Third-order Plant Research Articles

Unified Control Scheme of Grid-Connected Inverters for Autonomous and Smooth Transfer to Stand-Alone Mode

As one of the approaches for a grid-sustaining inverter, the inverter should cover not only grid-connected (GC) mode but also stand-alone (SA) mode for power supply to local loads; therefore, there are separate control loops for each mode. In order for an uninterruptible power supply to the local load, it should be seamless to change from GC mode to SA mode. This carries two types of issues. One is a transient state caused by switching the control loops. The other is an uncontrolled state during the time interval between a grid failure and its detection, called clearing time. These can lead to unstable voltage for the local load. Hence, a smooth and autonomous mode switching method is required even if the fault detection is late. Existing mode transfer methods considering both the issues have been accompanied by a slow dynamic response, additional sensors, restriction of adopting filter, or controller complexity due to third-order plant. To overcome them, in this article, a control scheme realized by a unified control loop is proposed for smooth and autonomous mode switching with a novel antiderailing control. Furthermore, the proposed control scheme can achieve a high bandwidth for the output power control in GC mode because it is based on controlling the current flowing the inverter-side inductor, and both filter types, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> , can be adopted. To validate the proposed concept, simulations and experiments were conducted. The results show that the proposed control scheme can be used to achieve autonomous and smooth mode transition even under reactive power reference and reactive load conditions.

Robust Current Control of Voice Coil Motor in Tip-Tilt Mirror Based on Disturbance Observer Framework

In this paper, a control methodology based on the disturbance observer (DOB) framework is proposed to improve the current dynamic characteristic and the robustness of the voice coil motor (VCM) in the tip-tilt mirror. It is shown that the open-loop current characteristic is a third-order plant, which is influenced obviously by both the electrical and mechanical uncertainties under different environment temperatures. Although the traditional PID control is helpful to improve the current dynamics, it is not able to provide enough robustness. Therefore, a new control methodology based on DOB is proposed. The plant model is simplified from third-order to first-order by considering the back-electromotive force (EMF) as the disturbance. The perturbation of the electrical parameters is compensated by the inner-loop of the DOB framework, and the perturbation of the mechanical parameters is compensated by suppressing the back-EMF. Moreover, new sufficient conditions for robust stability are presented in the control method based on H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> algorithm. Compared with the traditional researches, the upper bound of the uncertainties is calculated directly in this paper. Therefore, the ranges of the electrical parameters are very clear according to the Q-filter. Based on the stability conditions, new design guidelines for the DOB-based robust current control for induction motor are also presented. Experiment results are given to show the design details and the superiority of the proposed control method.

Discrete-Time Fractional, Variable-Order PID Controller for a Plant with Delay.

In this paper, we discuss the implementation and tuning algorithms of a variable-, fractional-order Proportional–Integral–Derivative (PID) controller based on Grünwald–Letnikov difference definition. All simulations are executed for the third-order plant with a delay. The results of a unit step response for all described implementations are presented in a graphical and tabular form. As the qualitative criteria, we use three different error values, which are the following: a summation of squared error (SSE), a summation of squared time weighted error (SSTE) and a summation of squared time-squared weighted error (SST2E). Besides three types of error values, obtained results are additionally evaluated on the basis of an overshoot and a rise time of the output signals achieved by systems with the designed controllers.

Синтез оптимального двопозиційного регулятора із мінімальною кількістю перемикань

. A method of synthesis of optimal on-off controllers with a minimum number of switchings is developed in the work. The essence of the method is in reducing the original problem to the problem of minimizing the function of the generalized criterion in the parameter domain of the controller. The topology of the latter makes it possible to sequentially find sets of controller parameters that ensure the fulfillment of ranked problem conditions. An on-off-PI-controller has been proposed in the paper. Its parameters (gains of proportional and integral components of the controller, as well as the threshold at which switching of the control function is carried-out) have been found in the article. In order to prove the effectiveness of the developed method, calculations were performed for four second- and third-order plants (one plant has a time delay). The quality of controlled processes was compared in terms of: average normal error, module of average control, overshoot, settling time and number of switchings. The results of the comparative analysis on these indicators showed that ceteris paribus the synthesized PI-controller has the least number of control switchings. This result extends the duration of use of the automatic control system actuators. The calculations showed that the method of minimizing the number of switchings can be successfully applied within the methodology of synthesis of optimal regulators, which had been developed in the previous author’s researches. Key words: on-off controller, synthesis, criterion, optimization, switching

