Constant Reference Signals Research Articles

SPEED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTOR IN SLIDING MODE

The paper examines a series of speed control algorithms for a synchronous permanent magnet motor in sliding mode, providing asymptotic stability of the first, second, and third order. In the sliding mode, the control system exhibits properties that are unattainable with classical continuous control algorithms. The control algorithms are developed based on the inverse dynamics method combined with the minimization of local instantaneous energy functionals. The key idea of the method lies in the reversibility of the direct Lyapunov method for stability analysis. The closed-loop control system has a predefined Lyapunov function, represented by the instantaneous energy. Notably, the control algorithms do not require knowledge of the object's parameters or differentiation operations, which facilitates their practical implementation. The regulator parameters consist solely of coefficients used to specify the desired duration and shape of current and motor speed transient processes. The vector speed control system comprises two controllers for the stator current components and the motor speed controller. All regulators operate in sliding mode. The output signals of the stator current component controllers and speed vary discontinuously from maximum to minimum values. Simulation results demonstrate the effectiveness and high-quality performance of the control algorithms. To determine the control performance indicators for the three synthesized speed controllers, the motor startup trajectory is formed from characteristic segments of constant, linearly increasing, and parabolic signals. The speed control algorithm with a first-order asymptote ensures zero tracking error only for a constant reference signal. With a linearly increasing reference signal, the steady-state relative tracking error is 2,5 %, while for a parabolic reference signal, the error varies between zero and 2,5 %. The second-order asymptotic speed control algorithm ensures zero steady-state tracking error for constant and linearly increasing reference signals, and for a parabolic reference signal, the steady-state relative tracking error is 0,125 %. The third-order asymptotic speed control algorithm ensures zero steady-state tracking error for constant, linearly increasing, and parabolic reference signals, with a maximum dynamic relative tracking error of 0,05 %.

Average-rendezvous with connectivity preservation for first-order multiagent systems with constant reference signals

Average-rendezvous problem with connectivity preservation of constant reference signals is investigated for first-order multiagent systems. According to a constructive potential function, a proportional–integral average-rendezvous algorithm is proposed to make agents converge to the average value of constant reference signals as well as the network connectivity is preserved all the time. Sufficient convergence conditions are obtained for the algorithm by designing the proper Lyapunov functions. Numerical examples illustrate the correctness of theoretical results.

A robust nonlinear tracking MPC using qLPV embedding and zonotopic uncertainty propagation

In this paper, we propose a novel Nonlinear Model Predictive Control (NMPC) framework for tracking for piece-wise constant reference signals. The main novelty is the use of quasi-Linear Parameter Varying (qLPV) embeddings in order to describe the nonlinear dynamics. Furthermore, these embeddings are exploited by an extrapolation mechanism, which provides the future behaviour of the scheduling parameters with bounded estimation error. Therefore, the resulting NMPC becomes computationally efficient (comparable to a Quadratic Programming algorithm), since, at each sampling period, the predictions are linear. Benefiting from artificial target variables, the method is also able to avoid feasibility losses due to large set-point variations. Robust constraint satisfaction, closed-loop stability, and recursive feasibility certificates are provided, thanks to uncertainty propagation zonotopes and parameter-dependent terminal ingredients. A benchmark example is used to illustrate the effectiveness of the method, which is compared to state-of-the-art techniques.

Virtual reference feedback tuning for linear discrete-time systems with robust stability guarantees based on set membership

In this paper we propose a novel methodology that allows us to design, in a purely data-based fashion and for linear single-input and single-output systems, both robustly stable and performing control systems for tracking piecewise constant reference signals. The approach uses both (i) virtual reference feedback tuning for enforcing suitable performance and (ii) the set membership framework for providing a-priori robust stability guarantees. Indeed, an uncertainty set for the system parameters is obtained through set membership identification, where an algorithm based on the scenario approach is proposed to estimate the inflation parameter in a probabilistic way. Based on this set, robust stability conditions are enforced as linear matrix inequality constraints within an optimization problem whose linear cost function relies on virtual reference feedback tuning. To show the generality and effectiveness of our approach, we apply it to two of the most widely used yet simple control schemes, i.e., where tracking is achieved thanks to (i) a static feedforward action and (ii) an integrator in closed-loop.The proposed method is not direct due to the set membership identification. However, the uncertainty set is used with the objective of providing robust stability guarantees for the closed-loop system and it is not used for the definition of the cost function, which instead is based on data. The effectiveness of the method is shown with reference to three simulation examples. A comparison with other data-driven methods is carried out.

