Feedback Disturbance Research Articles

Data-Driven Distributionally Robust MPC for Constrained Stochastic Systems

In this letter we introduce a novel approach to distributionally robust optimal control that supports online learning of the ambiguity set, while guaranteeing recursive feasibility. We introduce conic representable risk, which is useful to derive tractable reformulations of distributionally robust optimization problems. Specifically, to illustrate the techniques introduced, we utilize risk measures constructed based on data-driven ambiguity sets, constraining the second moment of the random disturbance. In the optimal control setting, such moment-based risk measures lead to tractable optimal controllers when combined with affine disturbance feedback. Assumptions on the constraints are given that guarantee recursive feasibility. The resulting control scheme acts as a robust controller when little data is available and converges to the certainty equivalent controller when a large sample count implies high confidence in the estimated second moment. This is illustrated in a numerical experiment.

Hybrid Physics-based and Data-driven Model Predictive Control for Multi-Zone Building's Thermal Comfort Under Disjunctive Uncertainty

This paper develops a hybrid approach that utilizes the distributional information of the disjunctive uncertainty sets and incorporates them into the model predictive control (MPC). This approach aims at the multi-zone building control to the thermal comfort, and it's robust to the uncertain weather forecast errors. The control objective is to maintain each zone's temperature and relative humidity within the specified ranges using the minimum cost of energy of the underlying heating system. The hybrid model is constructed using a physics-based and regression method for the temperature and relative humidity of each zone in the building. The uncertainty space is based on historical weather forecast error data, which are captured by a group of disjunctive uncertainty sets using k-means clustering algorithm. Machine learning approaches based on principal component analysis and kernel density estimation are used to construct each basic uncertainty set and reduce the conservatism of resulting robust control action under disturbances. A robust MPC framework is developed based on the proposed hybrid model and data-driven disjunctive uncertainty set. An affine disturbance feedback rule is employed to obtain a tractable approximation of the robust MPC problem. A case study of controlling temperature and relative humidity of a multi-zone building in Ithaca, New York, USA, is presented. The results demonstrate that the proposed hybrid approach can reduce 9.8% to 17.9% of total energy consumption compared to conventional robust MPC approaches. Moreover, the proposed hybrid approach can essentially satisfy the thermal constraints that certainty equivalent MPC and robust MPC largely violate.

Attitude control of flapping wing aircraft based on energy optimization and ESO

Aiming at the problem of insufficient endurance performance of flapping wing aircraft, a stable attitude control algorithm based on energy optimization and ESO (extended state observer) is designed, which effectively reduces the energy consumption in cruise phase. Firstly, the longitudinal dynamic model of flapping wing aircraft is established, and then the uncertain part of the system and various unknown external disturbances are taken as the total disturbance. ESO module is introduced to observe and track the total disturbance in real time. Therefore, the system is transformed into a series integral system through the total disturbance feedback, and then the energy optimal control law is designed on the base of the transformed system. The numerical simulation results show that, compared with the traditional PID control method, the designed energy optimal control method reduces the average energy consumption by 35.28%.

Управление и поддержка принятия решений в системе персонализированной инсулинотерапии

Insulin therapy automation is an actual research line in the glycemic control of diabetes mellitus type 1 patients. Development of closed-loop systems and methods will allow blood glucose maintaining in the physiological range. The work proposes the personalized insulin therapy system considered as a closed-loop control system based on feedback and external disturbances compensation principles. Automatic feedback-based glycemic control includes proportional reg-ulation of basal insulin infusion rate in relation to optimized thresholds inside the target range. To achieve bidirectional glycemic regulation the author proposes model predictive control for calculation of not only optimal profile of bolus infusion but also recommended corrective dose of carbohydrates. Besides, the comparative analysis of trends in measured and predicted profiles of blood glucose allows detecting and compensation of its unpredicted deviations. In silico testing of developed algorithms on nine virtual adults for 72 hours shows an ability for glucose maintaining in the target range for whole system operation time.

