A Data-driven Approach to Robust Control of Multivariable Systems by Convex Optimization

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of matrix polynomial functions and can be formulated as a centralized, decentralized or distributed controller. All standard performance specifications like $H_2$, $H_\infty$ and loop shaping are considered in a unified framework for continuous- and discrete-time systems. The control problem is formulated as a convex-concave optimization problem and then convexified by linearization of the concave part around an initial controller. The performance criterion converges monotonically to a local optimal solution in an iterative algorithm. The effectiveness of the method is compared with fixed-structure controllers using non-smooth optimization and with full-order optimal controllers via simulation examples. Finally, the experimental data of a gyroscope is used to design a data-driven controller that is successfully applied on the real system

Frequency-Aware Model Predictive Control

Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion infeasible on the real system. Model errors can be a result of model simplifications, but also naturally arise when deploying the robot in unstructured and nondeterministic environments. Predominantly, compliant contacts and actuator dynamics lead to bandwidth limitations. While classical control methods provide tools to synthesize controllers that are robust to a class of model errors, such a notion is missing in modern trajectory optimization, which is solved in the time domain. We propose frequency-shaped cost functions to achieve robust solutions in the context of optimal control for legged robots. Through simulation and hardware experiments we show that motion plans can be made compatible with bandwidth limits set by actuators and contact dynamics. The smoothness of the model predictive solutions can be continuously tuned without compromising the feasibility of the problem. Experiments with the quadrupedal robot ANYmal, which is driven by highly-compliant series elastic actuators, showed significantly improved tracking performance of the planned motion, torque, and force trajectories and enabled the machine to walk robustly on terrain with unmodeled compliance

IMPAC: An Integrated Methodology for Propulsion and Airframe Control

The National Aeronautics and Space Administration is actively involved in the development of enabling technologies that will lead towards aircraft with new/enhanced maneuver capabilities such as Short Take-Off Vertical Landing (STOVL) and high angle of attack performance. Because of the high degree of dynamic coupling between the airframe and propulsion systems of these types of aircraft, one key technology is the integration of the flight and propulsion control. The NASA Lewis Research Center approach to developing Integrated Flight Propulsion Control (IFPC) technologies is an in-house research program referred to as IMPAC (Integrated Methodology for Propulsion and Airframe Control). The goals of IMPAC are to develop a viable alternative to the existing integrated control design methodologies that will allow for improved system performance and simplicity of control law synthesis and implementation, and to demonstrate the applicability of the methodology to a supersonic STOVL fighter aircraft. Based on some preliminary control design studies that included evaluation of the existing methodologies, the IFPC design methodology that is emerging at the Lewis Research Center consists of considering the airframe and propulsion system as one integrated system for an initial centralized controller design and then partitioning the centralized controller into separate airframe and propulsion system subcontrollers to ease implementation and to set meaningful design requirements for detailed subsystem control design and evaluation. An overview of IMPAC is provided and detailed discussion of the various important design and evaluation steps in the methodology are included

Feedback MPC for Torque-Controlled Legged Robots

The computational power of mobile robots is currently insufficient to achieve torque level whole-body Model Predictive Control (MPC) at the update rates required for complex dynamic systems such as legged robots. This problem is commonly circumvented by using a fast tracking controller to compensate for model errors between updates. In this work, we show that the feedback policy from a Differential Dynamic Programming (DDP) based MPC algorithm is a viable alternative to bridge the gap between the low MPC update rate and the actuation command rate. We propose to augment the DDP approach with a relaxed barrier function to address inequality constraints arising from the friction cone. A frequency-dependent cost function is used to reduce the sensitivity to high-frequency model errors and actuator bandwidth limits. We demonstrate that our approach can find stable locomotion policies for the torque-controlled quadruped, ANYmal, both in simulation and on hardware.Comment: Paper accepted to IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2019

Modeling and H-Infinity Loop Shaping Control of a Vertical Takeoff and Landing Drone

abstract: VTOL drones were designed and built at the beginning of the 20th century for military applications due to easy take-off and landing operations. Many companies like Lockheed, Convair, NASA and Bell Labs built their own aircrafts but only a few from them came in to the market. Usually, flight automation starts from first principles modeling which helps in the controller design and dynamic analysis of the system. In this project, a VTOL drone with a shape similar to a Convair XFY-1 is studied and the primary focus is stabilizing and controlling the flight path of the drone in its hover and horizontal flying modes. The model of the plane is obtained using first principles modeling and controllers are designed to stabilize the yaw, pitch and roll rotational motions. The plane is modeled for its yaw, pitch and roll rotational motions. Subsequently, the rotational dynamics of the system are linearized about the hover flying mode, hover to horizontal flying mode, horizontal flying mode, horizontal to hover flying mode for ease of implementation of linear control design techniques. The controllers are designed based on an H∞ loop shaping procedure and the results are verified on the actual nonlinear model for the stability of the closed loop system about hover flying, hover to horizontal transition flying, horizontal flying, horizontal to hover transition flying. An experiment is conducted to study the dynamics of the motor by recording the PWM input to the electronic speed controller as input and the rotational speed of the motor as output. A theoretical study is also done to study the thrust generated by the propellers for lift, slipstream velocity analysis, torques acting on the system for various thrust profiles.Dissertation/ThesisMasters Thesis Electrical Engineering 201

Fractional transformation-based decentralized robust control of a coupled-tank system for industrial applications

Petrochemical and dairy industries, waste management, and paper manufacturing fall under the category of process industries where flow and liquid control are essential. Even when liquids are mixed or chemically treated in interconnected tanks, the fluid and flow should constantly be observed and controlled, especially when dealing with nonlinearity and imperfect plant models. In this study, we propose a nonlinear dynamic multiple-input multiple-output (MIMO) plant model. This model is then transformed through linearization, a technique frequently utilized in the analysis and modeling of fractional processes, and decoupling for decentralized fixed-structure H-infinity robust control design. Simulation tests based on MATLAB and SIMULINK are subsequently executed. Numerous assessments are conducted to evaluate tracking performance, external disturbance re jection, and plant parameter fluctuations to gauge the effectiveness of the proposed model. The objective of this work is to provide a framework that anticipates potential outcomes, paving the way for implementing a reliable controller synthesis for MIMO-connected tanks in real-world scenarios.This research was partially funded by FONDECYT grant number 1200525 (V.L.) from the National Agency for Research and Development (ANID) of the Chilean government under the Ministry of Science, Technology, Knowledge, and Innovation; and by Portuguese funds through the CMAT—Research Centre of Mathematics of University of Minho—within projects UIDB/00013/2020 and UIDP/00013/2020 (C.C.)