State Variable Feedback Control Research Articles

Empirical study of robust/developed PID control for nonlinear time-delayed dynamical system in discrete time domain

In addition to the high nonlinearity of liquid dynamics inside a tank, a study was conducted to overcome loading/unloading liquid storage tank control problems. In this study, the author developed a nonlinear control system to conquer both nonlinearity and the significant time delay arising from using a pressure-difference-based level sensor. To this end, this study proposes the implementation of nonlinear state dependent (SDP-PID+) control using the SDP transfer function model as a class of nonlinear descriptions of dynamical systems. By incorporating additional robust (plus) compensators alongside the traditional P-, I-, and D-compensators, the robust SDP-PID controller utilizes the complete state feedback to create a time-varying state variable feedback (SDP-SVF) control law. This approach effectively mitigates the effects of the discrete-time SDP-TF. It introduces the pole placement tuning approach, which renders significant performance using the laboratory test rig TPS8.2.2.4, for automatic liquid level control.

Formula omitted] control for singularly perturbed jumping delayed systems and its application in a tunnel diode circuit model

This paper investigates the slow state variable feedback control issue for a group of singularly perturbed Markov jump systems with time-varying state delay in the discrete-time domain. The primary goal of this paper is to propose a slow state controller design approach that ensures the closed-loop dynamics attain stochastic stability with an H∞ performance. First, the time-varying delay is introduced into system state and Markov jump chain is employed to depict system topological change. Secondly, by resorting to the Lyapunov functional theory and matrix analysis method, several necessary criteria are provided to guarantee the desired control performance. The derived conditions rely not only on the size of time-varying state delay and the upper bound of the singular perturbation parameter, but also on the order of the generated Markov jump mode sequence. Based on the established conditions, the gains of the desired slow state controller are obtained by means of the feasibility of a set of linear matrix inequalities. Eventually, a numerical simulation and a tunnel diode circuit model are presented to demonstrate the efficiency of the proposed technique.

Design, testing and implementation of a linear state variable feedback controller for providing tracking/regulation of a large platform of a Maglev vehicle

The basic parameters of an electromagnetic levitation systems are resistance of the coil, inductance of the coil, air-gap between magnet and the object, coil current, mass of the object, controller parameters and so on. The levitation systems are highly unstable and strongly non-linear. In real-life applications, these parameters are supposed to vary. A proportional–integral controller for the inner current control loop and a lead compensator for the position control loop have been designed and tested. The performance study under various parametric effects has been investigated broadly. Finally, both the stability for the proposed levitation system has been achieved with a better operating zone using linear state variable feedback controllers. The system dynamic performances have been recorded for variations of physical system parameters. The sensitivity/robustness of the set-up has been studied. This study will give an insight for designing any corrective measures and an overall idea to develop a levitation system.

Modelling and State Variable Feedback Control with Proportional Action of a One-Link Flexible Manipulator Incorporating Payload

This paper presents a state variable feedback (SVF) control with proportional gain to control a one-link flexible manipulator incorporating payload. The dynamic model of a one-link flexible manipulator is developed through a finite element method. The system is uncertain due to the variation of payloads and numbers of elements. There is a challenge in designing a controller for each number of elements. To obtain the effectiveness of the controllers, a combination of SVF control-based LQR controls with proportional gain is developed for a flexible link manipulator with payload variations. An assessment is conducted to examine the input tracking controller capability of the hub angular position, deflection, hub velocity and end-point residual of the one-link flexible manipulator. The responses of the system are shown in domains of time and frequency, while the SVF control with proportional gain schemes is also discussed. This study finds that the payload effects on the response incorporating payload with SVF control and proportional gain schemes can provide input tracking performance with zero steady state error.