Output feedback robust disturbance rejection tracking control design for a bipedal robotic system with articulation constraints

The design of an output-based robust disturbance rejection controller, aimed to solve the state tracking for the articulations of an experimental biped robot, was the main outcome of this study. The robust disturbance rejection controller included an auxiliary hybrid observer entailed to recover the angular velocity for each articulation. The estimated states served to perform the approximation of disturbances and non-modeled parts in the biped robot dynamics by implementing an extended state observer structure. The observer used the tracking position errors as input information, as well as considering the limb articular constraints, which are natural for biologically inspired biped robots. The effect of state constraints motivated the implementation of a hybrid observer with saturated output error injection. The controller design used the estimation of constraint velocity for solving the design of a tracking trajectory control to resolve the reproduction of the gait cycle by the bipedal robotic system. The Lyapunov stability theory served to obtain the laws which adjust the observer gains as well as to prove the ultimate boundedness of the tracking error as well. The evaluation of the suggested controller was realized on a numerical representation of the biped robot. These simulations illustrated the tracking performance of the hybrid robust disturbance rejection controller for all biped robot articulations in a decentralized structure. Experimental evaluations were also considered to validate the robust disturbance rejection controller design. A fully actuated biped robot was constructed and controlled by the robust disturbance rejection controller. The tracking results obtained by the robust disturbance rejection controller (in both the numerical and experimental evaluations) overcame the classical approach performances of diverse controllers as state feedback (proportional-derivative form) and regular robust disturbance rejection controller which did not consider the articulation constraints.

Generalized proportional integral disturbance observer-based fuzzy sliding mode control for active magnetic bearing system

This paper presents a generalized proportional integral disturbance observer-based a combination of a fuzzy logic control and sliding mode control for the suspension active magnetic bearing system. Firstly, a generalized disturbance observer based on proportional and integral is built to estimate the parameters variation and the outside disturbances. In order to guarantee the system-state will be stabilized on pre-defined states, a disturbance feedback is constructed with a low pass filter. Subsequently, the proportional integral derivative surface sliding mode control is designed. Finally, the Fuzzy logic controller is constructed to determine the hitting controller gain. The stability analysis is given following the Lyapunov law. The proposed control structure can guarantee the system transient response quite good, no overshoot value, and settling time is quite narrow. Two testing cases of the proposed controller with and without the generalized disturbance observe is compared.

Reference tracking stochastic model predictive control over unreliable channels and bounded control actions

A stochastic model predictive control framework over unreliable Bernoulli communication channels, in the presence of unbounded process noise and under bounded control inputs, is presented for tracking a reference signal. The data losses in the control channel are compensated by a carefully designed transmission protocol, and those of the sensor channel by a dropout compensator. A class of saturated, disturbance feedback policies is proposed for control in the presence of noisy dropout compensation. A reference governor is employed to generate trackable reference trajectories and stability constraints are employed to ensure mean-square boundedness of the reference tracking error. The overall approach yields a computationally tractable quadratic program, which can be iteratively solved online.

Extended State Functional Observer-Based Event-Driven Disturbance Rejection Control for Discrete-Time Systems.

In this article, an event-driven output feedback control approach is proposed for discrete-time systems with unknown mismatched disturbances. To estimate the unavailable states and disturbances, a reduced-order extended state functional observer is proposed, and by introducing an event-driven scheduler, the ZOH-based event-driven output feedback disturbance rejection controller is designed, and the stability and disturbance rejection analyses are performed. To further save the network resources, the predictive event-driven output feedback disturbance rejection control approach is proposed, and the stability and disturbance rejection analyses of the systems with predictive control are also conducted. It can be shown that the disturbances are compensated completely in output channels of the systems, and compared with the time-driven control schemes. And event-triggering frequency is greatly reduced with the proposed event-driven control methods. Finally, the effectiveness of the provided control approaches is demonstrated by numerical simulations.

Robust Output Feedback Sliding Mode State and Disturbance Observer-based Controller Design for Nonlinear Systems

This study uses an output feedback disturbance observer-based proportional derivative (PD) controller with variable damping ratios for a class of single-input, single-output nonlinear systems in the presence of unknown disturbances. The proposed sliding mode state and disturbance observer, in which the switching term of the output estimation error is employed to counteract the effect of external disturbance, ensures that the estimation error is finally bounded in a neighborhood and reconstructs simultaneously the system state and unknown disturbance. Herein, the characteristics of the proposed observer are presented in the frequency domain, followed by the corresponding analysis in the time domain. A nonlinear PD controller with a variable damping ratio designed using the estimation state and disturbances should achieve low overshoot and short settling time. Finally, the simulation results demonstrate the validity of the proposed method.

New Sensorless Vector Control System With High Load Capacity Based on Improved SMO and Improved FOO

In the existing sensorless vector control system of permanent magnet synchronous motor (PMSM), direct differential calculation or phase-locked loop (PLL) control is often used to estimate the rotor speed, but this method has some problems of weak load capacity and slow dynamic response. A new sensorless vector control method based on an improved sliding mode observer (SMO) and improved full-order observer (FOO) is proposed in this paper. The cut-off frequency of the low-pass filter is designed as a function of speed, the back EMF is fed back into the stator current estimation mathematical model, and the adaptive rate of feedback gains coefficient is proposed for improving the traditional SMO. The disturbance feedback matrix is introduced for improving the traditional FOO, and the estimated load torque is feedforward compensated to the given end of the quadrature current. An integrated system of corresponding algorithms is established, a test platform is built. The experimental results show that the speed and load torque estimation performance of the improved observer is better than that of the traditional observer in the process of sudden load change. The sensorless vector control system based on the proposed observer has a high dynamic response, load capacity, and reliability.

