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A definition of the degree of disturbance rejection

The problem of rejecting disturbances that are known a priori to reside in a particular function class is treated. Two scalar measures, the degree of disturbance rejection (DODR) and the degree of disturbability (DOD) are defined and shown to be useful in rating a candidate controller's ability to counter the expected disturbances. The measures can thus be used as criteria for controller design and actuator placement. It is shown that the DODR can guarantee that constraints on the control action will not be violated. The DOD assumes a closed-loop controller realization, and this gives a simplified formulation in terms of one state space region instead of two. With the DOD, a variety of performance indices can be considered, together with a spectrum of possible controller implementations.

Laskin, R. A.

Tracking and disturbance rejection of MIMO nonlinear systems with PI controller

The tracking and disturbance rejection of a class of MIMO nonlinear systems with linear proportional plus integral (PI) compensator is studied. Roughly speaking, it is shown that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.

Desoer, C. A.

Tracking and disturbance rejection of MIMO nonlinear systems with PI controller

The tracking and disturbance rejection of a class of MIMO nonlinear systems with a linear proportional plus integral (PI) compensator is studied. Roughly speaking, it is shown that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.

Desoer, C. A.

Multilevel Conditional Disturbance Rejection Control for Satellite Attitude Tracking

Recently, the conditional disturbance rejection controller (CDRC) was proposed to improve control performance by leveraging disturbances that have beneficial effects on the system. However, it only considers disturbances acting on the state variable directly influenced by them. Although fast convergence of this state can be achieved with the CDRC, it may unintentionally affect the convergence of the output (i.e., the primary state). Here, in this article, a multilevel CDRC is proposed to enhance satellite attitude control performance by accounting for the effect of disturbances on both attitude (output) and angular velocity. The extended state observer is employed to estimate the lumped disturbance, including the modeling errors and external disturbances. Then, a backstepping-based controller with the multilevel disturbance rejection law (ML-DRL) is designed for attitude tracking. The ML-DRL is developed to improve the control performance by using a disturbance with a damping effect on both attitude and velocity. Faster convergence of attitude and velocity can be achieved by conditionally compensating for the disturbance. The stability of the proposed control method is analyzed by demonstrating that the errors are bounded as time tends to infinity. The attitude control performance of the proposed method is evaluated through numerical examples conducted using the MATLAB/Simulink Multibody tool.

Active disturbance rejection control (ADRC)

Spacecraft Observatory Benchmark Problem for Optical Disturbance Rejection

Since mid-1980s NASA has launched several first-generation interplanetary observatory missions. A salient feature of these missions has been the mounting of the optical payload on top of a large flexible space structure. This imposes challenging control-structure interaction problems (CSI) that have been studied over several decades. The Dec. 2021 launch of the James Webb Telescope marks the latest example of such a mission. One way to encourage development of novel control methods is to provide a benchmark problem for researchers. By the mid-2000s, there were a few well-known benchmark problems developed by the control community with a focus on CSI applications. However, in the past 15 years, the control challenges in optical observation missions have shifted from CSI to line-of-sight (LOS) precision pointing. This is because popular designs of the second-generation (Gen II) space earth missions have eliminated the large structure interface by mounting the optical payload directly on top of a rigid bus platform. The focus now is to achieve accurate pointing with maximum rejection of the surrounding disturbances. The NASA Safety and Engineering Center (NESC) has tasked T he Aerospace Corporation to develop a Benchmark Problem to study the challenging control issues that Gen II observatory missions encounter. This software tool is to be released as a public domain platform aimed at government, academic, and industry researchers. The focus of this benchmark problem is for researchers to design a set of innovative payload control laws with the maximum Optical Disturbance Rejection (ODR) capability to meet a set of pre-defined μrad-level of LOS jitter requirements. This paper describes the development of the benchmark problem. Aerospace/NASA will provide an integrated LOS plant model and disturbance/command profiles for users to run their design and simulation with as well as a user’s guide describing the required interfaces. The Aerospace Corp is also working to develop a hardware fast steering mirror testbed for users to demonstrate their innovative design in real hardware, if so desired.

