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On Computing Maximum Allowable Time Delay of Lur’e Systems with Uncertain Time-invariant Delays
Thapana Nampradit,David Banjerdpongchai 제어·로봇·시스템학회 2014 International Journal of Control, Automation, and Vol.12 No.3
In this paper, we present an improved delay-dependent absolute stability criterion for Lur’e systems with time delays. The guarantee of absolute stability is provided by Lyapunov-Krasovskii theorem with the Lyapunov functional containing the integral of sector-bounded nonlinearities. The Lyapunov functional terms involving delay are partitioned to be associated with each equidistant fragment on the length of time delay. Employing the Jensen inequality and S-procedure, the sufficient condition is derived from time derivative of the Lyapunov functional. Then, the absolute stability criterion expressed in terms of linear matrix inequalities (LMIs) can be efficiently solved using available LMI solvers. The bisection method is used to determine the maximum allowable time delays to ensure the stability of Lur’e systems in the presence of uncertain time-invariant delays. In addition, the stability criterion is extended to Lur’e systems subject to norm-bounded uncertainties by using the matrix elim-inating lemma. Numerical results from two benchmark problems show that the proposed criteria give significant improvement on the maximum allowable time delays.
Thapana Nampradit,David Banjerdpongchai 제어·로봇·시스템학회 2015 International Journal of Control, Automation, and Vol.13 No.5
In this paper, we present a design of robust state-feedback stabilization and a design of robust state-feedback H∞ control for Lur’e systems with time-invariant delays and norm-bounded uncertainties. The criteria of state-feedback stabilization and state-feedback H∞ control are developed using Lyapunov-Krasovskii Theorem with a delay-partitioning Lyapunov-Krasovskii functional and an integral of sector-bounded nonlinearities. The design criteria are given in terms of bilinear matrix inequality, which is non-convex optimization. We develop algorithms based on coordinate optimization, which alternate between two LMI optimization problems, to solve for the robust state-feedback controllers. The proposed iterative LMI algorithm for H∞ control design is a local optimization procedure, but it can return satisfactory state-feedback controllers depending on the initialization. Numerical examples show that the proposed LMI algorithms can provide robust state-feedback stabilization to guarantee the closed-loop stability of LSTD and yield robust state-feedback control to guarantee the worstcase H∞ performance of the closed-loop LSTD.
Wathanyoo Khaisongkram,David Banjerdpongchai 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.3
This paper extends the worst-case norm (WCN) of linear systems subject to inputs with magnitude and rate bounds to the WCN of uncertain linear systems under the same inputs. While the WCN for linear systems can be accurately approximated by simply solving a sparse linear programming, the computation of the WCN for uncertain linear systems leads to an NP-hard problem. In this paper, a branch-and-bound algorithm is applied to calculate the WCN in the presence of uncertainty. Subsequently, we derive the bounds for two approximation errors, namely, the truncation error and the discretization error, which are resulted from the proposed WCN computation method. Based on these error bounds, we give a brief guideline for choosing appropriate values of the terminal time and the sampling time. Numerical examples demonstate that computation time of the proposed algorithm is reasonable within certain problem dimensions. An exhaustive search is employed to validate the branch-and-bound algorithm. Finally, we suggest a means to improve the WCN computation for prob-lems with higher dimension.
Sitthiphat Promchaiwattana,David Banjerdpongchai 제어로봇시스템학회 2022 제어로봇시스템학회 국제학술대회 논문집 Vol.2022 No.11
This paper presents the design of supervisory model predictive control for HVAC systems with consideration of peak demand shaving and thermal comfort. In this work, we analyze the operating points with the thermal comfort requirement. Afterwards, we linearize the nonlinear dynamic model to a linear time-varying model. In particular, we specify that the operating point of the open-loop HVAC system satisfies the thermal comfort condition. This makes the predicted mean vote (PMV) equal to zero or nearly to zero. Subsequently, we calculate the zone temperature, the zone humidity ratio, and the volumetric flow rate. When considering the time-varying disturbance profiles, it appears that the operating points are time-varying. We observe that the coefficient of performance (COP) and the operating points are time-varying which lead to time-varying model. Moreover, we design supervisory control (SC) and model predictive control (MPC) for linear time-varying model. In the SC design, we aim to find the optimal reference zone temperature which is used as the reference signal for MPC. In the MPC design, the objectives are twofold. First, the zone temperature tracks the reference signal. Second, both electrical energy cost and deviation of desired thermal comfort are minimized. The computer simulation shows that MPC of time-varying HVAC system yields the best reference tracking. In addition, it reduces total electrical energy cost the most. We conclude that the optimal temperature reference can be effectively applied to the building HVAC systems while the occupants feel comfortable and the total electrical energy cost is the lowest.
