A model structure-driven hierarchical decentralized stabilizing control structure for process networks

Based on the structure of process models a hierarchically structured state-space model has been proposed for process networks with controlled mass convection and constant physico-chemical properties. Using the theory of cascade-connected nonlinear systems and the properties of Metzler and Hurwitz matrices it is shown that process systems with controlled mass convection and without sources or with stabilizing linear source terms are globally asymptotically stable. The hierarchically structured model gives rise to a distributed controller structure that is in agreement with the traditional hierarchical process control system structure where local controllers are used for mass inventory control and coordinating controllers are used for optimizing the system dynamics. The proposed distributed controller is illustrated on a simple non-isotherm jacketed chemical reactor

Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Sets

Imitation learning enables the synthesis of controllers for complex objectives and highly uncertain plant models. However, methods to provide stability guarantees to imitation learned controllers often rely on large amounts of data and/or known plant models. In this paper, we explore an input-output (IO) stability approach to dissipative imitation learning, which achieves stability with sparse data sets and with little known about the plant model. A closed-loop stable dynamic output feedback controller is learned using expert data, a coarse IO plant model, and a new constraint to enforce dissipativity on the learned controller. While the learning objective is nonconvex, iterative convex overbounding (ICO) and projected gradient descent (PGD) are explored as methods to successfully learn the controller. This new imitation learning method is applied to two unknown plants and compared to traditionally learned dynamic output feedback controller and neural network controller. With little knowledge of the plant model and a small data set, the dissipativity constrained learned controller achieves closed loop stability and successfully mimics the behavior of the expert controller, while other methods often fail to maintain stability and achieve good performance

Limited-Communication Distributed Model Predictive Control for HVAC Systems

This dissertation proposes a Limited-Communication Distributed Model Predictive Control algorithm for networks with constrained discrete-time linear processes as local subsystems. The introduced algorithm has an iterative and cooperative framework with neighbor-to-neighbor communication structure. Convergence to a centralized solution is guaranteed by requiring coupled subsystems with local information to cooperate only. During an iteration, a local controller exchanges its predicted effects with local neighbors (which are treated as measured input disturbances in local dynamics) and receives the neighbor sensitivities for these effects at next iteration. Then the controller minimizes a local cost function that counts for the future effects to neighbors weighted by the received sensitivity information. Distributed observers are employed to estimate local states through local input-output signals. Closed-loop stability is proved for sufficiently long horizons. To reduce the computational loads associated with large horizons, local decisions are parametrized by Laguerre functions. A local agent can also reduce the communication burden by parametrizing the communicated data with Laguerre sequences. So far, convergence and closed-loop stability of the algorithm are proven under the assumptions of accessing all subsystem dynamics and cost functions information by a centralized monitor and sufficient number of iterations per sampling. However, these are not mild assumptions for many applications. To design a local convergence condition or a global condition that requires less information, tools from dissipativity theory are used. Although they are conservative conditions, the algorithm convergence can now be ensured either by requiring a distributed subsystem to show dissipativity in the local information dynamic inputs-outputs with gain less than unity or solving a global dissipative inequality with subsystem dissipativity gains and network topology only. Free variables are added to the local problems with the object of having freedom to design such convergence conditions. However, these new variables will result into a suboptimal algorithm that affects the proposed closed-loop stability. To ensure local MPC stability, therefore, a distributed synthesis, which considers the system interactions, of stabilizing terminal costs is introduced. Finally, to illustrate the aspects of the algorithm, coupled tank process and building HVAC system are used as application examples

Energy-Based Control for the Cart-Pole System in Implicit Port-Hamiltonian Representation

This master thesis is devoted to the design, analysis, and experimental validation of an energy-based control strategy for the well-known benchmark cart-pole system in implicit Port-Hamiltonian (PH) representation. The control scheme performs two tasks: swingup and (local) stabilization. The swing-up controller is carried out on the basis of a generalized energy function and consists of bringing the pendulum trajectories from the lower (stable) position to a limit cycle (homoclinic orbit), which passes by the upright (unstable) position, as well as the cart trajectories to the desired point. The (local) stabilizing controller is designed under a novel algebraic Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) technique and ensures the upright (asymptotic) stabilization of the pendulum as well as the cart at a desired position. To illustrate the effectiveness of the proposed control scheme, this work presents simulations and real-time experiments considering physical damping, i.e., viscous friction. The results are additionally contrasted with another energy-based control strategy for the cart-pole system in explicit Euler-Lagrange (EL) representation.Diese Masterarbeit widmet sich dem Entwurf, der Analyse und der experimentellen Validierung einer energiebasierten Regelstrategie für das bekannte Benchmarksystem des inversen Pendels auf einem Wagen in impliziter Port-Hamiltonscher (PH) Darstellung. Das Regelungssystem erfüllt zwei Aufgaben: das Aufschwingen und (lokale) Stabilisierung. Das Aufschwingen erfolgt auf Grundlage der generalisierten Energiefunktion und besteht darin, sowohl die Trajektorien des Pendels von der unteren (stabilen) Position in einen Grenzzyklus (homokliner Orbit) zu bringen, wobei die (instabile) aufrechte Lage passiert wird, als auch den Wagen in einer gewünschten Position einzustellen. Die (lokale) Regelung zur Stabilisierung ist nach einer neuartigen algebraischen Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) Methode konzipiert und gewährleistet die aufrechte (asymptotische) Stabilisierung des Pendels sowie die Positionierung des Wagens an einem gewünschten Referenzpunkt. Um die Funktionalität des entworfenen Regelungssystems zu veranschaulichen, werden in dieser Masterarbeit Simulationen und Echtzeit-Experimente unter Berücksichtigung der physikalischen Dämpfung, d.h. der viskosen Reibung, vorgestellt. Die Ergebnisse werden zusätzlich mit einem weiteren energiebasierten Regelungsansatz für das System des inversen Pendels auf einem Wagen in expliziter Euler-Lagrange (EL) Darstellung verglichen.Tesi

