3D Control Research Articles

Analytical IMC-PID design in terms of performance/robustness tradeoff for integrating processes: From 2-Dof to 1-Dof

This communication addresses the analytical PID tuning rules for integrating processes. First, this paper provides an analytical tuning method of two-degree-of-freedom (2-Dof) PID controller using an enhanced internal model control (IMC) principle. On the basis of the robustness analyses, the presented method can easily achieve the performance/robustness tradeoff by specifying a desired robustness degree. Second, an analytical tuning method of one-degree-of-freedom (1-Dof) PID also is proposed in terms of performance/robustness and servo/regulator tradeoffs, which are not commonly considered for 1-Dof controller design. The servo/regulator tradeoff is formulated as a constrained optimization problem to provide output responses as similar as possible to those produced by the 2-Dof PID controller. The presented PID settings are applicable for a wide range of integrating processes. Simulation studies show the effectiveness and merits of the proposed method.

2A1-S04 2自由度制御による天井クレーンの制振搬送(人間機械協調)

This paper deals with the sway control of the overhead crane using 2-DOF control. High operation skill is necessary in the transport with reduced vibration of the payload. However, a skilled operator has been reduced. For this reason, the operation support system that can be easily operated even a beginner is required. Many researchers report that are to be achieved the transport with reduced vibration using a feedforward control or a feedback control. Only a feedforward control can't be achieved the transport with reduced vibration in any operation, and only a feedback control can't be achieved an improvement in operability. Therefore, we use 2-DOF control to design the controller to achieve the transport with reduce vibration and improve operability. The experimental results show the transport with reduced vibration even if the beginner operator is operated.

FRIT for Non-Miminimum Phase Systems in the 2DOF Control Architecture: Simultaneous Attainment of Controllers and Models

This paper provides one of the practical and meaningful applications of controller parameter tuning in the Two-Degree-of-Freedom (2DOF) control architecture for non-minimum phase systems. The paper...

Design and Implementation of Two-Degree-of-Freedom Nonlinear PID Controller for a Nonlinear Process

A Two-Degree-of-Freedom (2-DOF) Nonlinear PID (NPID) controller is designed for a conical tank level process. The process is modeled using black box identification method as a First Order Process with Dead Time (FOPDT) model. Two nonlinear first order tracking differentiators are designed for the nonlinear PID controller. The closed loop control is implemented for a wide operating range of the process with the designed controller. The implementation and simulation is carried out using Mat-lab Simulink software. The online implementation of proposed controller shows that 2-DOF NPID is better than 1-DOF NPID. Index Terms: Two-Degree-of-Freedom, First order process with dead time, Nonlinear PID, Nonlinear tracking differentiator I. Introduction A conical tank level process is a nonlinear process due to the conical shape of the tank. The change in area of the conical tank for equal rise in level is nonlinear. The nonlinear process is modeled as piecewise linear models at some operating points. This inherent nonlinear behavior of the processes makes control of such processes more complex. Presence of the nonlinearity in the plant often causes degraded performance of the overall process. A nonlinear PID controller is developed by defining a nonlinear function which gives the controller settings depending upon the calculated error and some tuning parameters (1)(2). A nonlinear function may contain number of parameters and values of those should be decided by the designer and it varies from plant to plant. When the process and the controller both exhibit nonlinear characters, a 2-DOF control scheme is considered to improve servo and regulatory problems (3). In the 2-DOF control scheme the closed loop transfer functions for servo and regulatory can be adjusted independently (4)(5)(6). In this work, the tuning of 2-DOF nonlinear PID controller is demonstrated to achieve stability and desired performance measures. This paper is organized such that first the design of the 2-DOF nonlinear PID control structure using the nonlinear tracking differentiators and secondly conical tank level process is described. Then the simulation study and online implementation of designed controller with actual process are shown. e when e e when e e sign e f p p p p p          

Force/Position Hybrid Control of 6PUS-UPU Redundant Driven Parallel Manipulator Based on 2-DOF Internal Model Control

