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 Comparison of Run-to-Run Control Methods in Semiconductor Manufacturing Processes(2000) Zhang, Chang; Deng, Hao; Baras, John S.; Baras, John S.; ISRRun-to Run (RtR) control plays an important role in semiconductor manufacturing.In this paper, RtR control methods are generalized. The set-valued RtR controllers with ellipsoidapproximation are compared with other RtR controllers bysimulation according to the following criteria: A good RtR controller should be able to compensate for variousdisturbances, such as process drifts, process shifts (step disturbance)and model errors; moreover, it should beable to deal with limitations, bounds, cost requirement, multipletargets and time delays that are often encountered in realprocesses.
Preliminary results show the good performance of the set-valued RtRcontroller. Furthermore, this paper shows that it is insufficient to uselinear models to approximate nonlinear processes and it is necessary to developnonlinear model based RtR controllers.
Item The Set-Valued Run-to-Run Controller with Ellipsoid Approximation(2000) Zhang, Chang; Baras, John S.; Baras, John S.; ISRIn order to successfully apply Run-to-Run (RtR) control or real time control ina semiconductor process, it is very important to estimate the processmodel. Traditional semiconductor process control methods neglect theimportance of robustness due to the estimation methods they use.A new approach, namely the set-valued RtR controller with ellipsoidapproximation, is proposed to estimate the process model from acompletely different point of view. Because the set-valued RtRcontroller identifies the process model in the feasible parameter setwhich is insensitive to noises, the controller is robust to theenvironment noises.Ellipsoid approximation can significantly reduce the computation load for the set-valued method.
In this paper, the Modified Optimal Volume Ellipsoid (MOVE) algorithm is used toestimate the process model in each run. Designof the corresponding controller and parameter selection of the controller are introduced.Simulation results showed that the controller is robust toenvironment noises and model errors.
Item The Set-Valued Run-to-Run Controller in Semiconductor Manufacturing Processes(1999) Zhang, Chang; Baras, John S.; ISRIn semiconductor manufacturing, run-to-run (RtR) control is paid moreand more attention. In this paper a set-valuedRtR control scheme is introduced. Different from conventional RtR controlmethods, the set-valued method first calculates the feasibleparameter set at the beginning of each run, then estimates the modelparameters within this set. Compared to other RtR control schemes, itdoes not assume any statistical property of the noises. In simulation itwas shown that it is robust tomodel and sensor errors, and it has the potential to be applied tohighly nonlinear processes. Furthermore the set-valued method can beapplied to other fields such as signal processing and chemical processes.Item Stationary Bifurcation Control for Systems with Uncontrollable Linearization(1999) Taihyun Kim; Abed, Eyad H.; ISRStationary bifurcation control is studied under the assumption thatthe critical zero eigenvalue is uncontrollable for thelinearized system. The development facilitates explicit constructionof feedback control laws that render the bifurcation supercritical.Thus, the bifurcated equilibria in the controlled system are guaranteedstable.Bothpitchfork bifurcation and transcritical bifurcation are addressed.The results obtained forpitchfork bifurcations apply to general nonlinear models smoothin the state and the control. For transcritical bifurcations,the results require the system to be affine in the control.
Item Discrete-Time Risk-Sensitive Filters with Non-Gaussian Initial Conditions and their Ergodic Properties(1998) Dey, Subhrakanti; Charalambous, Charalambos D.; ISRIn this paper, we study asymptotic stability properties ofrisk-sensitive filters with respect to their initial conditions. In particular, we consider a linear time-invariant system with initial conditionsthat are not necessarily Gaussian. We show that in the case of Gaussianinitial conditions, the optimal risk-sensitive filter asymptoticallyconverges to any suboptimal filter initialized with an incorrect covariancematrix for the initial state vector in the mean square sense provided the incorrect initializing value for the covariance matrix results in arisk-sensitive filter that is asymptotically stable (that is, resultsin a solution for a Riccati equation that is asymptoticallystabilizing). For non-Gaussian initial conditions, we derive theexpression for the risk-sensitive filter in terms of a finite number ofparameters. Under a boundedness assumption satisfied by thefourth order moments of the initial state variable and a slow growthcondition satified by a certainRadon-Nikodym derivative, we show that a suboptimal risk-sensitive filterinitialized with Gaussian initial conditions asymptotically approachesthe optimal risk-sensitive filter for non-Gaussian initial conditions inthe mean square sense.The research and scientific content in this material has been submitted to the 1999 American Control Conference, San Diego, June 1999. Item A Framework for Mixed Estimation of Hidden Markov Models(1998) Dey, Subhrakanti; Marcus, Steven I.; ISRIn this paper, we present a framework for a mixed estimationscheme for hidden Markov models (HMM).A robust estimation scheme is first presented using the minimax method