Two-degree Of Freedom Controller Research Articles

Two-Degree-of-Freedom Control of a Micro-Robot Using a Dual-Rate State Observer

This brief presents a novel tracking control algorithm for a micro-robot based on dynamics and positional measurements. The algorithm improves the tracking performance and response time. We designed a two-degree-of-freedom (TDOF) control, which is widely utilized in industrial servo systems, for a micro-robot. Our TDOF control prevents undesirable effects, such as model uncertainty. The dynamic characteristics of a micro-robot were analyzed using the frequency response function (FRF), and a dynamic model specific for micro-robot motion was derived. This brief also addresses the dual-rate problem of micro-robot control systems by designing a dual-rate state observer (DSO) that provides positional information for the micro-robot when no camera updates are available. Thus, the TDOF controller provides feedback control at higher sampling frequencies. The performance of the controller was experimentally verified.

Tracking and Regulation Performance Limitations of Networked Control Systems Over Erasure Channel With Input Quantization

Limitations in communication networks, such as delays, packet dropouts, and insufficient bandwidth, create great challenges in the output tracking control and regulation performance of networked control systems. In this article, we propose some novel performance indexes for achieving the optimal tracking and regulation performance. By considering the influences of noise, packet dropouts, and logarithmic quantization on the channel input, the performance limitations of the networked systems are investigated by applying a two-degree-of-freedom (TDOF) control technique. The results obtained prove that the tracking and regulation performance is dependent not only on the position of the plant’s nonminimum phase zeros and unstable poles, but also on the directions. Furthermore, it is demonstrated that noise and quantization error have a negative influence on the control performance, and the design of the TDOF controller can eliminate the effect of packet dropouts on control performance. To validate the innovation results, several simulations are conducted.

Performance analysis method for NCSs with coding and quantization constraints

This paper studied the performance of networked control systems (NCSs) with coding and quantization constraints. In the forward channel of NCSs, the effects of noise and coding–decoding under a two-degree of freedom controller (2DOF) are considered, while in the feedback channel, the effects of quantization and bandwidth are taken into account. The performance expression is achieved by the spectral factorization. From the results, it can be concluded that the performance is determined by the given plant construction (non minimum phase (NMP) zeros, unstable poles), characteristics of the channel parameters. At the same time, the additive white Gaussian noise (AWGN), coding–decoding, quantization, bandwidth and other factors in the communication path also affect the performance of the network communication path. Finally, the effectiveness and merits of the proposed control scheme are verified by simulations.

Output Tracking Control of Single-Input-Multioutput Systems Over an Erasure Channel.

The output tracking control problem is investigated in this article. First, a new tradeoff performance index is presented for single-input-multioutput (SIMO) systems. Based on the frequency-domain method, the tracking performance limitations under time delay, packet loss, and channel noise effects are derived. We use a bivariate stochastic process to model the packet loss, and assume that channel noise is additive white Gaussian noise (AWGN). Two explicit expressions of the best tradeoff performance are given with the single-degree-of-freedom (SDOF) and two-degree-of-freedom (TDOF) control structures. It is shown that the tracking control performance has a close relation with the intrinsic characteristic of the plant, as well as the time delay, packet-dropouts rate, and power spectral density of AWGN. We also demonstrate that compared with the SDOF control structure, the TDOF control structure can improve the systems' attainable performance. A simulation example is finally discussed to validate the conclusions.

Dynamic Performance Improvement for Permanent Magnet Generator System Using Current Compensating Method With Two-Degrees-of-Freedom Control

This article proposes a two-degrees-of-freedom (TDOF) control with torque current compensating method (TCCM) to enhance the dynamic performance of permanent magnet generator (PMG) system when load changes. First, the mathematic model of PMG system with active front-end rectifier is introduced. Based on the system model, the proportional-integral controller of current loop is designed, and the TDOF controller designed with internal model control principle is derived for voltage loop control. There are two sets of parameters in the TDOF controller, one is used to regulate the system tracking performance when the command dc-link voltage changes, and the other is used to regulate the system antidisturbance capability when the electrical load changes. Second, the TCCM is proposed to further improve the system dynamic performance. The variation of torque current is applied to revise the command dc-link voltage, namely, the command dc-link voltage increases under loading occasion and decreases when unload occurs. The TCCM needs no additional hardware and is simple to implement. Simulation and experimental results verify the effectiveness of the proposed method.

How to Teach Control System Optimization (A Practical Decompisition Approach for the Optimization of TDOF Control Systems)

Abstract The optimality in a generic two-degree of freedom control system can be decomposed into three major steps, because the control error has three major parts: design-, realizability- and modeling-loss. The second term can be made zero for inverse stable processes only. This decomposition opens new ways for practical optimization of two-degree-of-freedom (TDOF) systems and helps the construction of new algorithms for robust identification and control. It is more reasonable to teach the optimization of control systems using these components.