To improve control performance of parallel manipulator, servo control is optimized according to 2-DOF control with Internal Model Control. Position loop of the controller is redesigned based on the original current loop and speed loop. The hybrid force/position control strategy on the basis of cross-coupling is proposed. With mechatronic cosimulation system, it is proved that the force/position hybrid control on the basis of 2-DOF Internal Model Control has better stability and position precision compared with the traditional PID control. The control precision and stability of the parallel manipulator are improved effectively in actual experiment. Two types of compliance operation including peg in hole and surface tracking are realized in 6PUS-UPU parallel manipulator and both have good applicable effect.

Adaptive Control of Membrane Conductivity of PEM Fuel Cell

Abstract Proton Exchange Membrane Fuel Cell is considered a key device in the hydrogen economy which is a promising energy carrier alternative for the fossil fuels. This paper approaches the problem of membrane conductivity in a PEM fuel cell which influences the major part of the voltage/current polarization curve of the cell. The control of conductivity is essential for stable operation and good performance of the cell. We propose an adaptive 2DOF controller in order to obtain certain control performances for membrane conductivity management. The controller is implemented with 2 PID structures and an adaptation rule which is based on gain-scheduling method. We have determined the controllers’ coefficients and the gain-scheduling change points. Our simulated results show good disturbance rejection while conductivity is maintained at desired level.

Two degrees of freedom control of a ball and beam system

In this paper, a two-degree of freedom (2DOF) controller is designed for a ball and beam system. The controller is developed based on the algebraic method. The ball and beam system is one of the most popular laboratory experiments for control education. The controller is designed such that the ball can track a square wave with a certain design specification. The advantages of 2DOF controller are the feedback controller takes care of the uncertainty and the feedforward filter ensures the tracking of the reference command. Though the control method is not new, the application of the technique on such unstable system is of interest. Controlling the ball on the beam is a challenging task because of the instability of the system and the fact that the output, i.e. the ball position, increases almost without limit for a fixed input beam angle. The controller needs to regulate the position of the ball by changing the angle of the beam at the pivot point. It is a difficult control task as the ball moves with an acceleration which is proportional to the tilt angle of the beam. Two types of 2DOF controllers are considered; based on dominant pole design and based on integral time absolute error (ITAE) design. The performances of the resulting controllers are compared. Simulations were run over various frequencies. The results indicate the effectiveness of the designed 2DOF controllers in achieving the design specification.

Self-tuning of 2 DOF control based on evolving fuzzy model

In this paper we present a self-tuning of two degrees-of-freedom control algorithm that is designed for use on a non-linear single-input single-output system. The control algorithm is developed based on the Takagi-Sugeno fuzzy model, and it consists of two loops: a feedforward loop and feedback loop. The feedforward part of the controller should drive the system output to the vicinity of the reference signal. It is developed from the inversion of the T-S fuzzy model. To achieve accurate error-free reference tracking a feedback part of the controller is added. A time-varying error-model predictive controller is used in the feedback loop. The error-model is obtained from the T-S fuzzy model. The T-S fuzzy model of the system, required in the controller, is obtained with evolving fuzzy modelling, which is based on recursive Gustafson-Kessel clustering algorithm and recursive fuzzy least squares. It employs evolving mechanisms for adding, removing, merging and splitting the clusters.The presented control approach was experimentally validated on a non-linear second-order SISO system helio-crane in simulation and real environment. Several criteria functions were defined to evaluate the reference-tracking and disturbance rejection performance of the control algorithm. The presented control approach was compared to another fuzzy control algorithm. The experimental results confirm the applicability of the approach.

