Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
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Item Modeling Biological Pathways: A discrete Event Systems Approach(1994) Reddy, V.N.; Mavrovouniotis, M.L.; ISRA discrete-event systems approach is proposed for the modeling of biochemical reaction systems. The approach is based on Petri nets, which are particularly suited to modeling stoichiometric transformations, i.e., the inter conversion of metabolites in fixed proportions. Properties of Petri nets and methods for their analysis are presented, along with their interpretation for biological systems. An example of the human erythrocyte metabolism is presented to illustrate the concepts of the methodology.Item State Estimation Model Based Algorithm for On-line Optimization and Control of Batch Processes(1994) Gattu, Gangadhar; Zafiriou, Evanghelos; ISRBatch/semi-batch processes are highly nonlinear and involve complex reaction mechanisms. Model-plant mismatch always exists. The lack of rapid direct or indirect measurements of the properties to be controlled makes the control task difficult. It is the usual practice to follow the prespecified setpoint profiles for process variables for which measurements are available, in order to obtain desired product properties. Modeling error can be the cause of bad performance when optimal profiles computed for the model, are implemented on the actual plant. In this paper, a state estimation model based algorithm is presented for on-line modification of the optimal profile and control with the goal of obtaining the desired properties at the minimum batch time. The effectiveness of the algorithm is demonstrated by its application to bulk polymerization of styrene.Item State Estimation Nonlinear QDMC with Input-Output Models(1994) Gattu, Gangadhar; Zafiriou, Evanghelos; ISRA State Estimation NLQDMC algorithm is presented for use with nonlinear input-output models. The proposed algorithm extends the state estimation NLQDMC [5] to nonlinear models identified based on input-output information. The algorithm preserves the computational advantages of [5] when compared to the other algorithms based on nonlinear programming techniques. The illustrating example demonstrates the usage of tuning parameters and points out the benefits and shortcomings of the algorithm.Item On the Quadratic Stability of Constrained Model Predictive Control(1994) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISRAnalytic and numerical methods are developed in this paper for the analysis of the quadratic stability of Constrained Model Predictive Control (CMPC). According to the CMPC algorithm, each term of the closed-form of control law corresponding to an active constraint situation can be decomposed to have an uncertainty block, which is time varying over the control period. By analytic method, if a quadratic Lyapunov function can be found for the CMPC closed-loop system with uncertainty blocks in the feedback control law by solving a Riccati type equation, then the control system is quadratic stable. Since no rigorous solving method has been found, this Riccati type equation is solved by a trial-and- error method in this paper. A numerical method that does not solve the Riccati type equation, the Linear Matrix Inequality (LMI) technique, was found useful in solving this quadratic stability problem. Several examples are given to show the CMPC quadratic stability analysis results. It is also noticeable that the quadratic stability implies a similarity to a contraction.Item The Strong H∞ Performance of Constrained Model Predictive Control(1994) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISRAn off-line performance index for the Constrained Model Predictive Control (CMPC) is defined by the strongly H∞ performance criterion in this paper. From the CMPC algorithm, each term of the closed-form of CMPC control law corresponding to an active constraint situation can be decomposed to have an uncertainty block, which is time varying over the control period. To analyze the strong H∞ performance and quantify the minimum upper bound of L2-induced gain of CMPC system with this type of control law, a numerical method, the Linear Matrix Inequality (LMI) technique, was found useful. Several examples are given to show the results on quantification and analysis of the control system performance.Item Observer Based Nonlinear Quadratic Dynamic Matrix Control for State Space and I/O Models(1994) Gattu, Gangadhar; Zafiriou, Evanghelos; ISRObserver based nonlinear QDMC algorithm is presented for use with nonlinear state space and input-output models. The proposed algorithm is an extension of Nonlinear Quadratic Dynamic Matrix Control (NLQDMC) by Garcia (1984) and its extension by Gattu and Zafiriou (1992a). Garcia proposed an extension of linear Quadratic Dynamic Matrix Control (QDMC) to nonlinear processes. Although a nonlinear model is used, only a single Quadratic Program (QP) is solved on-line. Gattu and Zafiriou extended this formulation to open-loop unstable systems, by incorporating a Kalman filter. The requirement of solving only one QP on-line at each sampling time makes this algorithm an attractive option for industrial implementation. This extension of NLQDMC to open-loop unstable systems was ad hoc and did not address the problem of offset free tracking and disturbance rejection in a general state space setting. Independent white noise was added to the model states to handle unstable processes. The approach can stabilize the system but leads to an offset in the presence of persistent disturbances. To obtain offset free tracking Gattu and Zafiriou added a constant disturbance to the predicted output as done in DMC-type algorithms. This addition is ad hoc and does not result from the filtering/prediction theory. The proposed algorithm eliminates the major drawbacks of the algorithm presented by Gattu and Zafiriou and extends that algorithm for nonlinear models identified based on input-output information. An algorithm schematic is presented for measurement delay cases. The algorithm preserves the computational advantages when compared to the other algorithms based on nonlinear programming techniques. The illustrating examples demonstrate the usage of tuning parameters for unstable and stable systems and points out the benefits and short comings of the algorithm.Item Estimation of Properties of Acyclic Organic Compounds through Conjugation(1993) Constantinou, Leonidas A.; Mavrovouniotis, Micheal L.; ISRSystematic methods for the prediction of thermodynamic and physical properties from the molecular structure of substances are essential for the modeling, analysis, and design of chemical processes. The objective of this work is to develop a new class of computer-based methods for the estimation of properties of organic compounds from their molecular structure. The proposed approach is based on the contributions of Atoms and Bonds to the properties of Conjugate forms (ABC) of a molecular structure. Conjugate forms are alternative formal arrangements of valence electrons in a molecule; a real chemical compound can be considered the hybrid of all its conjugates. Conjugates are extensively used in organic chemistry to draw qualitative conclusions on the stability and chemical properties of a compound. Until now, however, they have been completely ignored in property estimation for chemical engineering purposes.In the proposed ABC approach, we start by generating all conjugate forms of the molecule whose properties we wish to estimate. Physical and thermodynamic properties are assigned to each conjugate, simply by summing contributions from atoms and bonds in the particular electronic arrangement of the conjugate. To eliminate the number of adjustable parameters, we introduce conjugation operators, that is, recipes that yield recessive conjugates when applied to the dominant conjugate. Then, the properties of the conjugates are combined, through semi-empirical formulae, to derive the properties of the compound.