LMI-based robust tracking of a class of MIMO nonlinear systems

Reference tracking problem for MIMO Lipschitz nonlinear systems is examined here. Presently a vast literature exists on observer design of unforced systems containing Lipschitz nonlinearities. However, these existing results cannot be readily extended for controller design containing reference tracking ability. Here a Linear State Variable Feedback (LSVF) controller is designed for MIMO Lipschitz nonlinear systems with norm-bounded parametric uncertainties using the concept of input to state stability Lyapunov functions. The whole problem is cast into a framework of Linear Matrix Inequalities, to exploit its numerical capabilities. Analytical proofs are supplemented with simulation examples, which show certain advantages over existing results. Apart from state feedback, observer-based output feedback is also considered for controller design.

State-Variable Feedback Control for Micro Gas Turbine Applied to Combined Heat and Power Systems: a Case Study

This paper presents the application of a dynamic model for the Elliot 100 kW microturbine operating in the city of Barranquilla, Colombia under partial load conditions from the validation carried out in a model implemented in the Polytechnic of Turin, Italy, with different operating conditions, in which a mathematical model is developed by selecting the elements that most frequently affect the dynamics of the gas microturbine (MTG) through information in order to obtain the semi-physical models of the phenomenological base. This model can be used for the study of the applications of non-linear control systems on gas microturbines operating at partial loads. Four tests are presented (performance, robustness, uncertainty and disturbance performance) in order to analyze the developed controller where it is possible to quantify the behavior of the control loops with performance indices based on the error signal e(t), for each partial load to which the microturbine has been subjected. In addition, increasing by 10% the K matrices of the developed controller, in 3 different stages for each established partial load, being able to test the robustness by means of the Ackerman method, in the uncertainty test, where changes are made to the process variable that is critical for the study (LHVb; fuel), it has been noted that by decreasing the LHVb by 36%, fuel consumption increases by 56%, causing problems in the mechanical internals of the equipment. Finally, the controller scheme is modified, adding a disturbance to the states (Ppl, n, and T5), managing to establish that the system is only altered when the disturbance directly affects the third state (T5), testing the driver's performance in disturbances.

Immersion-and Invariance-Based Adaptive Control of Asteroid-Orbiting and - Hovering Spacecraft

The development of an immersion-and invariance-based adaptive state variable feedback control law for the closed orbit and hovering control of spacecraft in the vicinity of asteroids is the subject of this paper. The celestial body is assumed to be rotating with constant angular velocity about a fixed axis. Also, it is assumed that the mass and moments of inertia matrix of the asteroid, and the mass of the spacecraft are not known. The objective is to control the orbit of the spacecraft despite uncertainties in the system parameters. Based on the immersion and invariance theory, a noncertainty-equivalence adaptive control system is designed for steering the spacecraft along prescribe closed orbits or to fixed points for hovering control. The control system has a modular structure - consisting of an stabilizing control module and an parameter identifier. The control law is synthesized using filtered signals so as to circumvent the complexity of the immersion and immersion methodology. Unlike certainty-equivalence systems, the parameter estimates include judiciously selected nonlinear state-dependent algebraic functions and partial estimates derived from an integral update law. By the Lyapunov analysis, it is shown that the trajectory tracking error asymptotically converges to zero and all the signals in the closed-loop system are bounded. For illustration, numerical results are presented for control around 433 Eros and Ida asteroids. These results show that, despite uncertainties in the relative spacecraft dynamics, the adaptive law accomplishes closed orbit as well as hovering control.

Digital Noninterleaved High-Power Totem Pole PFC Based on Internal Model Design

When the control signal u(t) of totem pole PFC with GaN HEMTs is a function of measurable state variables, the state feedback gain matrix can be determined by applying state variable feedback control with Ackerman formula, so that the poles of closed-loop system can be allocated to the desired position. This correction method is especially beneficial to optimal system control according to performance requirements. By introducing the internal model of reference input, a state space function including the first-order and second-order differential of error is constructed; this novel controller makes controlled system track the reference input signal progressively with zero steady-state error. A 4 kW PFC prototype is designed to verify this design method.

