Closed-loop Stability Region Research Articles

Definition and Utilization of the Null Controllable Region for Model Predictive Control of Multi-Input Linear Systems

The problem of guaranteeing stability from the entire null controllable region (NCR) for multi-input linear dynamical systems is addressed in the present manuscript. The proposed controller design is inspired by results for single input systems and generalized to multiple input systems. The approach relies on utilizing the level sets of the NCR as level sets of a Lyapunov function. A contractive constraint is incorporated into a model predictive control design, guaranteeing feasibility for any horizon length, and resulting in the NCR as the closed-loop stability region. The proposed method is illustrated using a simulation example.

Event-triggered Dynamic Output Feedback Controller for Discrete-time LPV Systems with Constraints

This paper examines an event-triggered control design approach for discrete-time linear parameter-varying (LPV) systems under control constraints. A parameter-dependent dynamic output-feedback controller with an event-triggering condition is designed to ensure the regional asymptotic stability of the closed-loop system while minimizing a quadratic cost function. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) thanks to the use of a parameter-dependent quadratic Lyapunov function. Also, convex optimization schemes are proposed using these conditions to minimize an upper bound of a given cost function or to maximize the size of the region of closed-loop stability. Examples illustrate the proposal.

Regional stability and stabilization of a class of linear hyperbolic systems with nonlinear quadratic dynamic boundary conditions

This paper addresses the boundary control problem of fluid transport in a Poiseuille flow taking the actuator dynamics into account. More precisely, sufficient stability conditions are derived to guarantee the exponential stability of a linear hyperbolic differential equation system subject to nonlinear quadratic dynamic boundary conditions by means of Lyapunov based techniques. Then, convex optimization problems in terms of linear matrix inequality constraints are derived to either estimate the closed-loop stability region or synthesize a robust control law ensuring the local closed-loop stability while estimating an admissible set of initial states. The proposed results are then applied to application-oriented examples to illustrate local stability and stabilization tools.

Distributed data-based fault identification and accommodation in networked process systems

This paper presents a data-based framework for distributed actuator fault identification and accommodation in networked process systems controlled over a resource-constrained communication medium. Initially, a quasi-decentralized networked control structure is designed to stabilize the plant in the absence of faults. The structure consists of a set of local model-based control systems that communicate with one another at discrete times. An explicit characterization of the networked closed-loop stability region is obtained in terms of the update period, the accuracy of the models, and the choice of controller design parameters. To address the actuator fault identification problem, a set of local fault diagnosis agents are designed and embedded within the various subsystems. Each agent uses a moving-horizon parameter estimation scheme to estimate on-line the size and location of the local faults using the locally sampled states and the model state estimates for the interconnected units. Potential discrepancies or ambiguities in the local fault diagnosis results, which may be caused by the strong dynamic coupling between the individual subsystems and the presence of plant-model mismatch, are reconciled by means of a fault estimation confidence interval which is obtained by analyzing the networked closed-loop dynamics at update times. Once the locations and magnitudes of the actuator faults are identified, the resulting estimates are transmitted to a higher-level supervisor to select and implement a suitable fault accommodation strategy. A number of stability-preserving fault accommodation strategies are devised, including updating the post-fault models, adjusting the controllers’ parameters, or a combination of both. The selection of the appropriate fault accommodation strategy is made on the basis of the estimated fault magnitude and the characterization of the networked closed-loop stability region. Finally, the developed methodology is illustrated using a reactor–separator process example subject to both sudden and incipient control actuator faults.

Model-based Fault-Tolerant Control of Uncertain Particulate Processes: Integrating Fault Detection, Estimation and Accommodation

This work presents a methodology for the integrated identification, estimation and accommodation of control actuator faults in particulate processes with discretely-sampled measurements and plant-model mismatch. Initially, a stabilizing state feedback controller is designed on the basis of a reduced-order model of the infinite-dimensional system, and the closed-loop stability region is characterized in terms of the model uncertainty, the fault magnitude, the sampling period and the control design parameters. When state measurements are unavailable, the reduced-order inter-sample model predictor generates state estimates which are updated at each sampling time. A moving-horizon optimization problem is then formulated and solved for on-line actuator fault detection, isolation and estimation using past state and input data. The resulting estimates are used to locate the operating point with respect to the closed-loop stability region, which in turn is used to carry out the fault accommodation logic via updating the pot-fault control model and/or adjusting the controller design parameters. The developed methodology is illustrated using a non-isothermal continuous crystallizer example.

Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems

In this work, we propose a conceptual framework for integrating dynamic economic optimization and model predictive control (MPC) for optimal operation of nonlinear process systems. First, we introduce the proposed two-layer integrated framework. The upper layer, consisting of an economic MPC (EMPC) system that receives state feedback and time-dependent economic information, computes economically optimal time-varying operating trajectories for the process by optimizing a time-dependent economic cost function over a finite prediction horizon subject to a nonlinear dynamic process model. The lower feedback control layer may utilize conventional MPC schemes or even classical control to compute feedback control actions that force the process state to track the time-varying operating trajectories computed by the upper layer EMPC. Such a framework takes advantage of the EMPC ability to compute optimal process time-varying operating policies using a dynamic process model instead of a steady-state model, and the incorporation of suitable constraints on the EMPC allows calculating operating process state trajectories that can be tracked by the control layer. Second, we prove practical closed-loop stability including an explicit characterization of the closed-loop stability region. Finally, we demonstrate through extensive simulations using a chemical process model that the proposed framework can both (1) achieve stability and (2) lead to improved economic closed-loop performance compared to real-time optimization (RTO) systems using steady-state models.

Optimal controller tuning for nonlinear processes

The present work proposes a systematic methodology for the optimal selection of controller parameters in the sense of minimizing a performance index, which is a quadratic function of the tracking error and the control effort. The performance index is calculated explicitly as an algebraic function of the controller parameters by solving Zubov's partial differential equation (PDE). Standard optimization techniques are then employed for the calculation of the optimal values of the controller parameters. The solution of Zubov's PDE is also used to estimate the closed-loop stability region for the chosen values of the controller parameters. The proposed approach is finally illustrated in a chemical reactor control problem.

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.

OPTIMAL CONTROLLER TUNING FOR NONLINEAR PROCESSES

This work proposes a systematic methodology for the optimal selection of controller parameters, in the sense of minimizing a performance index which is a quadratic function of the tracking error and the control effort. The performance index is calculated explicitly as an algebraic function of the controller parameters by solving a Zubov-type partial differential equation. Standard nonlinear programming techniques are then employed for the calculation of the optimal values of the controller parameters. The solution of the partial differential equation is also used to estimate the closed-loop stability region for the chosen values of the controller parameters. The proposed approach is illustrated in a chemical reactor control problem.

Energy-predictive control: a new synthesis approach for nonlinear process control

The present work proposes a new controller synthesis framework, that is based on the methodological principles of Lyapunov design. A notion of short-horizon energy-predictive control is introduced, that predicts and optimizes the rate of energy dissipation of the system and leads to the derivation of a continuous state feedback control law. The control law possesses two adjustable parameters that directly influence the size of the closed-loop stability region and the performance characteristics. The derived state feedback law may be combined with an open-loop state observer, leading to a dynamic output feedback controller with integral action. Finally, the performance of the proposed controller design methodology is evaluated in a chemical reactor example, that exhibits nonminimum-phase characteristics.