Optimal control of non-minimum phase integrating processes with time delay using disturbance observer-based control scheme

In this paper, we present a global optimal and stable fuzzy controller design method for both continuous- and discrete-time fuzzy systems under both finite and infinite horizons. First, a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers. Based on this sufficient condition, we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory. The stability of the entire closed-loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant feedback continuous fuzzy system possesses an infinite gain margin; that is, its stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties.

In this paper, an H2 optimal input load disturbance rejection (ILDR) controller for three typical integrating processes with dead time is proposed based on the Internal Model Control (IMC) structure. Different from other load disturbance rejection methods, the proposed design method is to minimizing the ILDR criterion for integrating processes with dead time. Compared with previous advanced control methods, the proposed design method has three main advantages. First, the proposed design method can optimally suppress the input load disturbance. Second, the design procedure is simple. No weight functions need to be chosen in the design method. The designed controller is given in an analytical form. Third, the robustness stability can be achieved by monotonously tuning the parameters given in the designed controller. Numerical simulations are given to illustrate the effectiveness of the proposed method.

ABSTRACTAn analytical H2 input load disturbance rejection (ILDR) controller design approach is presented for the synchronised output regulation (SOR) of homogeneous time-delayed multi-agent systems. First, a closed-loop multi-input multi-output framework with transfer functions is introduced, and an SOR condition is given. Second, the decomposition method is utilised to simplify the analysis of internal stability and H2 performance index of the whole system to a set of independent optimisation problems with respect to the eigenvalues of the topology matrix. Finally, for each decomposed subsystem, the H2 optimal ILDR controller can be computed from all the stabilising controllers. By comparison with the conventional given-structured controllers, the contributions of the new approach are that the design procedure is calculated analytically for multi-agent systems with input disturbances, and a simple quantitative tuning way is developed to trade-off the nominal performance and robustness. The simulation example shows the effective ILDR capability of the proposed control strategy.

A modified disturbance observer based control scheme is proposed to control the processes with inverse response and dead-time. The two parts of proposed control scheme have explicit physical meanings: prefilter acts as a predictor of future control signal, and disturbance observer is used to reject the disturbance. It is a two degree-of-freedom control scheme. Two adjustable parameters are directly related to the performance of set-point response and disturbance rejection. Two disturbance observer design methods are proposed to reject step and ramp disturbances. Robustness of the closed-loop system is discussed. The proposed method is implemented on control software and applied on the dual-process simulator. Simulation and experimental results demonstrate the effectiveness of proposed method.

In hydraulic position servo systems, the parametric uncertainties, the inherent nonlinear characters of hydraulic system and the large variations of payload affect the tracking precision and robust performance. A disturbance observer based control scheme and an integral extended state observer based nonlinear control scheme called active disturbance rejection control are proposed in this paper. A comparison study of these two disturbance rejection control strategies for hydraulic position servo systems has been undertaken. Simulation and experimental results show that the active disturbance rejection control is much superior in dealing with system dynamic uncertainties and disturbances.

This paper proposes a disturbance observer based control scheme (DOBC) to stabilize the BTT (Bank-to-turn) missile outputs and decrease the effect of lumped disturbances (non-linear couplings and external disturbance) on missile. The missile dynamics are further divided as three subsystems namely yaw, roll, and pitch channels. For roll channel, a fuzzy PID (Proportional-Integral-Derivate) controller based on DOB (disturbance observer) has been proposed. For yaw and pitch channels, robust PID controllers based on DOB (disturbance observer) have been used. Kharitonov theorem is used for robust tuning of the parameter gains of PID controller in pitch, and yaw subsystems. The proposed DOB based control scheme effectiveness is demonstrated with simulation studies using MATLAB/SIMULINK.

In this paper, a disturbance observer based control strategy is proposed to regulate the dc-link voltage of three-phase two-level pulse-width-modulation active-front-end rectifiers. In the voltage regulation loop, a linear disturbance observer is designed to improve the system performance. The load connected to the dc-link capacitor is considered as an external disturbance and the observer is used to estimate its value. The estimated disturbance is compensated to the PI controller. Simulations are carried out to verify the effectiveness and advantage of the proposed control strategy. Three different loads have been provided to test the robustness of the control strategy. Simulation results show that the proposed control strategy improves the transient response of the dc-link voltage, meanwhile maintains the steady-state performance in term of the output current total harmonic distortion, and has strong robustness against the external load variation.

In this paper, we present an optimal control approach using Linear Matrix Inequalities (LMIs) for trajectory tracking control of a three-wheeled omnidirectional mobile robot in the presence of external disturbances on the robot's actuators and noise in the robot's sensor measurements. First, a state-space representation of the omnidirectional robot dynamics is derived using a point-mass dynamic model. Then, we propose an LMI-based full-state feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller for the tracking problem. The robot's tracking performance with the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is compared to its performance with a classical full-state feedback tracking controller in simulations with circular and bowtie-shaped reference trajectories. In order to evaluate our proposed controller in practice, we also implement the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal and classical controllers for these reference trajectories on a three-wheeled omnidirectional robot. The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller guarantees stabilization of the robot motion and attenuates the effects of frictional disturbances and measurement noise on the robot's tracking performance. Using the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller, the robot is able to track the reference trajectories with up to a 47.8% and 45.8% decrease in the maximum pose and twist errors, respectively, over a full cycle of the trajectory compared to the classical controller. The simulation and experimental results show that our LMI-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is robust to undesired effects of disturbances and noise on the dynamic behavior of the robot during trajectory tracking and can outperform the classical controller in attenuating their effects.