A novel discrete PID+ controller applied to higher order/time delayed nonlinear systems with practical implementation

This paper develops a novel approach for discrete time proportional integral derivative (PID) control, namely PID+, with application to manipulator arm with four-degrees of freedom. The approach utilizes extra proportional and input compensators to counteract the influence of the discrete time transfer functions higher than second order and having samples time delay more than unity, respectively. These plus compensators allow the exploiting of the full state feedback signals to construct the state variable feedback control law for the proposed PID+ controller. The work introduces two tuning approaches for the compensators of the novel PID+ controller; they are the Linear Quadratic (LQ) cost function by exploiting the non-minimal state space, namely the novel NMSS-PID+ form, and the pole placement. Simulation results verify the applicability of the proposed PID+ controller. Both tuning approaches, PID+/LQ and PID+/pole placement, show satisfactory steady state response with good control action, along with deadbeat response when applying the pole placement approach, in simulation. Finally, the paper shows successful practical implementation for the PID+ controller, when applied to the four degrees of freedom manipulator arm, for which all the control design criteria (tracking with acceptable response time, and input/output disturbance rejection) are met.

Non‐minimal state‐space polynomial form of the Kalman filter for a general noise model

The optimal refined instrumental variable (RIV) method for the estimation of the Box-Jenkins (BJ) model is modified so that it functions as an optimal filter and state-estimation algorithm. In contrast to the previously developed minimal and non-minimal state space (NMSS) forms for an Auto-Regressive Moving Average with eXogenous variables (ARMAX) model, the new algorithm requires the introduction of a novel extended NMSS form. This facilitates representation of the more general noise component of the BJ model. The approach can be used for adaptive filtering and state variable feedback control.

Điều khiển thích nghi vị trí trên cơ sở kỹ thuật vi xử lý Phần I: Hệ thống điều chỉnh vị trí nhờ quan sát và phản hồi trạng thái

In order to investigate different position control algorithms for numerical controlled machines and robots, a positional control system was built on the base of a microcomputer. In part I, the paper presents the observer algorithm for state variable estimation and the state variable feedback control algorithm applied to the position control of a particular machine-table. With the hardware and software structure of the microcomputer based digital system described in this paper different control algorithms can be realized flexibly. The position control problem for the plant with variations or uncertainties of parameters and load characteristics will be reported in part II.

Walking Posture Control of Transmission Line Single Arm Inspection Robot

To control the walking posture according to transmission line single arm inspection robot, the robot is divided into normal walking and climbing walking two state, and gives the definition, then based on the state space method of state variable feedback and PD control method is used to control the two states, two kinds of control method of simulation by using Matlab, in the end, the two control methods proposed is validated in the actual circuit structures. The results show that, the proposed control method is rapid and effective, and can meet the needs of practical application.

Simplified Model and Control Strategy of Three-Phase PWM Current Source Rectifiers for DC Voltage Power Supply Applications

Three-phase pulsewidth modulation (PWM) current source rectifiers (CSRs) that applied as dc voltage power supply include capacitors in the dc bus to obtain dc output voltage, which increase the system complexity and complicate the control strategy. In this paper, a dynamic model of the three-phase PWM CSR is first established in the dq -rotating frame for capacitive load applications. By aligning the vector of the ac capacitor voltage to the $d$ -axis, the model of the CSR can be simplified and decoupled into dc and ac side circuits, which can be controlled separately. Based on this model, a control strategy composed of a state-variable feedback control method for the dc side and an active-damping control method for the ac side is proposed. Moreover, a unity power factor of the CSR is achieved by regulating the $q$ component of the bridge currents. Simulation and experimental results are presented to validate the dynamic and static performance of the proposed control strategy.

A Unified State-Space Model of Constant-Frequency Current-Mode-Controlled Power Converters in Continuous Conduction Mode

While current-mode control of dc–dc converters provides numerous benefits over voltage-mode control, previous models of the control strategy have been limited to the form of classical control models. Through the use of a state-space averaged (SSA) model of current-mode control, both the open-loop and closed-loop circuit parameters of open-loop control-to-output frequency response, conducted susceptibility, input admittance, output impedance, and any other desired response can be easily obtained. In this paper, SSA models of current-mode-controlled converters are derived and presented for buck, boost, and flyback topologies operating in continuous conduction mode. The new model allows for simpler and more accurate modeling than possible with previous methods, facilitates the modeling of cascaded converters, and allows for the use of state-variable feedback and other modern control methods in applications that use current-mode control.

