This paper considers the problem of measurement noise rejection in a linear output-feedback control system. Specifically, we take into account not only the rejection of high-frequency stochastic noises, but also the compensation for low-frequency measurement errors like bias and drift which cannot be well-handled by classic frequency domain filters or Kalman filters. A novel noise estimator (NE)-based robust control solution is proposed. The NE is designed in the frequency domain by exploiting the system model and control structure information, and is embedded into the controller instead of being an independent functional module in the closed-loop system. The adverse effects of model uncertainties on the performance of NE-based solution are investigated, and an improved solution is proposed by incorporating a simple low-pass filter as the pre-filter of NE. This solution is applied to the angle tracking problem of a 2-DOF experimental helicopter platform equipped with a low-cost and low-accuracy MEMS IMU for angular position/rate measurements. Both numerical simulation and experimental comparisons with other existing approaches demonstrate: (i) constant bias and time-varying drift in the IMU measurements are systematically addressed by the solution; (ii) it is accessible to improve the steady-state tracking accuracy by tuning the parameter of NE to extend its bandwidth; and (iii) when model uncertainties limit the feasible bandwidth of NE, the improved solution is able to largely maintain its noise rejection performance.

This paper originates from two well-accepted challenges in the control of a quadrotor with a cable-suspended payload: 1) designing a refined controller based on high-precision payload swing modeling to achieve the quantized prescribed robustness; and 2) resolving the trajectory tracking performance degradation issue caused by input saturation. To combat these challenges, we start with establishing a precise payload swing model. The experimental investigation reveals the fact that neglect of realistic factors like cable-joint dry friction and cable elasticity has significant impacts on the precision of the existing models, especially under small swing angles. Therefore, we propose a new integrated drag model including a novel sign of the payload airspeed-dependent term, which lumps all payload swing damping factors together. This model is experimentally verified to be precise to provide the payload swing disturbance spectrum for quantitatively designing the bandwidth of the uncertainty and disturbance estimator (UDE). Furthermore, we resolve the input saturation issue by augmenting the classic UDE-based controller with a tracking differentiator (TD). Rigorous performance analysis derives a clear relationship between the control performance and the UDE parameter, which forms a simple yet effective parameter tuning guideline for practical applications to ensure the prescribed robustness and trajectory tracking accuracy. The effectiveness and advantage of the proposed controller are verified via comparative experiments in different flight scenarios. Note to Practitioners —The control input saturation issue and multi-parameter optimization are frequently encountered in engineering practices. When applying the TD to address the input saturation, the selection of parameter $r$ in the TD depends on the reference continuity. Specifically, if the reference is continuous, then $r$ can be large; otherwise $r$ should be small to smooth the reference to avoid input saturation. For the multi-parameter optimization, the feedback gains $k_p$ and $k_d$ should be tuned first to guarantee the system stability, followed by decreasing the UDE parameter $T$ to improve the system robustness. However, the feasible range of $T$ may be restricted by the measurement noise and actuator bandwidth in practice. The proposed algorithm is applicable not only in aerial transportation systems but also in addressing other disturbance rejection problems.

In recent years, the uncertainty and disturbance estimator (UDE) technique has been widely used for robustness improvement in state-feedback control systems. This paper extends the design of UDE to output feedback scenarios by considering the robust control problem of a class of Euler-Lagrange systems with a nonlinear velocity term but having no velocity measurements. We propose a simple feedback-control scheme that includes a modified Luenberger state observer (LSO) to estimate the velocity and a modified UDE to estimate exogenous disturbances. The novel feature of the scheme is that a mutual coupling between LSO and UDE is introduced to improve the estimation and control precision. To analyze the performance of the fifth-order nonlinear closed-loop system, we decompose it into a second-order tracking-error subsystem, and a third-order estimation-error subsystem and propose a linear non-singular state transformation and an ingenious parameter mapping for the estimation-error subsystem. Finally, by the singular perturbation theory, we derive a simple stability condition and a single-parameter tuning approach to reduce the steady-state estimation errors and tracking errors. The performance improvement resulting from the mutual coupling effect, as well as the effectiveness of the tuning approach, are demonstrated by numerical simulations and experimental verifications on a 3-DOF helicopter platform.

This paper explains how the method of system identification can be applied to a quadrotor helicopter. First the first principles model is studied. The open-loop model is an unstable system, which is simulated using a closed-loop scheme. Then, a 12th order Auto Regressive Moving Average with eXogenous inputs (ARMAX) model is obtained based on the simulation data.

While many countries have witnessed the retreat of the state from social housing under neoliberalism, the Chinese government has taken the opposite trajectory, significantly expanding its involvement in public rental housing (PRH) over the past decade through substantial investments. However, the effectiveness of the PRH program has come under scrutiny due to its inability to meet the demand for housing units while grappling with a substantial vacancy rate. This study aims to unravel this paradox by utilizing a unique city-level database that encompasses information on public rental housing stock, land supply, waiting time, and allocation practices. The data suggest that there is a structural mismatch between supply and demand for PRH in China, with both high and low vacancy rates in different cities, and even high vacancy and high allocation rates co-existing in one city. The results of estimating the OLS regression model of PRH supply and demand indicate that the actual supply fails to align with the policy objectives and the actual housing demand. Rather, they are more a result of the power relationship between the central and local governments, and cities with high fiscal autonomy provide fewer PRH. Furthermore, local governments fail to set eligibility criteria in response to housing supply, demand, and allocation, further exacerbating the mismatch. This paper provides policy recommendations that aim to enhance the sustainability and effectiveness of the PRH program, contributing to more equitable urban development.