Optimal Disturbance Rejection Research Articles

Improving the insulin therapy for diabetic patients using optimal impulsive disturbance rejection: Continuous time approach

The paper proposes a new model-based optimization approach to improve the clinical efficiency of compensatory insulin bolus treatment in diabetic patients, aiming to mitigate the consequences of diabetes. The most important contribution of this paper is a novel methodology for determining the optimal parameters of insulin treatment, namely the size and timing of insulin boluses, to effectively compensate for carbohydrate intake. This concept can be seen as the so-called optimal model-based bolus calculator. The presented theoretical framework deals with the problem of optimal disturbance rejection in impulsive systems by minimizing an integral quadratic cost function. The methodology considers a personalized empirical transfer function model with static gains and time constants as the only parameters assumed to be known, making the bolus calculator more straightforward to implement in clinical practice. Contrary to other techniques, the proposed methodology considers impulsive insulin administration in the form of boluses, which is more feasible than continuous infusion. In contrast to the conventional bolus calculator, the proposed algorithm allows for maximizing therapy performance by optimizing the relative time of insulin bolus administration with respect to carbohydrate intake. Another feature to highlight is that the solution of the optimization problem can be obtained analytically, hence no numerical iterative solvers are required. Additionally, the continuous-time domain approach allows for a much finer adjustments of the insulin administration timing compared to discrete-time models. The proposed approach was validated in an in-silico study, which demonstrated the importance of systematically determined insulin–carbohydrate ratio and the relative delay between disturbance and its compensation. The results showed that the proposed optimal bolus calculator outperforms the traditional suboptimal formula.

Optimal Active Disturbance Rejection Control for Second Order Systems

Optimal Active Disturbance Rejection Control for Second Order Systems

Optimal guidance law design for three-dimensional trajectory tracking of missiles based on fixed-gain disturbance observer

To address the trajectory tracking problem of missiles, an optimal disturbance rejection guidance law (ODRGL) in three dimensions is proposed under the premise of uncontrollable speed. Error models of the actual and the reference trajectory are built in channels of pitch and yaw, respectively. In the yaw channel, a modeling error is introduced as the model cannot be built directly. According to the separation theorem, the controller and the observer are designed respectively. A fixed-gain disturbance observer (FGDO) is proposed to estimate the disturbance such as wind disturbances and modeling errors, and the disturbance is compensated for feed-forward. The nominal error models of pitch and yaw channels are linearized by the differential geometric linearization theory, and then linear quadratic regulator (LQR) controllers are designed for the linearized models. The simulation results show that in the presence of wind disturbances and modeling errors, the optimal guidance law proposed in this paper can stabilize the original nonlinear system and ensure energy optimization.

Undiscounted reinforcement learning for infinite-time optimal output tracking and disturbance rejection of discrete-time LTI systems with unknown dynamics

This paper proposes a novel control structure to solve the infinite-time linear quadratic tracking (LQT) problem. The major challenge in the LQT problem is the boundedness issue of the cost function in an infinite time framework. In many studies, a discount factor is utilised to overcome the challenge. However, it can affect the stability of the closed-loop system and the steady-state error. This paper proposes an optimal control structure that guarantees zero steady-state error with bounded cost function without utilising the discount factor. The optimal gains of the proposed control structure are computed via model-based and model-free reinforcement learning (RL) algorithms. As a novelty in model-based RL algorithms, a model predictive RL algorithm is proposed to reduce the number of iterations in the learning phase. A model-free reinforcement learning algorithm is utilised to obtain optimal control for tracking the reference online and without any knowledge of system dynamics. Finally, the simulation results verify the advantages of the proposed optimal control structure.

Reinforcement learning based optimal synchronization control for multi-agent systems with input constraints using vanishing viscosity method

This paper investigates the optimal synchronization and disturbance rejection problem for leader-follower multi-agent systems (MASs) subject to constrained input using online actor-critic (A-C) algorithm. Different from the existing works on optimal synchronization problems, the common smoothness assumption on the value function used in the typically reinforcement learning (RL) formulations is not satisfied due to the input constraints. To relax this assumption, the vanishing viscosity method is introduced to construct a more general value function which makes the modified Hamilton–Jacobi-Isaacs (HJI) equation admit a smooth solution. Based on the modified HJI equation, an improved A-C neural networks (NNs) algorithm is developed to find a smooth approximation optimal control solution. Finally, a simulation is performed to demonstrate the effectiveness of the proposed approach.