Stochastic Model Predictive Control Using Simplified Affine Disturbance Feedback for Chance-Constrained Systems

This letter covers the model predictive control of linear discrete-time systems subject to stochastic additive disturbances and chance constraints on their state and control input. We propose a simplified control parameterization under the framework of affine disturbance feedback, and we show that our method is equivalent to parameterization over the family of state feedback policies. Using our method, associated finite-horizon optimization can be computed efficiently, with a slight increase in conservativeness compared with conventional affine disturbance feedback parameterization.

Output feedback disturbance rejection control for building structure systems subject seismic excitations

In this paper, the output feedback disturbance rejection control (OFDRC) problem is considered for buildings structures subject seismic excitations. First, based on a mild assumption and a linear transformation, the addressed problem of building structure system is translated into the output feedback disturbance rejection control problem large-scale system with disturbances. Then, by utilizing generalized-proportional-integral observer (GPIO) technique and output feedback domination approach, an output feedback decentralized disturbance rejection control law is derived via a systematic design manner. The multi-overlapping output feedback disturbance rejection controller is obtained according to the inverse transformation of a linear transformation. Strict theory analysis demonstrates that the states of the structure system will be stabilized to a small bounded region. Finally, an 8-story structure system is employed to evaluate the effectiveness of the proposed control strategy. Simulation results demonstrate that the proposed OFDRC exhibits better seismic loads attenuation ability and strong robustness against model uncertainties.

Data-Driven Robust Optimization for Greenhouse Temperature Control Using Model Predictive Control

This work proposes a novel data-driven robust model predictive control (DDRMPC) framework for automatic control of greenhouse temperature and CO2 concentration level. The essential concept is to combine dynamic models of greenhouse temperature and CO2 concentration level with data-driven models that identify uncertainty in weather forecast error. By leveraging a machine learning approach, support vector clustering with weighted generalized intersection kernel, data-driven uncertainty sets for ambient temperature and solar radiation are constructed from historical weather data. A training-calibration procedure that tunes the size of uncertainty sets is implemented to ensure that data-driven uncertainty sets attain appropriate performance guarantee. In order to solve the optimization problem in DDRMPC, an affine disturbance feedback policy that provides tractable approximations of optimal control is utilized. A case study of controlling temperature and CO2 concentration level in a greenhouse is carried out. The results show that the proposed DDRMPC framework can prevent the greenhouse climate from becoming harmful to plant and fruit. DDRMPC approach ends up with 20 % less total economic cost than rule-based control strategy. The proposed DDRMPC approach also gives better control performance comparing to certainty equivalent MPC and robust MPC.

A chance-constrained stochastic model predictive control for building integrated with renewable resources

Efficient operation of a building energy system integrated with renewable energy resources is one of the main challenges associated with economic and flexible discussions. This work focuses on a chance-constrained stochastic model predictive control (c-SMPC) based scheme to optimally schedule heating, ventilating and air conditioning system (HVAC) and electric storage system (ESS) coordinately, to enable the highly efficient utilization of solar power and economic energy conservation in the building. Specifically, adaptive control modes provided for HVAC according to the time-varying occupancy status offer the building more energy flexibility whilst maximally guarantee the inside thermal comfort with no physical constraint violation. In addition, the uncertain factors, e.g., environment condition disturbances, are integrated into the optimization model by using affine disturbance feedback and chance constraints formulation, providing the c-SMPC controller with tractability and tunability in its temporal receding optimization process. The case of an office building integrated with solar panels and ESS is studied to validate the proposed method, and results show that the method enables an efficient and cost-effective mechanism of optimally coordinating the energy usage of the building. Compared with the baseline controller, the proposed c-SMPC controller can achieve up to 46.6% energy cost reduction and less comfort violation.

Balanced Stochastic Optimal Control of Uncertain Linear Systems with Constraints

This paper addresses finite-time horizon optimal control for discrete-time dynamics with additional stochastic disturbances. In contrast to most existing approaches to this problem, we also minimize the uncertainty of future states arising from stochastic disturbances and from an uncertain initial state. Thus, the optimal control strategy balances the minimization of the expected distances to a reference signal, and the minimization of the uncertainty respectively. As opposed to prior work, the optimization is formulated subject to possible disturbance feedback policies. This enables to solve one semi-definite program over H steps, instead of solving H problems over one step, and the resulting reduced complexity allows one to use the scheme in online and predictive control. The proposed method is applicable to time-varying state constraints (in the sense of chance constraints) as well as time-invariant input constraints.

