Robotics and Control
Optimization and Control
Control in Power Electronics and Energy Systems
Cooperative robotics is becoming interesting and important in both academic and industrial areas. A multi-robot system is much more flexible because several robots can be grouped to handle large and heavy workloads together, while in other scenarios they can work individually on different smaller tasks in parallel for better efficiency. Due to the potential combination of such systems with human participants, safety must be considered during control design. The control algorithm should also properly exploit the redundancy of the robots to optimise group performance, and motion coordination between the robot agents is desired.
Applied optimization and control covers a broad range of mathematical methods, in particular, those that have connection with applications. Core topics include the interplay between control and optimization, and numerical techniques for their underlying linear and nonlinear systems. Of great interest are topics, like: numerical optimization, model predictive control, robust optimization, partial differential equations and vibrational analysis. Special interest lies on the application side of any technique. The performance of any proposed technique is to be demonstrated by solving an application problem. As an application a distributed parameter system of the stacker crane (STC) is considered. A laboratory setup with a real-time computer and a rapid prototyping tool are provided to simplify any application and gives an additional level of freedom.
Due to the weight reduction of construction systems, like the case with STC rigidity loss leads to flexibility in structure. As a result, structural vibrations within the systems are induced already for low accelerations. Therefore exact positioning can only be achieved after a specific settling time, which counteracts any fast maneuver requirements. The main control objective of the STC is to avoid vibrations as well as to ensure a corresponding robustness. To solve the problems that arise, appropriate methods are developed in the following areas:
1. Nonlinear Model Predictive Control
Model Predictive Control (MPC) is a modern and powerful framework for linear and nonlinear control, where physical constraints on both states and control are explicitly considered. Accordingly, the state of the system is predicted and then optimized over a future horizon. Complex and highly dynamical systems, e.g. mechatronic applications pose a great challenge for real-time applications. Both methodological and numerical, especially real-time capable methods are still ongoing development for addressing the vibrational issues in flexible bodies, with a focus on the practical feasibility.
2. Robust Optimization
In Model Predictive Control (MPC) constraints satisfaction is essential, especially when they are physical, which may be safety-critical. However non-ideal world contains always uncertainty, which makes constraints satisfaction a challenging task. Appropriate approaches introduce a little conservatism but leads to robust controllers that work very well in practice.
3. Partial Differential Equation Constrained Optimization
Distributed-parameter systems are characterized by the states, which are elements of an infinite-dimensional state-time space. New methods for optimal feedforward and feedback control are strived in combination with model predictive control. Important application areas range from flexible structures till heat propagation.
4. Vibrational Analysis
Typically, dealing with vibrational damping control requires a specification of the frequencies, which need to be controlled or avoided. To study the dynamical properties of a flexible body in frequency domain the powerful approach of modal analysis is used. One pre-condition is a partial differential equation model description. Dynamical structure analyses which study the behavior of a flexible structure under both dynamical load and input is still an ongoing topic.
Cooperative behavior of multi robots
In this field we focus on the cooperative behavior of multi robots in a distributed way, which reduces the burden of communication and computation for practical applications and guarantees the performance of the whole system.
Quadrotors are the most popular type of unmanned aerial vehicles (UAV). They can be achieved from cheap off-the-shelf components due to their simple and robust mechanical design. Furthermore, they are able to hover as well as takeoff and land vertically while still being able to perform agile maneuvers.
Quadrotors are deployed in numerous applications where sensors or payloads need to be moved to locations that are hard to reach or even unreachable for humans or ground robots. Among these applications are inspection of various infrastructure, monitoring and analysis in agriculture, surveillance, transportation, and aerial photography, which, together, form a multi-billion-dollar market.
The research focuses on control methods that makes quadrotors more autonomous and more agile brings the benefit of requiring fewer operators and completing tasks faster.
Designing control and learning algorithms
My research focuses on designing control and learning algorithms to make robot safely and intelligently work with people. I am deeply interested in combining AI with control theory to utilize the strength of both approaches. In cooperation with the work group wearHEALTH at TU Kaiserslautern and Zhejiang University of Technology, we develop data-driven methods for human motion recognition and prediction using wearable and vision-based sensor networks. The result are further used to develop learning-based motion planning and interaction control methods for robot. I am particularly interested in Bayesian Regression, Reinforcement Learning and Impedance Control as well as their applications in the context of human-robot collaboration.
Stochastic MPC – Intro:
Constrained control of dynamical systems subject to unknown disturbances is an active research topic since several decades. A common methodology is Robust MPC, where a conservative upper bound on the disturbances is assumed to be known. However, in Stochastic MPC approaches this conservatism is reduced by assuming a model of the underlying disturbance, e.g. the probability distribution. This allows us to characterize bounds on the error between the nominal and real system states in probability, e.g. in a Probabilistic Reachable Set, and furthermore relax the hard constraints as chance constraints that merely have to be satisfied with a predefined probability.
