同运行场景下所提出的综合控制方法具有较优的动稳态性能。结果表明该控制方法是可行和有效的。     

一种分数阶内模TIλDemμ控制器设计方法

针对整数阶、 分数阶被控对象,提出了一种分数阶内模TI^λD^μ控制器的设计方法．首先对原被控模型进行降阶处理,得到二阶分数阶延时系统模型．然后将内模控制思想引入到降阶模型,设计内模控制器G_IMC（s）．最后将G_IMC（s）与所提的新型TI^λD^μ控制器进行参数对照,能够清晰地得出参数间的对应关系,从而得出分数阶TI^λD^μ的各参数．仿真结果表明,TI^λD^μ控制器能够获得良好的控制品质和鲁棒性．     

Robust adaptive control of a bio-inspired robot manipulator using bat algorithm

This paper proposes a novel adaptive fractional order PID sliding mode controller (AFOPIDSMC) using a Bat algorithm to control of a Caterpillar robot manipulator. A fractional order PID (FOPID) control is applied to improve both trajectory tracking and robustness. Sliding mode controller (SMC) is one of the control methods which provides high robustness and low tracking error. Using hybridization, a new combined control law is proposed for chattering reduction by means of FOPID controller and high trajectory tracking through using SMC. Then, an adaptive controller design motivated from the SMC is applied for updating FOPID parameters. A metaheuristic approach, the Bat search algorithm based on the echolocation behavior of bats is applied for optimal design of the Caterpillar robot in order to tune the parameter AFOPIDSMC controllers (BA-AFOPIDSMC). To study the effectiveness of Bat algorithm, its performance is compared with five other controllers such as PID, FOPID, SMC, AFOPIDSMC and PSO-AFOPIDSMC. The stability of the AFOPIDSMC controller is proved by Lyapunov theory. Numerical simulation results completely indicate the advantage of BA-AFOPIDSMC for trajectory tracking and chattering reduction.     

基于最优Oustaloup的分数阶PID参数整定

目前工程控制中大部分系统采用传统PID控制,由于分数阶PID继承了传统PID的优点,并且具有更好的控制品质及更强的鲁棒性,因此针对分数阶微积分的高精度数字实现及分数阶PID控制器在工程复杂系统中的实际应用,提出一种新的分数阶微积分高精度数字实现算法-最优Oustaloup数字实现,并建立控制系统的仿真模型,利用框图式模型结合最优ITAE性能指标来整定分数阶PID的参数。通过实例仿真验证,该方法能进一步优化控制器参数,提高控制精度及获得更好的控制效果,便于非线性系统及复杂系统的分数阶PID参数整定。     

Landing Force Control for Humanoid Robot by Time-Domain Passivity Approach

This paper proposes a control method to absorb the landing force or the ground reaction force for a stable dynamic walking of a humanoid robot. Humanoid robot may become unstable during walking due to the impulsive contact force of the sudden landing of its foot. Therefore, a control method to decrease the landing force is required. In this paper, time-domain passivity control approach is applied for this purpose. Ground and the foot of the robot are modeled as two one-port network systems that are connected, and exchange energy with each other. The time-domain passivity controller with admittance causality is implemented, which has the landing force as input and foot's position to trim off the force as output. The proposed landing force controller can enhance the stability of the walking robot from simple computation. The small-sized humanoid robot, HanSaRam-VII that has 27 DOFs, is developed to verify the proposed scheme through dynamic walking experiments.     

Camera Recognition and Laser Detection based on EKF-SLAM in the Autonomous Navigation of Humanoid Robot

The ability of autonomous navigation of the humanoid robot under unknown environment is very important to real-life applications. EKF-SLAM based on the camera recognition and laser detection for humanoid robot NAO is presented in this paper. Camera recognition is used to recognize if the object is a landmark. Because the computational resources needed for the feature-based position estimation are quite expensive, the laser instead of the camera provides the position of the landmark. A fractional order proportional-integral (PI) controller is designed to reduce the derivation of the NAO robot from the desired path during autonomous navigation. Experiments show that the proposed method is valid and reliable for autonomous navigation of the NAO robot under unknown environment.