A chance-constrained stochastic model predictive control problem with disturbance feedback

In this paper, we develop two algorithms for stochastic model predictive control (SMPC) problems with discrete linear systems. Participially, chance constraints on the state and control are considered. Different from the state-of-the-art robust model predictive control (RMPC) algorithm, the proposed is less conservative. Meanwhile, the proposed algorithms do not assume the full knowledge of the disturbance distribution. It only requires the mean and variance of the disturbance. Rigorous computational analysis is carried out for the proposed algorithms. Numerical results are provided to demonstrate the effectiveness and the superior of the proposed SMPC algorithms.

Comparative study of motor speed synchronization control for an integrated motor–transmission powertrain system

This paper compares several kinds of methods for motor speed synchronization control, which plays an important role in gear shifting of emerging clutchless automated manual transmissions for battery electric vehicles and other powertrain systems for hybrid electric vehicles. Specifically, four controllers, namely, proportional-integral control, disturbance observer–based proportional control, integral sliding mode–based proportional control, and disturbance observer–based act-and-wait control, are compared in transient responses regarding settling time, overshoot, and steady-state error. Each is formulated by combining one nominal controller for speed tracking and another for disturbance compensation. For disturbance observer–based proportional control, model-based determination of the feedback gain and disturbance observer gain is discussed. Simulations and experiments are carried out to study effects of different controller parameter settings and evaluate performances of different methods under different operation conditions with disturbances and uncertainties like plant parameter drift, communication time delay, unknown load torques, and so on. Based on the results, it is advised that disturbance observer–based proportional control with the reference signal set as the nominal speed trajectory be used in practice, since it comes with merits of few controller parameters to be determined as well as robust, consistent, and satisfactory performances.

Power Scheduling of Fuel Cell Cars in an Islanded Mode Microgrid With Private Driving Patterns

A microgrid in the islanded mode is considered where a fleet of fuel cell cars is used as a distributed power generation system. The objective of the proposed control system is to minimize the operational cost of the system, subject to the physical and operational constraints of the system. In order to deal with uncertainty in the prediction of the microgrid's load, two model predictive control methods, a min-max (MM) approach and disturbance feedback MM approach, are proposed. We develop three distributed control algorithms and we show that by using these algorithms, the driving patterns of the fuel cell cars can be kept private. In other words, no privacy sensitive data on the usage of the cars are collected by a central control agent. Numerical case studies are presented to demonstrate the excellent performance of the proposed control methods.

Spacecraft attitude control using model-based disturbance feedback control strategy

In this paper, the performance of the spacecraft attitude control system is enhanced using model-based disturbance feedback control (DFC) strategy in the presence of disturbance. This control strategy is applied to a single-axis spacecraft attitude control with thruster, reaction wheel, and magnetic torqrod actuators, separately. An anti-windup observer-based modified PI-D is utilized for each actuation system as a main controller. The controller gains are tuned using genetic algorithm when the time average of absolute value of pointing error is chosen as an objective function. The performance of DFC with the modified PI-D controller is investigated under disturbance and model uncertainties. The numerical simulation shows that the DFC strategy can reject disturbance effect and improve the pointing error for the three mentioned actuators; however, for a very large value of external disturbance, a critical value for uncertainty is observed for the thruster lag at which the pointing error is suddenly increased. For this critical value, the control system cannot tolerate any longer lag uncertainty in comparison with the two other actuation systems. Increasing the value of disturbance decreases the tolerable value of uncertainty in the thruster lag.

Minimum time output regulation for general linear heterodirectional hyperbolic systems

ABSTRACT This paper considers the minimum time output regulation problem for general linear heterodirectional hyperbolic systems with spatially-varying coefficients. For this, a state feedback regulator achieving output regulation in minimum time is determined. In order to obtain an output feedback regulator, finite-time reference and disturbance observers are designed. The latter observer achieves the estimation of the disturbance model and plant states in minimum time. For this, only an additional ODE has to be added to the usual asymptotic-time disturbance observer. The combination of the state feedback regulator with these observers results in an output feedback regulator, for which minimum time output regulation is verified. The output regulation approach is formulated for general signal models, that need not be diagonalisable, and is applied to an unstable hyperbolic system. The comparison of the obtained results with an asymptotic-time design confirms the performance increase gained by the solution of the minimum time output regulation problem.