Spacecraft Observatory Benchmark Problem

Inertial-space disturbance rejection for robotic manipulators

The disturbance rejection control problem for a 6-DOF (degree of freedom) PUMA manipulator mounted on a 3-DOF platform is investigated. A control algorithm is designed to track the desired position and attitude of the end-effector in inertial space, subject to unknown disturbances in the platform axes. Conditions for the stability of the closed-loop system are derived. The performance of the controller is compared for step, sinusoidal, and random disturbances in the platform rotational axis and in the neighborhood of kinematic singularities.

Holt, Kevin

Identification and Active Disturbance Rejection for the JPL Phase B Test Bed

Active disturbance rejection to minimize optical path length error is illustrated by experimental results from the JPL Phase B Test Bed, which incorporates an interferometric sensor and a controllable trolley mounted on a flexible truss structure. The controller actively isolates the optical instruments from structural vibrations induced by external disturbances consisting of linear combinations of sinusoidal signals.

Active

Active disturbance rejection in large flexible space structures

The design of an active control law for the rejection of persistent disturbances, in large space structures is presented. The control system design approach is based on a deterministic model of the disturbances and it optimizes the magnitude of the disturbance that the structure can tolerate without violating certain predetermined constraints. In addition to closed-loop stability, the explicit treatment of state, control, and control rate constraints, such as structural displacement and control actuator effort, guarantees that the final design will exhibit desired performance characteristics. The technique is applied to a simple two-bay truss structure, and its response is compared with that obtained using a linear-quadratic-Gaussian/loop-transfer-recovery (LQG/LTR) compensator. Preliminary results indicate that the proposed control system can reject persistent disturbances of greater magnitude by utilizing most of the available control, while limiting the structural displacements to within desired tolerances.

Parlos, Alexander G.

A nonlinear optimization approach for disturbance rejection in flexible space structures

In this paper the design of an active control law for the rejection of persistent disturbances in large space structures is presented. The control system design approach is based on a deterministic model of the disturbances, with a model-based-compensator (MBC) structure, optimizing the magnitude of the disturbance that the structure can tolerate without violating certain predetermined constraints. In addition to closed-loop stability, the explicit treatment of state, control and control rate constraints, such as structural displacement, control actuator effort, and compensator time guarantees that the final design will exhibit desired performance characteristics. The technique is applied for the vibration damping of a simple two bay truss structure which is subjected to persistent disturbances, such as shuttle docking. Preliminary results indicate that the proposed control system can reject considerable persistent disturbances by utilizing most of the available control, while limiting the structural displacements to within desired tolerances. Further work, however, for incorporating additional design criteria, such as compensator robustness to be traded-off against performance specifications, is warranted.

Parlos, Alexander G.

Inertial-space disturbance rejection for space-based manipulators

The implementation of a disturbance rejection controller for a 6-DOF PUMA manipulator mounted on a 3-DOF platform was described. A control algorithm is designed to track the desired position and attitude of the end-effector in inertial space, subject to unknown disturbances in the platform axes. Experimental results are presented for step, sinusoidal, and random disturbances in the platform rotational axis and in the neighborhood of kinematic singularities. Robotic manipulators were proposed as a means of reducing the amount of extra vehicular activity time required for space station assembly and maintenance. The proposed scenario involves a robotic manipulator attached to some mobile platform, such as a spacecraft, satellite, or the space station itself. Disturbances in the platform position and attitude may prevent the manipulator from successfully completing the task. The possibility of using the manipulator to compensate for platform disturbances was explored. The problem of controlling a robotic manipulator on a mobile platform has received considerable attention in the past few years. Joshi and Desrochers designed a nonlinear feedback control law to carry out tasks (with respect to the robot base frame) in the presence of roll, pitch and yaw disturbances in the platform axes. Dubowsky, Vance, and Torres proposed a time-optimal planning algorithm for a robotic manipulator mounted on a spacecraft, subject to saturation limits in the attitude control reaction jets. Papadopoulos and Dubowsky developed a general framework for analyzing the control of free-floating space manipulator systems. Most recently, Torres and Dubowsky have presented a technique called the enhanced disturbance map to find manipulator trajectories that reduce the effect of disturbances in the spacecraft position and attitude. One common assumption in the literature is that the disturbance signal is exactly known. If this is the case, then the end-effector location can be calculated without relying on direct end-point sensing. However, this assumption is invalid if there is a significant delay in the platform position and attitude measurements, or if the kinematics of the platform are not well known, or if the platform is a non-rigid structure. In the more likely case that only the nominal platform location and upper bound on the disturbance signal are known, direct end-point sensing is needed to measure the end-effector location.