Comparison of performances of several Cuckoo search algorithm based 2DOF controllers in AGC of multi-area thermal system

This paper presents the automatic generation control (AGC) of an unequal three area thermal system with single reheat turbine and generation rate constraints of 3%/min in each area. A two degree of freedom (2DOF) controller called 2DOF – integral plus double derivative (2DOF – IDD) is proposed for the first time in AGC as secondary controller. Secondary controller gains and other parameters are simultaneously optimized using a more recent and powerful evolutionary computational technique called Cuckoo search algorithm (CS). The system dynamic responses obtained with 2DOF – IDD controller are compared with that obtained with other 2DOF controllers such as 2DOF – Proportional-Integral (2DOF – PI), 2DOF Proportional – Integral-Derivative (2DOF – PID). Investigations reveals that 2DOF – PI, and 2DOF – PID provide more or less same response where as 2DOF – IDD controller provides much better response than the others. Sensitivity analysis reveals that the CS optimized 2DOF – IDD controller parameters obtained at nominal condition of loading and nominal size of step load perturbation (SLP) are robust and need not be reset with wide changes in system loading and (SLP).

Internal model based robust inversion feedforward and feedback 2DOF control for LPV system with disturbance

To reduce the adverse effects on the control performance and disturbance rejection caused by system uncertainty, a novel internal model based robust inversion feedforward and feedback 2DOF control approach was proposed for LPV system with disturbance. The proposed control approach combines the internal model control and robust inversion based 2DOF control, it utilizes internal model based control to reject external disturbance, utilizes robust inversion 2DOF control to enhance the control resolution and guarantee the system control performance. At first, a LMI synthesis approach for LPV system model identification and a disturbance compensator optimization design method which could minimize H∞ norm of output error caused by disturbance are presented. Then, combined with internal loop for disturbance compensation, a robust inversion feedforward controller is designed by robust inversion approach and the feedback controller which could render the requirements of reference signal tracking performance and robustness satisfied is obtained by the H∞ mixed sensitivity synthesis approach. Finally, atomic force microscopy (AFM) vertical positioning simulation experiments are conducted and the experiment results showed that the proposed control approach could achieve better output performance and disturbance rejection compared with conventional internal model based control and robust inversion based 2DOF control approach.

Visual Trajectory-Tracking Model-Based Control for Mobile Robots

In this paper we present a visual-control algorithm for driving a mobile robot along the reference trajectory. The configuration of the system consists of a two-wheeled differentially driven mobile robot that is observed by an overhead camera, which can be placed at arbitrary, but reasonable, inclination with respect to the ground plane. The controller must be capable of generating appropriate tangential and angular control velocities for the trajectory-tracking problem, based on the information received about the robot position obtained in the image. To be able to track the position of the robot through a sequence of images in real-time, the robot is marked with an artificial marker that can be distinguishably recognized by the image recognition subsystem. Using the property of differential flatness, a dynamic feedback compensator can be designed for the system, thereby extending the system into a linear form. The presented control algorithm for reference tracking combines a feedforward and a feedback loop, the structure also known as a two DOF control scheme. The feedforward part should drive the system to the vicinity of the reference trajectory and the feedback part should eliminate any errors that occur due to noise and other disturbances etc. The feedforward control can never achieve accurate reference following, but this deficiency can be eliminated with the introduction of the feedback loop. The design of the model predictive control is based on the linear error model. The model predictive control is given in analytical form, so the computational burden is kept at a reasonable level for real-time implementation. The control algorithm requires that a reference trajectory is at least twice differentiable function. A suitable approach to design such a trajectory is by exploiting some useful properties of the Bernstein-Bézier parametric curves. The simulation experiments as well as real system experiments on a robot normally used in the robot soccer small league prove the applicability of the presented control approach.