Event-Triggered Observers and Distributed H∞ Control of Physically Interconnected Nonholonomic Mechanical Agents in Harsh Conditions

In this article, event-triggered (ET) observers and ET-distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\boldsymbol {\mathcal {H}}_{\boldsymbol \infty }}$ </tex-math></inline-formula> controllers are investigated for physically interconnected nonholonomic mechanical agents in harsh conditions, such as skidding, slipping, and dead-zone disturbances. The agents’ models are presented by strict-feedback nonlinear large-scale systems, but unlike the existing studies, unknown dynamics with feedback outputs are considered, and assumptions of polynomial-type nonlinearities for physical interconnection functions are relaxed. Initially, the observer of unmeasurable states via the outputs is designed. Then, ET augmented controllers are established to transform the physically interconnected system into isolated subsystems connected by a communication network. By utilizing the local information of each agent and adaptive dynamic programming (ADP), ET-distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\boldsymbol {\mathcal {H}}_{\boldsymbol \infty }}$ </tex-math></inline-formula> optimal control laws and disturbance rejection laws are derived. The parameters of the ET observers and controllers are synchronously updated online by event-triggering mechanisms; thus, it reduces computational complexity and communication. It is guaranteed that the states in the closed dynamics are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> -gain bounded and the Zeno behavior is avoided. Additionally, the convergence of cost functions to the near-optimal values is accelerated by a concurrent learning technique, avoiding dependence on the online examination of the persistence of excitation conditions. Finally, the control performance of a nonholonomic multirobot system in a comparative simulation study shows that the proposed observers and controllers are effective.

Optimal disturbance predictive and rejection control of a parabolic trough solar field

Optimal disturbance predictive and rejection control of a parabolic trough solar field

A Two-Degree-of-Freedom Controller Design Satisfying Separation Principle With Fractional-Order PD and Generalized ESO

This article proposes a two-degree-of-freedom fractional-order proportional derivative (FOPD) controller with a general extended state observer (GESO) to achieve both optimal set-speed tracking and disturbance rejection performance for a typical permanent magnet synchronous motor servo system. The GESO simplifies the control plant, estimates and actively rejects total disturbances. The FOPD controller achieves fast speed tracking with almost no overshoot. Furthermore, it is verified that the control system with the proposed FOPD-GESO controller design meets the separation principle through mathematical derivation and simulation illustration. It shows that the proposed controller breaks the inherent tradeoff on tracking performance and disturbance robustness of the typical traditional proportional–integral–derivative (PID) control. Meanwhile, a systematic scheme for designing the FOPD-GESO controller to satisfy both frequency-domain and time-domain specifications is proposed in this article. Simulation illustration and experimental validation are performed to demonstrate that the proposed FOPD-GESO controller is superior to the typical integer-order PID controller, integer-order active disturbance rejection control with a typical extended state observer, and fractional-order PID controller in terms of speed tracking, antiload disturbance, and robustness to internal uncertainties.

Robust optimal tracking control for multiplayer systems by off‐policy Q‐learning approach

SummaryIn this article, a novel off‐policy cooperative game Q‐learning algorithm is proposed for achieving optimal tracking control of linear discrete‐time multiplayer systems suffering from exogenous dynamic disturbance. The key strategy, for the first time, is to integrate reinforcement learning, cooperative games with output regulation under the discrete‐time sampling framework for achieving data‐driven optimal tracking control and disturbance rejection. Without the information of state and input matrices of multiplayer systems, as well as the dynamics of exogenous disturbance and command generator, the coordination equilibrium solution and the steady‐state control laws are learned using data by a novel off‐policy Q‐learning approach, such that multiplayer systems have the capability of tolerating disturbance and follow the reference signal via the optimal approach. Moreover, the rigorous theoretical proofs of unbiasedness of coordination equilibrium solution and convergence of the proposed algorithm are presented. Simulation results are given to show the efficacy of the developed approach.