A 2-Dof LQR based PID controller for integrating processes considering robustness/performance tradeoff

This paper focuses on the analytical design of a Proportional Integral and Derivative (PID) controller together with a unique set point filter that makes the overall Two-Degree of-Freedom (2-Dof) control system for integrating processes with time delay. The PID controller tuning is based on the Linear Quadratic Regulator (LQR) using dominant pole placement approach to obtain good regulatory response. The set point filter is designed with the calculated PID parameters and using a single filter time constant (λ) to precisely control the servo response. The effectiveness of the proposed methodology is demonstrated through a series of illustrative examples using real industrial integrated process models. The whole range of PID parameters is obtained for each case in a tradeoff between the robustness of the closed loop system measured in terms of Maximum Sensitivity (Ms) and the load disturbance measured in terms of Integral of Absolute Errors (IAE). Results show improved closed loop response in terms of regulatory and servo responses with less control efforts when compared with the latest PID tuning methods of integrating systems.

Optimal design of two-degree-of-freedom control scheme for non-minimum phase processes with time delay

This paper proposes an analytical two-degree-of-freedom (TDOF) control scheme for non-minimum phases systems with time delay, which leads to remarkable improvement of regulator capacity for both of reference input tracking and input load disturbance rejection. All controllers that make the closed-loop system internally stable and have no steady-error have been employed firstly. Then, the set-point tracking controller and the disturbance rejection controller are analytically derived in terms of the integral squared error performance specifications. The nominal set-point response is decoupled from the load disturbance response in the adopted TDOF control scheme. In consequence, both of the set-point tracking performance and load disturbance rejection performance can be optimised simultaneously and separately. Finally, an illustrative example is included to demonstrate the superiority of the proposed method.

Optimal design of two-degree-of-freedom control scheme for non-minimum phase processes with time delay

This paper proposes an analytical two-degree-of-freedom (TDOF) control scheme for non-minimum phases systems with time delay, which leads to remarkable improvement of regulator capacity for both of reference input tracking and input load disturbance rejection. All controllers that make the closed-loop system internally stable and have no steady-error have been employed firstly. Then, the set-point tracking controller and the disturbance rejection controller are analytically derived in terms of the integral squared error performance specifications. The nominal set-point response is decoupled from the load disturbance response in the adopted TDOF control scheme. In consequence, both of the set-point tracking performance and load disturbance rejection performance can be optimised simultaneously and separately. Finally, an illustrative example is included to demonstrate the superiority of the proposed method.

Optimal disturbance rejection controller design for integrating processes with dead time based on algebraic theory

ABSTRACTIn this paper, an H2 optimal input-load disturbance rejection (ILDR) controller for integrating processes with dead time is proposed based on the internal model control principle. The main contribution of this work is that the optimal solution under ILDR criterion for integrating processes with dead time and input constant disturbances has been derived based on algebraic theory. To further improve the performance for both set-point tracking and input disturbance rejection, a two-degree-of-freedom (TDOF) control design method has also been developed. Compared with previous advanced control methods, the proposed design method has three main advantages. First, the optimal ILDR controller is derived systematically on the basis of algebraic theory. The designed controller is given in an analytical form. Second, a simple tune principle is developed. The set-point tracking performance specification and robustness stability specification can be quantitatively achieved by monotonously tuning the performance degree in the designed controller. Finally, both optimal set-point tracking performance and input disturbance rejection can be achieved by the proposed TDOF control structure. Numerical simulations are given to illustrate the effectiveness of the proposed method.

Longitudinal stability and control augmentation with robustness and handling qualities requirements using the two degree of freedom controller

This paper presents a practical design of longitudinal stability and control augmentation system (SCAS) using a two degree of freedom (TDOF) controller. It is based on the linear quadratic regulator (LQR) technique in the frequency domain, via spectral factorization. The controller exhibits robustness to plant uncertainties, related with variation due to different operation conditions, and incorporates various aircraft handling qualities (HQ) requirements to comply with certification authority’s requests. The project results in an unique set of fixed gain TDOF controller for a plant dynamics which changes with a $$V_{\text {CAS}}\times x_{\text {cg}}$$ envelope. The project is done aiming at the industrial implementation of TDOF controller in fly-by-wire aircrafts.

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.

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.