A Robust Two-Degree-of-Freedom Control Strategy for an Islanded Microgrid

This paper presents a new robust control strategy for an islanded microgrid in the presence of load unmodeled dynamics. The microgrid consists of parallel connection of several electronically interfaced distributed generation units and a local load. The load is parametrically uncertain and topologically unknown and, thus, is the source of unmodeled dynamics. The objective is to design a robust controller to regulate the load voltage in the presence of unmodeled dynamics. To achieve the objective, the problem is first characterized by a two-degree-of-freedom (2DOF) feedback-feedforward controller. The 2DOF control design problem is then transformed to a nonconvex optimization problem. Furthermore, the nonconvex optimization problem is reduced to a convex linear matrix inequality-based optimization problem which can be easily solved. To achieve optimal performance for the system, unlike the most conventional 2DOF design approaches, the feedback and feedforward controllers are jointly designed. Finally, simulation case studies performed in the MATLAB/SimPowerSystems Toolbox show that the proposed control scheme is strongly robust against uncertainties in the load parameters and against the unknown dynamics.

2자유도 H∞제어기 종합 프레임웍에 기반한 유압식 Dipod 플랫폼의 강인제어기 설계

유압식 Dipod 플랫폼은 기동차량에서 위성을 지향하는 안테나의 안정화 및 추적에 사용된다. 이러한 플랜트의 제어기 설계에는 외란제거와 추적 두 가지 성능목표 뿐만 아니라 강인성을 함께 절충해야 하는 제약조건으로 인해 1자유도 제어기에 비해 설계 유연성이 큰 2자유도 H<SUB>∞</SUB> 제어기가 선호된다. H<SUB>∞</SUB> 기반한 2자유도 제어기 종합방법에는 두 가지 프레임웍이 사용되는데 유압식 Dipod 플랫폼의 예를 통해서 일괄종합 방법이 더 우수한 성능을 보인 반면 분리종합 방법은 더 우수한 강인성을 보임을 확인할 수 있었다. H<SUB>∞</SUB> 2자유도 종합방법에 따른 이러한 두 결과의 차이를 시스템 정합행렬의 구조화 특성을 통해 비교하여 보았다.

Data-driven criteria synthesis of system with two-degree-of-freedom controller

This paper is concerned with the problem of designing a two-degree-of-freedom (2-DOF) controller based on data. Without requiring the specific mathematical model of a plant, the parameters of stabilising controller are calculated directly from data for a linear time-invariant system. In fact, using the traditional unity feedback control, the existing results which focus on calculating stabilising PID or first-order controllers have been reported in the literature. However, there exists certain steady-state error in these approaches if the integrators are not added into the controller. In this paper, a 2-DOF controller is designed to ensure no changes in characteristic polynomial of the closed-loop systems, furthermore, in terms of a pre-specified criterion function, by applying the iterative feedback tuning technique, a local optimal performance is achieved. Especially, for the step input, through tuning the parameters of controller, the steady-state error can be reduced to zero. Finally, a numerical example is given to illustrate the effectiveness of this method.

A unified approach to the design of advanced proportional-integral-derivative controllers for time-delay processes

A unified approach for the design of proportional-integral-derivative (PID) controllers cascaded with first-order lead-lag filters is proposed for various time-delay processes. The proposed controller’s tuning rules are directly derived using the Pade approximation on the basis of internal model control (IMC) for enhanced stability against disturbances. A two-degrees-of-freedom (2DOF) control scheme is employed to cope with both regulatory and servo problems. Simulation is conducted for a broad range of stable, integrating, and unstable processes with time delays. Each simulated controller is tuned to have the same degree of robustness in terms of maximum sensitivity (Ms). The results demonstrate that the proposed controller provides superior disturbance rejection and set-point tracking when compared with recently published PID-type controllers. Controllers’ robustness is investigated through the simultaneous introduction of perturbation uncertainties to all process parameters to obtain worst-case process-model mismatch. The process-model mismatch simulation results demonstrate that the proposed method consistently affords superior robustness.