A New PID Controller Design with Constraints on Relative Delay Margin for First-Order Plus Dead-Time Systems

The maximum sensitivity function as the conventional robustness index is often used to test the robustness and cannot be used to tune the controller parameters directly. To reduce analytical difficulties in dealing with the maximum sensitivity function and improve the control performance of the proportional-integral-derivative controller, the relative delay margin as a good alternative is proposed to offer a simple robust analysis for the proportional-integral-derivative controller and the first-order plus dead-time systems. The relationship between the parameters of the proportional-integral-derivative controller and the new pair, e.g., the phase margin and the corresponding gain crossover frequency, is derived. Based on this work, the stability regions of the proportional-integral-derivative controller parameters, the proportional gain and the integral gain with a given derivative gain, are obtained in a simple way. The tuning of the proportional-integral-derivative controller with constraints on the relative delay margin is simplified into an optimal disturbance rejection problem and the tuning procedure is summarized. For convenience, the recommended parameters are also offered. Simulation results demonstrate that the proposed methodology has better tracking and disturbance rejection performance than other comparative design methodologies of the proportional-integral/proportional-integral-derivative controller. For example, the integrated absolute errors of the proposed proportional-integral-derivative controller for the tracking performance and disturbance rejection performance are less than 91.3% and 91.7% of the integrated absolute errors of other comparative controllers in Example 3, respectively. The proposed methodology shows great potential in industrial applications. Besides, the proposed method can be applied to the design of the proportional-integral-derivative controller with filtered derivative which is recommended for practical applications to weaken the adverse influence of the high-frequency measurement noise.

Robust &lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$\mathcal {H}_{\infty }$&lt;/tex-math&gt; &lt;/inline-formula&gt; State Feedback Controllers Based on Linear Matrix Inequalities Applied to Grid-Connected Converters

This paper provides robust $\mathcal {H}_{\infty }$ state feedback controllers suitable for implementation in three-phase grid-connected converters. This control strategy is known to provide optimal rejection of disturbances, but usually leads to high control gains, that may be difficult to be implemented in practice. To mitigate this problem, a linear matrix inequality condition based on slack variables is proposed, which allows to impose bounds on the control gains in a less conservative way than conventional quadratic stability. The performance is proven to be superior to similar $\mathcal {H}_{\infty }$ state feedback controllers in the literature, providing an upper bound for the converter output admittance and experimental grid currents complying with the IEEE Standard 1547.

Dynamic Friction Characterization of a Linear Servo Motor Using an Optimal Sinusoidal Reference Tracking Controller

This letter presents the design of an optimal sinusoidal tracking and disturbance rejection controller for a linear voice-coil motor. The optimal tracking and disturbance rejection system is used to characterize the nonlinear dynamic friction of the servo motor. The control scheme allows investigating the hysteresis characteristics of friction as a function of frequency. Experimental results indicate the effectiveness of the proposed identification procedure for the dynamic friction estimation.

Optimal Disturbance Rejection with Zero Steady-State Error for Nonlinear Vehicle Suspension Systems under Persistent Road Disturbances

The road disturbance rejection problem for vehicle active suspension involving the nonlinear characteristics is researched in this paper. A continuous-time state space of nonlinear vehicle active suspension is established first, in which the road disturbance is generated from the output of an introduced exosystem based on the ground displacement power spectral density. After that, based on the dynamics of road roughness and the internal model principle, a disturbance compensator with zero steady-state error is designed, which is related to the dynamic characteristics of road disturbance and independent of the control system model. By combining the vehicle active suspension system and the designed road disturbance compensator, an augmented system is obtained without explicit indication of road disturbance. Then by solving a series of decoupled nonlinear two-point-boundary-value problem and employing an iterative computing algorithm, an approximation optimal road disturbance rejection controller is obtained. Finally, the simulation results illustrate that the proposed approximation optimal road disturbance rejection controller can reduce the values of sprung mass acceleration, tire deflection, suspension deflection, and energy consumption and compensate the nonlinear behaviors of vehicle active suspension effectively.

Optimal tracking and disturbance rejection with invariant zeros on the unit circle: a polynomial spectral factorization design

We present a simple algorithm for computation of H2-optimal tracking and disturbance rejection controller of discrete-time systems possessing invariant zeros on the unit circle, based on polynomial spectral factorization. We prove that the column degrees of the associated para-hermitian polynomial matrix to be factorized are equal to the plant controllability indices. A numerical/computer simulation example is given.