Two-Degree-of-Freedom Controller Design for an Ill-Conditioned Process Using H2 Decoupling Control

In this paper, a two-degree-of-freedom (TDOF) controller is designed for an ill-conditioned process based on the H2 decoupling control method. The ill-conditioned process considered stems from the benchmark problem formulated in the IEEE Conference on Decision and Control (CDC). The goal of this paper is to show that lower order controllers can be reached with respect to the given plant and the corresponding design specifications. The orders of the designed TDOF controllers are 2 and 1, respectively, which is much lower than the previously developed methods. The additional benefit is that the new design procedure is simpler than the developed methods as well. In the proposed design procedure, no weight function needs to be chosen and the controller is given in an analytical form. Simulation shows that the designed controllers satisfy all design specifications of the CDC problem.

Two‐degree‐of‐freedom controller design for linear parameter‐varying systems

AbstractA design strategy for linear parameter‐varying (LPV) systems is considered in a two‐degree‐of‐freedom (TDOF) control framework. First, a coprime factorization for LPV systems is introduced. Second, based on the coprime factorization, a TDOF control framework of linear timeinvariant systems is extended to that of LPV systems. Good tracking performance and good disturbance rejection are achieved by a feedforward controller and a feedback controller, respectively. Furthermore, each controller design problem can be formulated in terms of a linear matrix inequality related to the L2 gain performance. Finally, a simple design example is illustrated. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

역동력학과 퍼지기법을 이용한 DC 모터용 2자유도 제어기

본 논문에서는 역동력학과 퍼지기법을 기반으로 하는 DC 모터 속도제어용 2자유도 제어기를 설계한다. 제안된 제어기는 DC 모터 시스템의 역동력학 모델, 전처리필터와 퍼지보상기로 구성된다. 모델은 쿨롱마찰을 내포하는 비선형 방정식으로 표시되며, 전처리필터는 역동력학 모델에 의해 유발될 수 있는 고주파 영향을 막아주며, 퍼지보상기는 모델의 불확실성, 외란 등으로 인한 오차를 보상한다. 퍼지보상기는 기준 입력 변화에 대한 추종성능과 외란에 대한 오차 제거성능을 동시에 개선하도록 설계된다. 모델과 보상기의 파라미터는 각각 실수코딩 유전알고리즘으로 추정되고 동조된다. 제안된 기법의 유효성은 실험을 통해 검증된다. In this paper, a Two-Degree-of-Freedom-Controller(TDFC) for DC motors based on inverse dynamics and the fuzzy technique is presented. The proposed controller includes the inverse dynamic model of a DC motor system, a prefilter and a fuzzy compensator. The model of the system is characterized by a nonlinear equation with coulomb friction. The prefilter eliminates high frequency effects occurring when the inverse dynamic model is implemented. The fuzzy compensator is designed for tracking the change of the reference input and simultaneously regulating the error between the reference input and the system output which can be caused by disturbances. The optimal parameters of both the model and the compensator are identified by a real-coded genetic algorithm. An experimental work on a DC motor system is carried out to verify the performance of the proposed controller.

A two degree of freedom level control

A two degree of freedom control is proposed for liquid level control. The load estimation is achieved in an indirect manner. Only one design parameter is required for the load estimation. As for the feedback loop, a P-only feedback action is employed. It is equivalent to a P control at disturbance free condition and becomes a PI controller under load disturbance. Steady-state characteristics, dynamic properties and robustness issues are explored. Design procedures are also proposed. A surge tank example is used to illustrate the performance of the proposed control. The results show that the two-degree of freedom control gives good nominal performance and is robust with respect to modeling errors. Improved performance are also observed for systems with time delay or right-half-plane zero.

Anti-Windup Strategy for Two Degree of Freedom Control System Based on Left Coprime Factorization

In this paper, the anti-windup strategy for two degree of freedom (TDOF) control system is proposed. In TDOF control system, the input saturation can be avoided by designing the suitable command response property for nominal model. In real controlled systems, however, the input saturation may occur because of unknown disturbance or plant variation. The proposed method can suppress the windup phenomena by modelling the limiter into TDOF controller and adjusting the limitation between feedback and feedforward control. The proposed anti-windup controller (AWC) has the form of left coprime factorization of feedback and feedforward controllers. The proposed method is evaluated by simulation and experiment of position control system of DC servo motor.

Novel reference signal generation for two-degree-of-freedom controllers for hard disk drives

This paper considers the determination of reference trajectories for use with a two-degree of-freedom (2-DOF) controller for the head positioning of hard disk drives (HDD). The reference trajectories are designed in two stages-off-line simulation and online reference generation. The HDD model used for the design includes the back electromotive force of the voice coil motor. In the second stage, the idea of structural vibration minimized acceleration trajectory is utilized to adjust the errors at the end of the trajectories. 2-DOF control with the proposed reference trajectory is compared to conventional mode-switching control, and its effectiveness is verified.

二自由度制御手法を用いた慣性比の小さい二慣性位置決めシステムの外乱抑圧特性

二自由度制御手法を用いた慣性比の小さい二慣性位置決めシステムの外乱抑圧特性