Bifurcation analysis for non-local design of a hybrid observer for the impulsive Goodwin\u2019s oscillator

The impulsive Goodwin’s oscillator is a mathematical model capturing the dynamics arising in a closed-loop system, where a third-order linear time-invariant plant is subject to an intrinsic pulse-modulated feedback. Originally, the model was motivated by pulsatile regulation in endocrine systems but also has other potential applications. The asymptotic estimation of the hybrid state of the impulsive Goodwin’s oscillator is considered in this paper. A hybrid observer makes use of the continuous plant output to correct the estimates of the state vector through two output error feedbacks: a continuous and a discrete one. When the hybrid state estimation error is zero, the observer is in a synchronous mode characterized by the firings of the impulses in the observer feedback and those of the plant occurring simultaneously. The synchronous mode thus corresponds to an equilibrium point of the hybrid state error dynamics. To guarantee asymptotic convergence of the observer to the synchronous mode, the basin of attraction of the equilibrium has to include all feasible initial deviations of the state estimates. To guarantee the above properties, a numerical observer design approach based on bifurcation analysis of a discrete map capturing the observer state transitions from one impulse firing to another is proposed and its efficacy is demonstrated in simulation.

Output Feedback Algorithm for Nonlinear Systems with Compensation of Bounded Disturbances and Measurement Noises

The output feedback algorithm for dynamic plants with compensation of parametric uncertainty, external disturbances and measurement noises is synthesized. The plants are described by a nonlinear system of differential equations with vector input and output signals. Unlike most existing control schemes in this paper the dimensions of the measurement interference and the output signal are equal, the sources of the signals of disturbances and disturbances are different, parametric and external disturbances can be present in any equation of the plant model. For simultaneous compensation of disturbances and measurement noises it is proposed to consider two channels. On the first channel a part of the measurement noises will be estimated which will allow partial recovery the information about the plant noisy output. On the second channel the disturbances will be compensated. Thus, at least two independent measurement channels are required for simultaneous compensation of disturbances and measurement noises. Sufficient conditions for calculating the parameters of the algorithm in the form of solvability of the linear matrix inequality are obtained. It is shown that the equation of a closed-loop system obtained on the basis of the proposed algorithm depends on the disturbances and the smallest component of the measurement noise. However, if the smallest component cannot be identified a priory, the results of the transients depend on the component of the noise that will be selected in the synthesis of the control system. Thus, unlike most existing control schemes, where the equation of a closed-loop system depends on disturbance and noise, the resulting algorithm provides better transients, because they do not depend on the entire noise vector, but only on its smallest (one) component. The simulations for a third-order nonlinear plant and the synchronization of an electrical generator connected to the power grid are presented. Numerical examples illustrate the effectiveness of the proposed scheme and the robustness with respect to random components in the noises and disturbances.

PID Controller Tuning via Dominant Pole Placement in Comparison with Ziegler-Nichols Tuning

The paper provides PID controller tuning for the third-order plants with delay. For obtaining the PID setting the dominant three-pole placement is applied to achieve desired dynamics. This dynamics is proposed such that to overcome well-known Ziegler-Nichols (Z-N) tuning rule. The desired dynamics proposal is found out by the integrated absolute error (IAE) optimization of the fourth-order PID control loop with delay. The initial guess for this optimization is based on ultimate frequency assessment and the IAE optimization is performed with respect to disturbance rejection. The dominant three-pole placement approach to the PID tuning is designed for oscillatory, aperiodic and integrating plants of the third-order. On examples the proposed PID tuning is demonstrated overcoming the Z-N tuning.