Robust offset‐free nonlinear model predictive control for systems learned by neural nonlinear autoregressive exogenous models

AbstractThis paper presents a robust model predictive control (MPC) scheme that provides offset‐free setpoint tracking for systems described by neural nonlinear autoregressive exogenous (NNARX) models. To this end, a NNARX model that learns the dynamics of the plant from input‐output data is augmented with an explicit integral action on the output tracking error. A robust tube‐based MPC is finally designed, leveraging the unique structure of the model, to ensure robust offset‐free convergence to constant reference signals even in case of plant‐model mismatch. Numerical simulations on a water heating system show the effectiveness of the proposed control algorithm.

Robust adaptive tube tracking model predictive control for piece‐wise constant reference signals

AbstractRobust tracking of piece‐wise constant reference signals for constrained systems with parametric plant uncertainty and additive disturbances is addressed in this paper. The parametric uncertainty is decreased online by set‐membership estimation and a nominal model is updated for improving set‐point tracking. The online estimated parametric uncertainty is used for an online‐determined terminal set which enlarges the set of reachable references close to the system constraints when compared to an offline worst‐case consideration. An artificial target state is introduced which can deviate from the nominal target state. This new target state is used to ensure recursive feasibility for unreachable references and changes in the reference signal. Moreover, a novel “recovery mode” is specified which is deployed in case the new nominal model yields an infeasible control problem. Control algorithms are developed for time‐invariant systems and systems with arbitrarily fast changing plants but known relative bounds. Constraint satisfaction and ‐stability are guaranteed for the proposed algorithms. Controlling the engine load of a self‐propelled work machine is used as a practical example.

Distributed Optimization of Uncertain Multiagent Systems With Disturbances and Actuator Faults via Exosystem Observer-Based Output Regulation

This paper investigates a distributed optimization problem for heterogeneous linear multi-agent systems with uncertain parameters and external disturbances. For each agent, the optimal solution of the global objective functions can be regarded as an unknown constant reference signal. From this angle, the problem is transformed into an output regulation problem for an exosystem whose states and outputs are to be estimated. To ensure the trackability of the estimated signal, a fundamental design condition for the exosystem observer to achieve robust output regulation is given in the context of internal model control. Exact global optimization is then realized by embedding an appropriate distributed optimization algorithm (i.e., the exosystem observer) in each agent to estimate the global optimal solution. The result for exosystem observer design is extended to yield an adaptive fault-tolerant control algorithm to deal with a class of practical actuator fault uncertainties. The exosystem observer-based output regulation method provides a general distributed robust optimization framework for uncertain systems with disturbances and actuator faults, which can directly apply to various consensus problems. Simulations are provided to illustrate the effectiveness of the method.

Optimal output tracking of Boolean control networks

The traditional output tracking problem for a system is to design a controller such that the output of the system tracks a constant signal or a network after a finite time. However, when the output of the system can not completely track the reference signal, there is no result to show how to deal with this situation. To solve such problem, we investigate the optimal output tracking problem of Boolean control networks (BCNs) with a constant reference signal in this paper, that is, to design an appropriate control scheme such that each state will evolve to their optimal output tracking trajectory. Firstly, the optimal output tracking cycle (OTC) of each state is defined. Secondly, a method is presented to compute the cycle with certain length in the system, and the least upper bound of the length for the optimal OTC is derived. Finally, a constructive algorithm is presented to design the state feedback controllers that enable the system to realize optimal output tracking. Moreover, an illustrative example is given to show the obtained results.

On offset-free Model Predictive Control with Long Short-Term Memory Networks

This paper addresses offset-free reference tracking of asymptotically constant reference signals and disturbances using Model Predictive Control with a Long Short-Term Memory Network model. Basically, an error free output estimation and an error free nominal tracking for time-varying references are proposed for an Incremental Input-to-State Stable Long Short-Term Memory Network. This implies an offset-free Model Predictive Control algorithm.