The method was applied to the estimation of a number of thermodynamic and physical properties of hydrocarbons and organic acyclic compounds containing oxygen, nitrogen, or sulfur. It was also employed for the approximate estimation of properties of unstable intermediates. Compared to the typical group-contribution methods, our method is more accurate in all these cases.
The ABC technique enables simple yet accurate estimation of physical and thermodynamic properties, and therefore improves the modeling, analysis, or design of products and processes.
Item The Closed-Form Control Laws of the Constrained Model Predictive Control Algorithm(1993) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISRThe Analysis of quadratic Stability and strongly Hperformance of Model Predictive Control (MPC) with hard constraints (or called Constrained Model Predictive Control (CMPC)) can be accomplished by reformulating the hard constraints of CMPC. From the CMPC algorithm, each term of the closed-form of CMPC control law corresponding to an active constraint situation can be decomposed to have an uncertainty block, which is time varying over the control period. The control law also contains a bias from the bounds of the constraints which cause difficulty in stability and performance analysis. An alternative way to avoid this difficulty is to reformulate the hard constraints to adjustable constraints with time varying adjustable weights on the adjustable variables added to the on-line objective function. The time varying weights in the adjustable constraint control law make the control action just the same as the hard constrained control. Theoretical derivatives and examples are given. The same reformulation is applied to the softened constraint cases.On the analysis of the quadratic stability and strongly H performance, the control system for hard constraint control law without bias satisfies the stability and performance criteria if and only if the control system for adjustable constraint control law with time varying adjustable weights satisfies the same criteria. The details will be shown in the technical reports on quadratic stability and strongly Hperformance analysis, which are in preparation.
Item A Local Small Gain Theorem and Its Use for Robust Stability of Uncertain Feedback Volterra Systems(1993) Zheng, Q.; Zafiriou, E.; ISRThe requirement to evaluate a gain over the whole signal space is one of the restrictions in the well-known small gain theorem. Using the concepts of local gain and strict causality a local form of small gain theorem is proposed, which can be used to analyze input magnitude dependent stability problems of feedback nonlinear systems, such as a Volterra system. Since only finite order Volterra series can be handled in practice, an uncertainly model is derived to address the robustness issue of approximating a nonlinear system by a finite Volterra series in the context of closed-loop control. The local small gain theorem is then used to analyze the feedback properties of the uncertain Volterra system and a sufficient condition for robust stability is obtained.Item Stability Analysis of Inverse Volterra Series(1993) Zhang, Q.; Zafiriou, E.; ISRAmong various nonlinear control methods, the one based on the Volterra series expansion is a promising approach for chemical process control. Almost all compensator design methods based on Volterra series system models utilize the inverse or some type of pseudo-inverse of the models. It is well known that this inverse is usually stable only for a limited amplitude of input signals, and this limited range is not understood quantitatively. Traditional input-output stability analysis methods cannot be used to analyze such an input amplitude dependent stability problem. Under the assumption of the open-loop system being strictly causal, Local Small Gain Theorem (LSGT) is first developed in the paper, which states a sufficient condition for the stability of the closed-loop nonlinear system. Using the new theorem, not only can one determined the local stability of the closed-loop system but also obtain a bound on the external input signal which guarantees BIBO stability. Then, this theorem is used to analyze the stability problem of inverse Volterra series. It so happens that for the Volterra series models an approximation of the local system gain can be easily obtained. By solving a simple single-variable optimization problem, a bound on the external input signal can be obtained, which guarantees the stability of the inverse Volterra series. Both mathematical analysis and simulation results are presented.