Cells respond to biochemical and physical internal as well as external signals. These signals can be broadly classified into two categories: (a) ``actionable'' or ``reference'' inputs that should elicit appropriate biological or physical responses such as gene expression or motility, and (b) ``disturbances'' or ``perturbations'' that should be ignored or actively filtered-out. These disturbances might be exogenous, such as binding of nonspecific ligands, or endogenous, such as variations in enzyme concentrations or gene copy numbers. In this context, the term robustness describes the capability to produce appropriate responses to reference inputs while at the same time being insensitive to disturbances. These two objectives often conflict with each other and require delicate design trade-offs. Indeed, natural biological systems use complicated and still poorly understood control strategies in order to finely balance the goals of responsiveness and robustness. A better understanding of such natural strategies remains an important scientific goal in itself and will play a role in the construction of synthetic circuits for therapeutic and biosensing applications. A prototype problem in robustly responding to inputs is that of ``robust tracking'', defined by the requirement that some designated internal quantity (for example, the level of expression of a reporter protein) should faithfully follow an input signal while being insensitive to an appropriate class of perturbations. Control theory predicts that a certain type of motif, called integral feedback, will help achieve this goal, and this motif is, in fact, a necessary feature of any system that exhibits robust tracking. Indeed, integral feedback has always been a key component of electrical and mechanical control systems, at least since the 18th century when James Watt employed the centrifugal governor to regulate steam engines. Motivated by this knowledge, biological engineers have proposed various designs for biomolecular integral feedback control mechanisms. However, practical and quantitatively predictable implementations have proved challenging, in part due to the difficulty in obtaining accurate models of transcription, translation, and resource competition in living cells, and the stochasticity inherent in cellular reactions. These challenges prevent first-principles rational design and parameter optimization. In this work, we exploit the versatility of an Escherichia coli cell-free transcription-translation (TXTL) to accurately design, model and then build, a synthetic biomolecular integral controller that precisely controls the expression of a target gene. To our knowledge, this is the first design of a functioning gene network that achieves the goal of making gene expression track an externally imposed reference level, achieves this goal even in the presence of disturbances, and whose performance quantitatively agrees with mathematical predictions.
more »
« less
Distributed Model Predictive Control for Autonomous Droop-Controlled Inverter-Based Microgrids
Microgrids must be able to restore voltage and frequency to their reference values during transient events; inverters are used as part of a microgrid's hierarchical control for maintaining power quality. Reviewed methods either do not allow for intuitive trade-off tuning between the objectives of synchronous state restoration, local reference tracking, and disturbance rejection, or do not consider all of these objectives. In this paper, we address all of these objectives for voltage restoration in droop-controlled inverter-based islanded micro-grids. By using distributed model predictive control (DMPC) in series with an unscented Kalman Filter (UKF), we design a secondary voltage controller to restore the voltage to the reference in finite time. The DMPC solves a reference tracking problem while rejecting reactive power disturbances in a noisy system. The method we present accounts for non-zero mean disturbances by design of a random-walk estimator. We validate the method's ability to restore the voltage in finite time via modeling a multi-node microgrid in Simulink.
more »
« less
- Award ID(s):
- 1743772
- NSF-PAR ID:
- 10190925
- Date Published:
- Journal Name:
- 2019 IEEE 58th Conference on Decision and Control (CDC)
- Page Range / eLocation ID:
- 6242 to 6248
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This paper examines the problem of real-time optimization of networked systems and develops online algorithms that steer the system towards the optimal trajectory without explicit knowledge of the system model. The problem is modeled as a dynamic optimization problem with time-varying performance objectives and engineering constraints. The design of the algorithms leverages the online zero-order primal-dual projected-gradient method. In particular, the primal step that involves the gradient of the objective function (and hence requires a networked systems model) is replaced by its zero-order approximation with two function evaluations using a deterministic perturbation signal. The evaluations are performed using the measurements of the system output, hence giving rise to a feedback interconnection, with the optimization algorithm serving as a feedback controller. The paper provides some insights on the stability and tracking properties of this interconnection. Finally, the paper applies this methodology to a real-time optimal power flow problem in power systems, and shows its efficacy on the IEEE 37-node distribution test feeder for reference power tracking and voltage regulation.more » « less
-
Abstract We present an analytical design and experimental verification of trajectory tracking control of a 7-DOF robot manipulator, which achieves convergence of all tracking errors to the origin within a finite terminal time, also referred to as the “settling time.” A key feature of this control strategy is that the settling time is explicitly assigned by the control designer to a value desired, or “prescribed” by the user and that the settling time is independent of the initial conditions and of the reference signal. In order to achieve this beneficial property with the controller, a scaling of the state by a function of time that grows unbounded toward the terminal time is employed. Through Lyapunov analysis, we first demonstrate that the proposed controller achieves regulation of all tracking errors within the prescribed time as well as the uniform boundedness of the joint torques, even in the presence of a matched, nonvanishing disturbance. Then, through both simulation and experiment, we demonstrate that the proposed controller is capable of converging to the desired trajectory within the prescribed time, despite large distance between the initial conditions and the reference trajectory, i.e., in spite of large initial tracking errors, and in spite of a sinusoidal disturbance being applied in each joint.more » « less
-
In this paper we design a hybrid predictive controller for the tracking of a sinusoidal reference signal. The stability and forward invariance of a set of points around the reference state, named the tracking ellipse, is established by using tools for hybrid dynamical systems. Moreover, prediction of solutions for a finite number of switching events is used to minimize the number of switches. The control algorithm is shown to be robust to small perturbations and input disturbances. Simulations illustrating the main results are included.more » « less
-
null (Ed.)This paper proposes a finite-time event-triggered secondary frequency and voltage control for islanded AC microgrids (MGs) in a distributed fashion. The proposed control strategy can effectively perform frequency restoration and voltage regulations, while sharing the active and reactive power among the distributed generators (DGs) based on their power ratings. The finite-time control enables a system to reach consensus in a finite period of time enhanced from the asymptotic convergence. The event-triggered communication is utilized to reduce the communication burden among the DG controllers by transmitting data among DGs if an event-triggering condition is satisfied. The performance of the proposed finite-time event-triggered frequency control is verified utilizing a hardware-in-the-loop experimental testbed which simulates an AC MG in Opal-RT.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CDC40024.2019.9028938