Robust Output-Feedback Stabilization of a Nonlinear Bioreactor: A Matrix Inequality Approach
Tanagorn Jennawasin,David Banjerdpongchai 제어로봇시스템학회 2019 제어로봇시스템학회 국제학술대회 논문집 Vol.2019 No.10
This paper deals with an output-feedback stabilization problem of a nonlinear continuous bioreactor, whose vector fields are rational functions. In this problem, the control input must be bounded in some specified range in order to prevent the system reaching into undesired properties, such as bifurcation. To cope with this practical issue, we propose in this paper a novel condition for static output feedback design for nonlinear polynomial or rational systems with constraints on input magnitudes. The proposed design condition is bilinear in the decision variables, and hence we provide an iterative algorithm to solve the design problem. At each iteration, the design condition can be cast as standard convex optimization using the sum-of-squares technique and thus can be efficiently solved via the existing software tools. In addition, the novel parameter-dependent Lyapunov functions allow extension to robust static output-feedback design of systems subject to parametric uncertainty. Validity and effectiveness of the proposed approach are demonstrated by numerical simulations.
Design of Output Feedback Nonlinear Model Predictive Control for Inverted Pendulum on Cart
Petchakrit Pinyopawasutthi,David Banjerdpongchai,Yasuaki Oishi 제어로봇시스템학회 2018 제어로봇시스템학회 국제학술대회 논문집 Vol.2018 No.10
This paper presents designing of output feedback nonlinear model predictive control (NMPC) for nonlinear systems. NMPC employs the state feedback and updates the control input at each sampling step. The control design of NMPC is formulated as optimal control which requires the information of states of the process. However, in practice, we can measure only some states of the process. This paper aims to use the state observer to estimate the unknown states and use them as feedback for NMPC. We apply output feedback NMPC to inverted pendulum on cart. Numerical results show the response of output feedback NMPC asymptotically converges to that of state feedback NMPC.
Robust Iterative Learning Control for Linear Systems with Time-Invariant Parametric Uncertainties
DinhHoa Nguyen,David Banjerdpongchai 제어로봇시스템학회 2009 제어로봇시스템학회 국제학술대회 논문집 Vol.2009 No.8
This paper presents a novel algorithm of the robustiterative learning control for linear systems subject to time-invariant parametricuncer tainties. The design problem is formulated as a min-max problem with aquadratic performance criterion. Then, we derive an upper-bound of the worst-case performance. Applying Lagrange duality to the minimization problem leads to adual problem which can be reformulated as an optimization problem over linear matrixn equalities. An algorithm is given after ward and its convergence properties are proved. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
Sasita Anucha,David Banjerdpongchai 제어로봇시스템학회 2015 제어로봇시스템학회 국제학술대회 논문집 Vol.2015 No.10
A regenerative thermal oxidizer (RTO) is a treatment process of exhaust air. The RTO system absorbs heat from the exhaust gas and uses the captured heat to preheat the incoming gas stream and destroy air pollutants emitted from process exhaust streams at high temperatures. In order to regulate the gas stream output, temperature control loop is an important requirement. This paper presents an application of nonlinear model predictive control (NMPC) designed for RTO system. Applying the Wiener and Hammerstein model to NMPC can transform the design criterion into a quadratic function. The performance of NMPC based on Wiener and Hammerstein model is compared to linear MPC. Effects of each control parameter are also obtained. Simulation results indicate that NMPC provides better transient performance while error converges to zero.