Robust Control for Continuous LPV System with Restricted-Model-Based Control

This paper deals with the robust stabilization of a class of linear parameter varying systems in the continuous control case. Instead of using a state observer or searching for a dynamic output feedback, the considered controller is based on output derivative estimation. This allows the stabilization of the plant with very large parameter variation or uncertainties. The robustness of such controller, for any all-poles single-input/single-output system, is provided for second- and third-order plants. The proof of stability is based on the polytopic representation of the closed loop under Lyapunov conditions and system transformations. The result is a control structure with only one parameter tuned via very simple conditions.

Multi(2)-Rate Control From a 2-Periodic Perspective: Generalized 2-Rate Control

This technical note finds that a conventional 2-rate controller (which receives feedback at T-but provides control at 2T-intervals) has a 2-periodic core, and augments this core to have a generalized 2-rate control that has complete loop-zero (and pole) placement capability. An algorithm for controller parameter evaluation for pole-zero placement using only linear algebraic steps has been developed. The controller also ensures zero steady-state and improved transient ripples. Its superiority in respect of gain-margin compensation is illustrated for a third-order plant with an unstable pole and a non-minimum-phase zero.

Linear quadratic output tracking and disturbance rejection

This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed.

Robust Positively Invariant Cylinders in Constrained Variable Structure Control

This paper proposes the use of cylinders as primary invariant sets to be used in certain state-constrained control designs. Following the idea originally introduced by O'Dell, the primary invariant set is intersected with the state constraints to yield sets which retain the invariance under some conditions. Although several results presented here apply to fairly general nonlinear systems and primary invariant sets of any shape, the focus is on constrained sliding-mode control (SMC) using infinite cylinders as the primary invariant set. Their use is motivated by a coordinate transformation where the sliding motion is decoupled from the overall convergence to the origin. Robust positive invariance conditions are given for cylinders having convex and compact cross sections. For the case of cylinders with ellipsoidal cross sections, the invariance condition is given in the form of a linear matrix inequality. Further, a decision procedure to qualify each state constraint is given as a tool for the selection of the switching gain. A numerical example for a third-order plant illustrates the method.

Autonomous Component Health Management with Failed Component Detection, Identification, and Avoidance

This article describes a novel scheme for autonomous component health management (ACHM) with failed actuator detection and identification and failed sensor detection, identification, and avoidance. This new scheme has features that are very superior to those with triple redundant sensing and voting, yet requires fewer sensors; it can be applied to any system with redundant sensing. Relevant background to the ACHM scheme is provided in this article. Simulation results for its application to a single-axis spacecraft attitude control system with a third-order plant and dual-redundant measurements of the system states are presented. The ACHM scheme fulfills key functions needed by an integrated vehicle health monitoring (IVHM) system. It is autonomous; is adaptive; works in real time; provides optimal state estimation; identifies failed components; avoids failed components; reconfigures for multiple failures, reconfigures for intermittent failures; works for hard-over, soft, and zero-output failures; and works for both open- and closed-loop systems. The ACHM scheme combines a prefilter that generates preliminary estimates of the system states, detects and identifies failed sensors and actuators, and avoids failed sensors in generating preliminary estimates of the system states with a fixed-gain Kalman filter that provides model-based state estimates, which are utilized in the failure detection logic, and generates optimal estimates for the system states. The simulation results show that ACHM can successfully detect, identify, and avoid sensor failures that are single or multiple; persistent and intermittent; and hard-over, soft, and zero-output types. It is now ready to be tested on a computer model of an actual system.

Optimal State Estimation With Failed Sensor Discrimination and Identification

A new estimation scheme is presented that combines a fixed-gain Kalman filter for optimal state estimation with a prefilter that discriminates against failed sensors and identifies a failed sensor in real time. This new scheme has features characteristic of systems with triple-redundant sensing and voting, but with fewer sensors. It is tested on second- and third-order plants with dual-redundant measurements of the system states and is shown to out perform the stand-alone Kalman filter by a factor of two or more in terms of the rms estimation errors. Strategies for application to systems higher than third order are discussed.