Energy Shaping Control for Stabilization of Interconnected Voltage Source Converters in Weakly-Connected AC Microgrid Systems

With the ubiquitous installations of renewable energy resources such as solar and wind, for decentralized power applications across the United States, microgrids are being viewed as an avenue for achieving this goal. Various independent system operators and regional transmission operators such as Southwest Power Pool (SPP), Midcontinent System Operator (MISO), PJM Interconnection and Electric Reliability Council of Texas (ERCOT) manage the transmission and generation systems that host the distributed energy resources (DERs). Voltage source converters typically interconnect the DERs to the utility system and used in High voltage dc (HVDC) systems for transmitting power throughout the United States. A microgrid configuration is built at the 13.8kV 4.75MVA National Center for Reliable Energy Transmission (NCREPT) testing facility for performing grid-connected and islanded operation of interconnected voltage source converters. The interconnected voltage source converters consist of a variable voltage variable frequency (VVVF) drive, which powers a regenerative (REGEN) load bench acting as a distributed energy resource emulator. Due to the weak-grid interface in islanded mode testing, a voltage instability occurs on the VVVF dc link voltage causing the system to collapse. This dissertation presents a new stability theorem for stabilizing interconnected voltage source converters in microgrid systems with weak-grid interfaces. The new stability theorem is derived using the concepts of Dirac composition in Port-Hamiltonian systems, passivity in physical systems, eigenvalue analysis and robust analysis based on the edge theorem for parametric uncertainty. The novel stability theorem aims to prove that all members of the classes of voltage source converter-based microgrid systems can be stabilized using an energy-shaping control methodology. The proposed theorems and stability analysis justifies the development of the Modified Interconnection and Damping Assignment Passivity-Based Control (Modified IDA-PBC) method to be utilized in stabilizing the microgrid configuration at NCREPT for mitigating system instabilities. The system is simulated in MATLAB/SimulinkTM using the Simpower toolbox to observe the system’s performance of the designed controller in comparison to the decoupled proportional intergral controller. The simulation results verify that the Modified-IDA-PBC is a viable option for dc bus voltage control of interconnected voltage source converters in microgrid systems

Data-Driven Nonlinear Control Designs for Constrained Systems

Systems with nonlinear dynamics are theoretically constrained to the realm of nonlinear analysis and design, while explicit constraints are expressed as equalities or inequalities of state, input, and output vectors of differential equations. Few control designs exist for systems with such explicit constraints, and no generalized solution has been provided. This dissertation presents general techniques to design stabilizing controls for a specific class of nonlinear systems with constraints on input and output, and verifies that such designs are straightforward to implement in selected applications. Additionally, a closed-form technique for an open-loop problem with unsolvable dynamic equations is developed. Typical optimal control methods cannot be readily applied to nonlinear systems without heavy modification. However, by embedding a novel control framework based on barrier functions and feedback linearization, well-established optimal control techniques become applicable when constraints are imposed by the design in real-time. Applications in power systems and aircraft control often have safety, performance, and hardware restrictions that are combinations of input and output constraints, while cryogenic memory applications have design restrictions and unknown analytic solutions. Most applications fall into a broad class of systems known as passivity-short, in which certain properties are utilized to form a structural framework for system interconnection with existing general stabilizing control techniques. Previous theoretical contributions are extended to include constraints, which can be readily applied to the development of scalable system networks in practical systems, even in the presence of unknown dynamics. In cases such as these, model identification techniques are used to obtain estimated system models which are guaranteed to be at least passivity-short. With numerous analytic tools accessible, a data-driven nonlinear control design framework is developed using model identification resulting in passivity-short systems which handles input and output saturations. Simulations are presented that prove to effectively control and stabilize example practical systems