Optimal disturbance rejection controllers design for synchronised output regulation of time‐delayed multi‐agent systems

An optimal disturbance rejection controller design method is put forward analytically for the synchronised output regulation of time-delayed multi-agent systems (MAS). All kinds of linear MAS can be described by a novel block diagram based on transfer functions in a unified framework. For each subsystem without intercommunication, the optimal output, input and balancing output–input load disturbance rejection controllers are designed independently. A filter is used to be in series with each controller to not only stabilise the whole systems but also achieve a tradeoff between nominal performance and robustness by adjusting a single tuning parameter. The proposed distributed H 2 controllers calculated by algebraic solution perform better capacity of disturbance attenuation than the conventional given-structured protocols. Two simulation examples demonstrate the validity of the new algorithm.

Optimal Disturbances Rejection Control for Autonomous Underwater Vehicles in Shallow Water Environment

To deal with the disturbances of wave and current in the heading control of Autonomous Underwater Vehicles (AUVs), an optimal disturbances rejection control (ODRC) approach for AUVs in shallow water environment is designed to realize this application. Based on the quadratic optimal control theory, the AUVs heading control problem can be expressed as a coupled two-point boundary value (TPBV) problem. Using a recently developed successive approximation approach, the coupled TPBV problem is transformed into solving a decoupled linear state equation sequence and a linear adjoint equation sequence. By iteratively solving the two equation sequences, the approximate ODRC law is obtained. ALuenbergerobserver is constructed to estimate wave disturbances. Simulation is provided to demonstrate the effectiveness of the presented approach.

Fictitious Reference Iterative Tuning-Based Two-Degrees-of-Freedom Method for Permanent Magnet Synchronous Motor Speed Control Using FPGA for a High-Frequency SiC MOSFET InverterMOSFET Inverter

This paper proposes proportional-integral/proportional gain controller parameter tuning in a two-degrees-of-freedom (2DOF) control system using the fictitious reference iterative tuning (FRIT) method for permanent magnet synchronous motor (PMSM) speed control using a field-programmable gate array (FPGA) for a high-frequency SiC MOSFET (metal oxide semiconductor field-effect transistor) inverter. The PI-P (proportional-integral/proportional) controller parameters can be tuned using the FRIT method from one-shot experimental data without using a mathematical model of the plant. Particle swarm optimization is used for FRIT optimization. An inverter that uses a SiC MOSFET is presented to achieve high-frequency operation at up to100 kHz using a switching pulse-width modulation (PWM) technique. As a result, a high-responsivity and high-stability PMSM (permanent magnet synchronous motor) control system is achieved, where the speed response follows the ideal response characteristic for both the step response and the disturbance response. High-responsivity and optimal disturbance rejection can be achieved using the 2DOF control system. FPGA-based digital hardware control is used to maximize the switching frequency of the SiC MOSFET inverter. Finally, an experimental system is set up, and experimental results are presented to prove the viability 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.

Control design methods for floating wind turbines for optimal disturbance rejection

An analysis of the floating wind turbine as a multi-input-multi-output system investigating the effect of the control inputs on the system outputs is shown. These effects are compared to the ones of the disturbances from wind and waves in order to give insights for the selection of the control layout. The frequencies with the largest impact on the outputs due to limited effect of the controlled variables are identified. Finally, an optimal controller is designed as a benchmark and compared to a conventional PI-controller using only the rotor speed as input. Here, the previously found system properties, especially the difficulties to damp responses to wave excitation, are confirmed and verified through a spectral analysis with realistic environmental conditions. This comparison also assesses the quality of the employed simplified linear simulation model compared to the nonlinear model and shows that such an efficient frequency-domain evaluation for control design is feasible.

Optimal disturbance rejection for PI controller with constraints on relative delay margin

Performance optimization with robustness constraints is frequently encountered in process control. Motivated by the analytical difficulties in dealing with the conventional robustness index, e.g., maximum sensitivity, we introduce the relative delay margin as a good alternative, which gives much simpler robust analysis. This point is illustrated by designing an optimal PI controller for the first-order-plus-dead-time (FOPDT) model. It is first shown that the PI controller parameters can be analytically derived in terms of a new pair of parameters, i.e., the phase margin and gain crossover frequency. The stability region of PI controller is subsequently obtained with a much simpler procedure than the existing approaches. It is further shown that a certain relative delay margin can represent the robustness level well and the contour can be sketched with a simpler procedure than the one using maximum sensitivity index. With constraints on the relative delay margin, an optimal disturbance rejection problem is then formulated and analytically solved. Simulation results show that the performance of the proposed methodology is better than that of other PI tuning rules. In this paper, the relative delay margin is shown as a promising robustness measure to the analysis and design of other advanced controllers.