A Fuzzy Gain Scheduling Scheme for the PIIσD Controllers

This article proposes a new fuzzy gain scheduling scheme for the PII>rD controller. Fuzzy IF-THEN rules are used online to adjust the parameters of the PID controller based on the system error and its derivative. Simulation results clearly reveal that the proposed scheme outperforms the previously developed controllers. Performance metrics used in the evaluation are: settling time, 1% peak overshoot, and integral of the time multiplied by the square error. Computer simulations numerical examples are demonstrated using first-order plant with signal transmission delay and third-order plant.

Design of Continuous Time Controllers Having Almost Minimum Time Response

A class of near time-optimal nonlinear controllers—the Continuous Proximate Time-Optimal (CPTO) controllers—which involves continuous, rather than discontinuous, nonlinear feedback control functions is introduced. The CPTO controllers give near time-optimal response for large state errors, and provide smooth, stable response with near linear control for small state errors. In this paper, the CPTO controllers for three second-order (two stable and one unstable) plants and one third-order plant are introduced. Complete stability proofs, using the CPTO control law, are given for all the systems considered. It has been shown through the simulation that response times are indeed near time-optimal for all cases considered.

State Space Approach to the Stability Analysis of a Class of Fuzzy Control Systems meant for Third-Order Plants

The paper proposes a stability analysis method that is applicable to the fuzzy control of a class of third-order nonlinear plants, with the right-hand term of the state equation restricted to being a continuous and partially differentiable function. The paper derives stability conditions that are expressed by a set of indices that verify the character of the equilibrium point and its uniqueness, and also measure the relative degree of stability. The stability conditions are useful to the development of the type-II state feedback fuzzy controller (in terms of (Sugeno, 1999)) meant for controlling the mentioned class of plants, and are obtained as a particular case to those presented in (Precup, et al, 2000). The application presented in the paper deals with the control of a real-world plant consisting of the development of a fuzzy control system that copes with the level control of a three-tank system.

Derivation of Fuzzy Rules for Model-Free Tuning of PID Controllers

In this article we derive the rules for a fuzzy logic based PID tuner expert for dominant pole systems with large rise times. We present applications of the expert to a third-order plant, separator temperature control, and pH control. It is observed that the expert can successfully tune the PlD gains without requiring any process identification.

The robustness of a proximate time-optional controller [optional read optimal

Two practical time-optimal controllers for rapid slewing of type-3 and type-2 third-order plants, PTOS3 and PTOS3/spl tau/, respectively, were previously proposed. In this paper, we present results showing that the PTOS3/spl tau/ is more robust than the corresponding time-optimal controller to both plant parameter variations and feasible unmodeled dynamics. In addition, a useful numerical method to calculate the time-optimal controls for general linear systems is presented. The results for the PTOS3 and the time-optimal controller for type-3 third-order plants are similar and thus are not detailed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Proximate time-optimal control of third-order servomechanisms

The problem of proximate time-optimal control of third-order systems is considered. Two proximate time-optimal servomechanisms, PTO53 and PTO53 tau , are proposed for type-3 and type-2 third-order plants, respectively. Theorems stating sufficient conditions on each system's control design parameters to ensure global stability are given, and it is shown that the control parameters can be adjusted to accommodate, more or less, disturbances and unmodeled dynamics in the system. The approach used to develop the controllers is that of constructing a 'slab' in three-dimensional state space that describe the 'switching' structure of the control. The technique relies on three-dimensional phase-space analysis, which is rarely applied to systems of order three or higher. Simulation and experimental results demonstrate the performance of the algorithms developed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A family of linear, time-invariant universal adaptive controllers for linear and non-linear plants

Abstract A ‘universal adaptive controller’ is a single adaptive controller that can automatically accommodate a significant range of plants having different structures. In this paper, a family of three universal adaptive controllers is presented, one for each of the three cases: first-order plants, second-order plants, and third-order plants. The family of universal adaptive controllers presented here is rather novel in the respect that each controller is all-linear and completely time-invariant. Numerous examples and simulation results are presented to illustrate the ‘universality’ of the proposed adaptive controllers.