Low‐gain integral control for a class of discrete‐time Lur'e systems with applications to sampled‐data control

AbstractWe study low‐gain (P)roportional (I)ntegral control of multivariate discrete‐time, forced Lur'e systems to solve the output‐tracking problem for constant reference signals. We formulate an incremental sector condition which is sufficient for a usual linear low‐gain PI controller to achieve exponential disturbance‐to‐state and disturbance‐to‐tracking‐error stability in closed‐loop, for all sufficiently small integrator gains. Output tracking is achieved in the absence of exogenous disturbance (noise) terms. Our line of argument invokes a recent circle criterion for exponential incremental input‐to‐state stability. The discrete‐time theory facilitates a similar result for a continuous‐time forced Lur'e system in feedback with sampled‐data low‐gain integral control. The theory is illustrated by two examples.

Self-triggered MPC with performance guarantee for tracking piecewise constant reference signals

This paper considers a self-triggered MPC controller design strategy for tracking piecewise constant reference signals. The proposed triggering scheme is based on the relaxed dynamic programming inequality and the idea of reference governor; such a scheme computes both the updated control action and the next triggering time. The resulting self-triggered tracking MPC control law preserves stability and constraint satisfaction and also satisfies certain a priori chosen performance requirements without the need to impose stabilizing terminal conditions. An illustrative example shows the effectiveness of this self-triggered tracking MPC implementation.

Adaptive backstepping control for master-slave AC microgrid in smart island

To control a smart-island (which comprises three distributed generation (DG) units with their autonomous converters), based on a nonlinear backstepping control (BSC) scheme, an adaptive reference signal, and a state observer are designed to improve the steady-state performance of the system. An adaptive reference value has been designed and used instead of a constant reference signal to improve the system's steady-state performance, e.g., total harmonic distortion (THD), peak value, and effective value in the voltage control mode. The presented adaptive reference is changed based on the error between the reference signal and the output voltage signal to tend the error to zero. Compared to the classical backstepping controllers, the reference signal is pursued with a fast response and a low steady-state of loads alternations. To demonstrate the efficiency, authenticity, and compatibility of the proposed control strategy, offline digital time-domain simulation studies are carried out on a master-slave organized inverter-based microgrids in various load variations like linear and nonlinear loads in MATLAB/Simulink software environment. The obtained results are compared with previously reported techniques. Moreover, the obtained simulation results are verified by performing laboratory-based experimental tests based on digital signal processing (DSP), which validate the proposed control strategy's accuracy, authenticity, and effectiveness under different conditions.

Stationary average-tracking problem of unmatched constant reference signals based on delayed-state feedback

Stationary average-tracking problems of unmatched constant reference signals are investigated for first-order multi-agent systems, and an integral-type average-tracking algorithm with delayed-state feedback is constructed. With identical communication delays and different introduced self-delays, sufficient conditions are obtained for the agents converging to the average-value of unmatched reference signals asymptotically by using the frequency-domain analysis method. To our delight, introducing delayed-state feedback improves the robustness to communication delay and unmatched reference signals. Simulation results show the effectiveness of our proposed algorithm.

An event-triggered model predictive control with exponentially stable offset free for PWA systems with model-plant mismatch

A new event-triggered model predictive control (MPC) method is proposed for PWA systems with model-plant mismatch, such that, for a given asymptotically constant reference signal, exponential stability and unbiased tracking can be achieved. Firstly, for the PWA system, an observer is designed to estimate state and the model-plant mismatch. To guarantee the exponential stability, an event is introduced, and an event-triggered model predictive controller is designed as well. By introducing state error and estimate error, an augmented model is constructed. Then, using the model-dependent average dwell time (MDADT) method and Lyapunov stability theory, exponentially stable condition of the closed-loop system is derived, which is formulated by linear matrix inequalities (LMIs), and zero offset is also guaranteed under some mild assumptions. Moreover, the MDADT of each sub-system is given simultaneously. Finally, simulations have been taken to verify the effectiveness of the proposed method.

The experimental identification method of the dynamic efficiency for frequency regulation algorithms of AEDs

The article proposes and substantiates a method for studying the dynamics of an asynchronous electric drives with frequency control from the input side of the signal for setting the speed of rotation of the electric motor. In this method, a constant speed reference signal is added to a harmonic variable frequency signal. The set of amplitude changes and phase shifts of velocity oscillations are the initial data for identifying the dynamics of the studied control method. The logic of this method is determined by the previously obtained nonlinear transfer function of the link that forms the mechanical moment in the asynchronous electric drive with frequency control. Experiments have shown the dynamic benefits of the drive with positive stator current feedback.