Comparative analysis of single and two DOF controllers for integrating and time-delay processes

In all process industries, the system with feedback nature should satisfy desirable dynamic and steady state response characteristics for given test signals for which the effect of disturbances should be minimum and set point tracking should be smooth and rapid. Also, the insensitiveness to parameter variations with all acceptable dynamic characteristics cannot be met when system is with single controller. This can be met with the two degrees of freedom (2-DOF) controller which can enhance the above aspects, particularly for integrating processes with longer time delay. In this proposed method the process transfer function is developed into an infinite Taylor series which consists of time-weighted integrals of the process impulse response. The moments can be obtained by calculating repetitive (multiple) integrals of the process input (u) and output (y) signals during the change of the process steady-state. The method used for tuning the 2-DOF controller is the magnitude optimum multiple integration. The control loop robustness and performance indices are also experimented by comparing the responses of the processes having 1-DOF controller tuned by popular tuning methods to show the effectiveness of 2-DOF controller qualitatively.

Robust control of a cell micro-manipulation system with IPMC actuators

A precise and robust controller has been developed and implemented on a novel ionic polymer–metal composite (IPMC) actuated micro–manipulator to demonstrate its ability to enable safe and reliable manipulation of biological cells. A 2 degree–of–freedom (2DOF) control structure was employed to enable the system to be optimised for both the disturbance response (DR) and set–point (SP) tracking. The controller is adaptively tuned using a model–free iterative feedback tuning (IFT) approach which is ideal for operation in unknown cellular environments and handling the time–varying behaviour of the IPMCs themselves. IFT experiments have tuned the IPMCs to an 87% and 81% performance improvement in DR and SP respectively. Experiments then reveal that the tuned controller has equipped the manipulator with an accuracy of <7.1% of full scale, with up to 7° of motion in both axes. The controller has also demonstrated its ability to naturally cope with load disturbances up to 10 mN.

Design and Implementation of Model Reference Adaptive Controller using Coefficient Diagram Method for a nonlinear process

Abstract: In this work an adaptive control along with robust control have been developed to address the problem of system performance in the face of system uncertainty in control-system design without excessive reliance on system models. The direct MRAC control scheme with unknowns is designed with control law that is to be combined with an adaptive law. The adaptive laws are developed using the SPR-Lyapunov design approach and are driven by the estimation error for continuous-time systems guaranteeing asymptotic stability of the system states. CDM is a polynomial approach which was developed and introduced for a good transient response of the control systems. An MRAC is constructed in two-degree offreedom (2DOF) control structure and the adaptation gains of controller parameters are found through CDM. Spherical tank level process is used for validating the design procedure of CDM-MRAC in real time and the performance of controller is compared with linear PI controller. Simulation is carried out using Mat Lab Simulink software.

Robust 2-Degrees-Of-Freedom Vibration Suppression Controller Design Based on Simultaneous Optimization between Feedforward and Feedback Compensators

This paper presents a novel simultaneous optimization between feedforward (FF) and feedback (FB) compensators in 2-degree-of-freedom (2-DOF) positioning systems for robust vibration suppression control against frequency perturbations of mechanical vibration modes. The authors have already proposed a coordinate design between the FF and the FB compensators of the 2-DOF controller to improve the robust properties in the positioning. In the conventional approach, however, residual vibrations due to the frequency perturbations still remained after the settling because the conventional coordinate design was a quasi-optimization of the 2-DOF controller. In this study, therefore, a simultaneous optimization is adopted to suppress the residual vibration. The effectiveness of the proposed controller design has been verified by numerical simulations and experiments using a prototype of a galvano scanner.

Computationally efficient receding horizon trajectory tracking control for a tubular reactor example

AbstractFlatness‐based feedforward control and receding horizon trajectory tracking control can be combined within a two‐degrees‐of‐freedom (2dof) control scheme to obtain robust trajectory tracking for nonlinear systems. The key to a computationally efficient solution of the optimization problem underlying the receding horizon control is the linearization of the time‐variant tracking error dynamics such that the nonlinear optimal control problem may be replaced by a linear‐quadratic formulation. The approach is demonstrated for setpoint transitions of a nonlinear boundary‐controlled parabolic partial differential equation (PDE), which is semi‐discretized for the control design using finite differences on the spatial derivatives. (© 2012 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)