1. Distributed Stochastic MPC
We are currently working on distributed MPC algorithms for large-scale networks of dynamical systems subject to stochastic disturbances. The main challenge hereby is to find distributed reformulations, so that the resulting control scheme can be implemented fully parallelizable via distributed optimization. For additive disturbances, this includes the computation of distributed Probabilistic Reachable Sets, which need to satisfy certain structural properties in order to be decomposable. However, in the multiplicative case the propagation of block diagonal covariance upper bounds is mandatory to obtain exact reformulations of the chance constraints. More details can be found in our recent publications:
Mark, Christoph, and Steven Liu. "Distributed Stochastic Model Predictive Control for dynamically coupled Linear Systems using Probabilistic Reachable Sets. "European Control Conference (ECC2019). IEEE, 2019.
Mark, Christoph, and Steven Liu. "A stochastic output-feedback MPC scheme for distributed systems." 2020 American Control Conference (ACC2020), Denver/USA (accepted)
Mark, Christoph, and Steven Liu. "A stochastic MPC scheme for distributed systems with multiplicative uncertainty." arXiv preprint arXiv:1908.09337 (2019).
2. Distributionally Robust MPC
In Stochastic MPC we initially assumed that the exact disturbance distribution is known. In this research project we weaken this assumption and merely require an empirical distribution, which can be computed from a given (and possibly small) data set of disturbance samples, e.g. inferred from closed-loop operation. The distributional uncertainty of the empirical distribution can now be captured in a so called ambiguity set, which describes plausible variations of the empirical distribution, such that the true distribution is an element of the ambiguity set with high probability. In recent work we opt to use Wasserstein ambiguity sets for ellipsoidal distributions, whereas the worst-case distribution of that set is utilized to compute a Probabilistic Reachable set. The method is complemented by a data-driven design procedure. Currently we are pursuing a learning-based MPC approach for black-box systems with arbitrary disturbances, where we utilize ambiguity sets to obtain risk-averse control policies.
Mark, Christoph, and Steven Liu. "Distributionally Robust Stochastic Model
Predictive Control using Probabilistic Reachable Sets." IFAC World Congress, 2020, (submitted)
Model-predictive control in building automation
The advent of modern control concepts is beginning in building automation. Especially the model-predictive control is of interest here, due to the consideration of constraints. The focus of the scientific work is the technical modelling of the conditions, especially with regard to the locally varying solar energy input into the system. The main problem is the reduced and control oriented modelling. The aim is to cover all relevant properties for the use in model-predictive control systems. Final is a complete workflow in progress, starting with the modelling up to the implementation of the controller.
Hydrokinetic energy conversion (HEC)
Interest in the advancement of hydrokinetic energy conversion (HEC) technology has grown substantially in recent years, yet facing energy cost and optimization challenges.
My research focuses on:
• Optimization of HEC in arrays configuration with the consideration of wake effect
• Voltage and frequency control of HEC in islanded-microgrid during extreme weather
Modular Multilevel Converters (MMC)
Modern power converters encompassing latest Solid State devices and advance control techniques are now trending the conventional power systems.
Their prevailing success is concealed in more precise system modeling involving nonlinear dynamics with supporting control to provide operational safety, reliability and power quality.
My research aims on modeling and control of Modular Multilevel Converters (MMC) providing high efficiency, ancillary services of Power Oscillation Damping (POD) and active filtering.
The application area involves Medium Voltage DC distribution systems, electrical drives and power compensators.
Control of Power Electronics
From Agriculture, Automotive, Aerospace, Healthcare, Energy Generation and Transmission to IT, Power Electronics is a hidden industry present on every major industry of our modern society. Power electronics is the application of solid-state electronics to the control and conversion of electric power. In order to obtain a stable power supply and still obey a very wide range of different requirements, many control related challenges emerge. The arise of Renewable Energy Sources (RES) and Energy Storage Systems (ESS), has been changing the traditional electrical grid, towards a more resilient, flexible and efficient one. Consequently, the development of DC grids, based on power electronics converters has become a hot topic. The recent and very promising Modular Multilevel Converter (MMC) topology offers high modularity, reliability, easy maintenance and low losses. Moreover, this topology features a unique energy storage capability, highly useful, to decouple the source from the load. In other perspective, it offers a high number of degrees of freedom, which results in the design of complex control algorithms. In more conventional topologies, direct vector control is used to enhance the dynamic response of the converter. Due to high number of available and redundant vectors offered by the MMC topology, one can apply different vectors to find the same best output voltage to run a certain load. However, such flexibility opens the possibility of controlling the internal energy balance of the MMC without compromising the load supply. Combining both features has been a very challenging and rewarding research topic.