A novel method of disturbance observer-based integral backstepping control is proposed for the two-tank liquid level system with external disturbances. The problem of external disturbances can be settled in this paper. Firstly, the mathematical model of the two-tank liquid level system is established based on fluid mechanics and principle of mass conservation. Secondly, an integral backstepping control strategy is designed in order to ensure liquid level tracking performance by making the tracking errors converge to zero in finite time. Thirdly, a disturbance observer is designed for the two-tank liquid level system with external disturbances. Finally, the validity of the proposed method is verified by simulation and experiment. By doing so, the simulation and experimental results prove that the scheme of disturbance observer-based integral backstepping control strategy can suppress external disturbances more effective than the disturbance observer-based sliding mode control method and has better dynamic and steady performance of the two-tank liquid level system.

A new nonlinear disturbance observer-based tracking control scheme for an underwater manipulator is presented in this paper. This observer overcomes the disadvantages of existing disturbance observers, which are designed or analyzed by the linear system techniques. It can be applied in underwater manipulator systems for various purposes such as payload compensation, interaction effects compensation, underwater current or external disturbance compensation, and independent system control. The performance of the proposed tracking control scheme is demonstrated numerically by the payload compensation and interaction effects compensation for a two degrees of freedom vertical underwater manipulator.

To mitigate torque fluctuations arising from clutch engagement and multi-power-source coupling during the mode transition from electric vehicle (EV) mode to engine-driving mode in a single-axle parallel hybrid electric vehicle (SPHEV), this paper proposes a disturbance observer-based dynamic coordination control strategy (DOBDCCS). Its novelty lies in treating engine and clutch output torques as stage-specific system load disturbances, designing observers addressing parameter perturbations and model uncertainties. Specifically, the transition process is divided into four stages: engine start-up stage, engine acceleration stage, speed synchronization stage, and torque coordination stage. For each stage, dynamic models of the hybrid powertrain are established, incorporating considerations of parameter perturbations and model uncertainties. Dedicated disturbance observers are designed to treat engine and clutch output torques as system load disturbances. These observers accurately estimate both parameter perturbations and load disturbances and provide first-order filtering to suppress high-frequency torque fluctuations. A motor torque compensation strategy based on feedback compensation is further developed to ensure smooth power coupling leveraging the motor’s fast torque response. A simulation model built in Matlab is used to validate the effectiveness of DOBDCCS under preset driving cycle, a preset driving cycle with parameter perturbations, and standard driving cycles (UDDS and WLTC). Statistical results demonstrate that the proposed DOBDCCS significantly improves ride comfort by keeping the maximum vehicle jerk consistently below 8 m/s 3 , which is well below China’s recommended threshold, and achieving notably lower jerk values.

SummaryThis paper proposes an optimal control method of an unmanned aerial helicopter (UAH) with unknown disturbances. Solving the Hamilton‐Jacobi‐Bellman (HJB) equation is considered as the common approach to design an optimal controller under a meaningful cost function when facing the nonlinear optimal control problem. However, the HJB equation is hard to solve even for a simple problem. The inverse optimal control method that avoids the difficulties of solving the HJB equation has been adopted. In this inverse optimal control approach, a stabilizing optimal control law and a particular cost function that are obtained by a control Lyapunov function are required. An integrator backstepping method is used in designing the optimal control law of the UAH. Furthermore, a disturbance‐observer–based control (DOBC) approach has been adopted in the optimal control law for dealing with the unknown disturbances of the UAH system. Simulation results have been given to certify the stability of the nonlinear UAH system and the validity of this developed control method.

Robust autopilot design for bank-to-turn (BTT) missiles under disturbances and uncertainties is investigated in this article using the disturbance observer concept. It is well known that the BTT missile dynamics undergo substantial change during its flight. In this disturbance observer-based control (DOBC) setting, the influences caused by parameter variations are merged into disturbance terms and regarded as parts of the lumped disturbances. Disturbance observers are employed to estimate the lumped disturbances, and then a disturbance observer-based robust control (DOBRC) method is proposed in this article to compensate the influences of parameter variations and the disturbances from the output channels. Similar to the baseline linear quadratic regulator design, the DOBRC is analysed and designed using linear techniques. Very promising performance has been achieved for the BTT missile as shown in simulation. It is demonstrated that DOBC approach provides a simple, intuitive, and practical solution for many challenging control problems where systems are subject to significant external disturbances, and uncertainties such as BTT missiles.

Disturbance observer-based disturbance attenuation control for a class of stochastic systems

This paper proposes a disturbance observer-based anti-disturbance control strategy for a class of stochastic systems subject to two kinds of disturbances. One represents the stochastic disturbance with partially-known information. The other is an independent Wiener process. The stochastic disturbance observer can be constructed separately from the controller design to estimate the first kind of disturbance. Based on stochastic disturbance observer, a novel anti-disturbance control scheme is proposed to improve the ability of anti-disturbance for stochastic systems. A simulation example is given to demonstrate the effectiveness of the proposed method.