Distributed guidance-based formation control of marine vehicles under switching topology

Because of the limited and unreliable communication topology in complex marine environment, the formation control of marine vehicles under switching topology is investigated in this paper, whereas the most previous works for marine formation focused on the fixed communication topology. In order to simplify the formation control design, a novel distributed guidance system, rather than the traditional distributed control system, is established based on leader-follower strategy only using a portion of communication links. To address the problem of input saturation of marine vehicle, the model predictive control is therefore employed to design the marine formation controller; furthermore, the predictive mechanism allows model predictive control to prevent the constraint violation in advance, which brings advantages against the large inertia of ship motion. Both formation tracking control and formation regulation control are studied herein. For application of formation tracking control of marine vehicles, i.e., the time-varying reference signal, the formation control can be realized under switching topology with the condition that the communication topology contains a directed spanning tree. For application of formation regulation control of marine vehicles, i.e., the constant reference signal, the formation control can be realized under switching topology with a relative milder condition that the union of communication topology contains a directed spanning tree. Multiple simulations are included to show the effectiveness of the presented distributed guidance-based MPC formation controllers.

Asymptotic Output Tracking of Probabilistic Boolean Control Networks

In this paper, we investigate the asymptotic output tracking control problem of probabilistic Boolean control networks. Firstly, based on the largest control invariant subset and the limit theory of Markov chains, the conditions are proposed to judge whether the output trajectory of a probabilistic Boolean control network can asymptotically track a constant reference signal via the state feedback control and output feedback control, respectively. Next, based on an augmented system, similar criteria are obtained to judge whether the output of a reference Boolean network is asymptotically trackable by the output trajectory of a probabilistic Boolean control network under the state feedback control and output feedback control, respectively. The corresponding controller design methods are given. Two examples are shown to illustrate the effectiveness of the obtained results.

Output Robustness of Probabilistic Boolean Control Networks With Respect to One-Bit Perturbation

Robustness is an important property for the analysis of network systems. In this article, we investigate the ability of probabilistic Boolean control networks (PBCNs) to keep output tracking to a constant reference signal under one-bit perturbation, and it is briefly termed as output robustness thereafter. Considering the output robustness of PBCNs, the traditional approaches in the preceding literature are disabled. To this end, we use the strongly connected components to characterize the invariant subset. The salient advantage of this approach is that the obtained invariant subset is equipped with a minute structure. Then, a component digraph is constructed. Based on it, two necessary and sufficient criteria are, respectively, derived for finite-time and asymptotic output tracking of PBCNs. Moreover, one-bit perturbation is classified into three categories with respect to different influence on the output tracking. Finally, a biological example demonstrates the availability of our theoretical results.

Set‐point output tracking problem for linear plants via periodic event‐triggered control

This study addresses event-triggered tracking control for linear systems with constant reference signals and disturbances. A remote observer-based proportional–integral controller, which communicates with the plant only at some discrete instants, is designed. The transmissions, involving both the sensor-to-controller and the controller-to-actuator channels, are scheduled by periodic event-triggered control. A new kind of summation-based triggering condition is proposed which can ensure that there exists a positive minimum inter-event time uniformly for a family of controllers parameterised by the verification periods. Then, it is proved that the proposed periodic event-triggered control can solve the set-point tracking problem asymptotically without the assumption that the reference signal is accessible to the sensor. Finally, simulation results are provided to illustrate the efficiency and feasibility of the obtained results.

Model Predictive Control for Offset-Free Reference Tracking

<span style="font-family: 'Times New Roman',serif; font-size: 10pt; -ms-layout-grid-mode: line; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-GB; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-GB">The paper deals with the offset-free reference tracking problem of the Model Predictive Control (MPC). That problem is considered for a class of the constant or occasionally changed constant reference signals. Proposed solution arises from a simple subtraction of the ARX model <br /> of two consecutive time steps. The solution is adapted <br /> to a state-space form and it corresponds to usual predictive control design without increase of the design complexity. The construction of the prediction equations and pre­dictive controller structure is explained in the paper.</span>