Experiment of the State Variable Feedback for a Quadrotor

This work is the design of the robust attitude stabilization of a quadrotor. The dynamics model of the quadrotor is normally non-linear and it is difficult to obtain an accurate dynamic model. The linearized model is obtained based on data from experiments. The Multiple Input Multiple Output (MIMO) state variable feedback control is implemented to stabilize the system. The dynamic model based on approximated torques (roll, pitch, and yaw) as inputs and the dynamic model based on rotational speeds of the four rotors are used for design the controller. The experimental results from both dynamic model has very similar characteristic and perform much better than the conventional controller.

Adaptive control strategy‐based reference model for spacecraft motion trajectory

SummaryIn aerospace field, the economic realization of a spacecraft is one of the main objectives that should be accomplished by conceiving the optimal propulsion system and the best control algorithms. This paper focuses on the development of a viable adaptive control approach (ACA) for spacecraft motion trajectory (SMT). The proposed strategy involves the nonlinear mathematical model of SMT expressed in the central field, which is linearized by the Taylor expansion, and the second Lyapunov method to offer a high rate and unfailing performance in the functioning. The adaptive control system is composed of the cascade of adaptation loop and feedback control loop. When the spacecraft deviates from its reference trajectory model, the ACA acts on the control system to correct this deviation and follow the optimal reference trajectory. Therefore, when the states of the adjustable model are different from its reference values, then the error signal is provided as an input to the adaptation law, which contains the adaptation algorithm. The output will be the state variable feedback control matrix, which will be used to calculate the new control law vector. The efficiencies of the linearization procedure and the control approach are theoretically investigated through some realistic simulations and tests under MATLAB. The steady‐state errors of control between the reference model and the adjustable model of SMT converge to zero. Copyright © 2014 John Wiley & Sons, Ltd.

Design and ARM Platform-Based Realization of Digital Color Image Encryption and Decryption via Single State Variable Feedback Control

In this paper, discrete-time chaotic systems under single state variable feedback control are studied, and drive-response synchronization is investigated. To that end, ARM platform-based digital color image encryption and decryption using a chaotic stream cipher is designed and implemented, with experimental results demonstrated.

Robust Control of An Uncertain Nonlinear System With Unobservable Dynamics

This work examines controller design based on feedback linearisation of a nonlinear system in the presence of parametric uncertainty and unobservable dynamics. In this case various analytic constraints make it difficult to design a robust controller in the conventional manner (Isidori (1995)). Through a design example, linear state variable feedback controllers are computed via eigen structure assignment to illustrate the effectiveness of the proposed method. Also sufficient conditions are mentioned which guarantee the stability of the closed-loop system.

Active Queue Management Based on State Variable Feedback Control

A new AQM algorithm based on state variable feedback control (SPC) is proposed. The future dynamic queue length in data buffer predicted by state space model is successfully introduced into feedback data's advanced prediction to compensate feedback delay. Finally, the control requirement of congestion is converted to optimal control objective function, and drop probability is obtained by solving the optimal problem. The simulation results show that the queue length with SPAQM algorithm reaches the desired value with minimal tracking error and lower drop probability. SPAQM algorithm has better performance than PID algorithms and RED algorithms in terms of disturbance rejection, stability, and robustness.

Improved control of individual blade pitch for wind turbines

This paper is concerned with improved control of individual blade pitch for wind turbines. The controller is based on the proportional-integral-plus (PIP) algorithm, considered an extension of conventional proportional-integral/proportional-integral-derivative (PI/PID) controllers, in which full state variable feedback control is implemented directly from the measured input and output signals. In particular, the design and implementation of a PIP algorithm based on either standard or advanced individual blade pitch control is presented in the paper. The preliminary results reported in this article, based upon simulations using a linear transfer function representation of the pitch control system, have demonstrated that the proposed approach is robust to stochastic influences arising from both parametric uncertainty and system disturbance. The work presented in this paper constitutes a step towards the development of an advanced individual blade pitch controller.