Holt, Kevin

Extended active disturbance rejection controller

Multiple designs, systems, methods and processes for controlling a system or plant using an extended active disturbance rejection control (ADRC) based controller are presented. The extended ADRC controller accepts sensor information from the plant. The sensor information is used in conjunction with an extended state observer in combination with a predictor that estimates and predicts the current state of the plant and a co-joined estimate of the system disturbances and system dynamics. The extended state observer estimates and predictions are used in conjunction with a control law that generates an input to the system based in part on the extended state observer estimates and predictions as well as a desired trajectory for the plant to follow.

Gao, Zhiqiang

Extended Active Disturbance Rejection Controller

Multiple designs, systems, methods and processes for controlling a system or plant using an extended active disturbance rejection control (ADRC) based controller are presented. The extended ADRC controller accepts sensor information from the plant. The sensor information is used in conjunction with an extended state observer in combination with a predictor that estimates and predicts the current state of the plant and a co-joined estimate of the system disturbances and system dynamics. The extended state observer estimates and predictions are used in conjunction with a control law that generates an input to the system based in part on the extended state observer estimates and predictions as well as a desired trajectory for the plant to follow.

Gao, Zhiqiang

Extended Active Disturbance Rejection Controller

Multiple designs, systems, methods and processes for controlling a system or plant using an extended active disturbance rejection control (ADRC) based controller are presented. The extended ADRC controller accepts sensor information from the plant. The sensor information is used in conjunction with an extended state observer in combination with a predictor that estimates and predicts the current state of the plant and a co-joined estimate of the system disturbances and system dynamics. The extended state observer estimates and predictions are used in conjunction with a control law that generates an input to the system based in part on the extended state observer estimates and predictions as well as a desired trajectory for the plant to follow.

Gao, Zhiqiang

Analysis of Handling Qualities and Power Consumption for Urban Air Mobility (UAM) eVTOL Quadrotors with Degraded Heave Disturbance Rejection and Control Response

A piloted handling qualities study of urban air mobility (UAM) electric vertical take-off and landing (eVTOL) quadrotors was performed utilizing the Vertical Motion Simulator (VMS) facility at NASA Ames Research Center. Rotor speed and variable pitch-controlled variants of a six-passenger conceptual design vehicle were assessed with different levels of degradation to control response and disturbance rejection bandwidth (DRB) in the heave axis. In previous work, preliminary trends across several handling quality rating categories reflected the effects of these degradations. Additionally, the impact of using different test standards and turbulence on the ratings were discussed. This paper elaborates on those results, but also provides insight into unexpected trends observed during the study including: a disharmony in attitude response, subpar ratings for the baseline Level 1 performance vehicle, and excessive drift and yaw couplings observed in a lateral reposition maneuver. Moreover, shortcomings of the handling quality scales and comparisons of power consumption among the vehicles in the various test conditions are presented.

Handling Qualities

Disturbance rejection in repetitive controllers

The p-integrator is a digital controller that learns from previous experience executing a repetitive command in order to improve its performance in future repetitions. This class of repetitive controller is an analog of the integral controller of classical control theory. This paper addresses several issues related to the performance of the p-integrator. This is followed by a derivation that will demonstrate the repetitive disturbance rejection capabilities of the controller. The effect of the tracking performance in practical implementations with prefiltering and postfiltering devices are studied - using an exact and approximate formulation. Relations showing the actual system response during steady state operation with these filters are derived. The results are then extended to include the tracking error performance of systems subjected to repetitive disturbances. Finally, the system response between sample times is developed.

Solcz, Edward J.