thatminimizes a worst case cost for HMMs with bounded uncertainties.Then we present a mixed estimation scheme that minimizes arisk-neutral cost with a constraint on the worst-case cost. Somesimulation results are also presented to compare these different estimationschemes in cases of uncertainties in the noise model.The research and scientific content in this material has been accepted for presentation in the 37th IEEE Conference on Decision and Control, Tampa, December 1998. Item Absolute Stability Theory, Theory, and State-Space Verification of Frequency-Domain Conditions: Connections and Implications for Computation(1997) Chou, Y.S.; Tits, A.L.; Balakrishnan, V.; ISRThe main contribution of the paper is to show the equivalence between the following two approaches for obtaining sufficient conditions for the robust stability of systems with structured uncertainties: (i) apply the classical absolute stability theory with multipliers; (ii) use the modern theory, specifically, the upper bound obtained by Fan, Tits and Doyle [IEEE TAC, Vol. 36, 25-38]. In particular, the relationship between the stability multipliers used in absolute stability theory and the scaling matrices used in the cited reference is explicitly characterized. The development hinges on the derivation of certain properties of a parameterized family of complex LMIs (linear matrix inequalities), a result of independent interest. The derivation also suggests a general computational framework for checking the feasibility of a broad class of frequency- dependent conditions, and in particular, yields a sequence of computable ﲭixed- -norm upper bounds , defined with guaranteed convergence from above to the supremum over frequency of the aforementioned upper bound.Item Simultaneous and Robust Stabilization of Nonlinear Systems by Means of Continuous and Time-Varying Feedback(1996) Ho-Mock-Qai, Bertina; Dayawansa, W.P.; ISRIn this dissertation, we address the stabilization of uncertain systems described by finite, countably infinite or uncountable families of systems. We adopt an approach that enables us to consider control systems with merely continuous dynamics as well as continuous time-invariant and time-varying feedback laws.We show that for any countable family of asymptotically stabilizable systems, there exists a continuous nonlinear time-invariant controller that simultaneously stabilizes (not asymptotically) the family. Although these controllers do not achieve simultaneous asymptotic stabilization in the general case, we manage to modify our construction in order to design continuous time-invariant feedback laws that simultaneously asymptotically stabilize certain pairs of systems in the plane.
By introducing continuous time-varying feedback laws, we then prove that an finite family of linear time-invariant (LTI) systems is simultaneously asymptotically stabilizable by means of continuous nonlinear time-varying feedback if each system of the family is asymptotically stabilizable by a LTI controller. We also provide sufficient conditions for the simultaneous asymptotic stabilizability of countably infinite families of LTI systems, by means of continuous time-varying feedback.
We then obtain sufficient conditions for the existence of a continuous time- varying feedback law that simultaneously asymptotically stabilizes a finite family on nonlinear systems. We illustrate these results by establishing the simultaneous asymptotic stabilizability of the elements of a class of pairs of homogeneous nonlinear systems We finally consider a class of parameterized families of systems in the plane [where the parameter lies in an uncountable set] that are not robustly asymptotically stabilizable by means of C1 feedback. We solve their robust asymptotic stabilization by means of continuous feedback, through a new approach where a robust asymptotic stabilizer is considered as a feedback law that simultaneously robustly asymptotically stabilizes two sub-families of the family under consideration.
Item Development and Analysis of a Nonlinear Dynamic Inverse Control Strategy(1996) Reilly, J.; Levine, W.S.; ISRAircraft control normally relies on gain-scheduling of linear control laws, an approach that has been very successful. One can characterize nonlinear dynamics in high-alpha maneuvers by using a large number of linear models, but his method may not be adequate, especially since some of the chosen operating points may not be equilibrium points. One can build robustness into the control strategy (e.g., by requiring more gain and phase margins), but this approach translates to a more conservative control, which means possible performance degradation. An alternative method is to take explicitly into account the nonlinearities in the control design, thus better utilizing the existing dynamics and control power. We choose to investigate the dynamic inverse control technique because of its ease of implementation, and the simply way that maneuvers can enter into the control. The objective of nonlinear dynamic inversion is to invert the dynamic equations of the plant directly in order to find the control necessary to yield the given output.We elaborate the dynamic inverse methods first described by Meyer and Cicolani. We expand the method to a more complex aerodynamics and airframe description, that of the full nonlinear simulation (wind-tunnel and flight tested model) of the X-29. To achieve additional realism, the simulation contains actuator redundancy and actuator limits. We first formulate a reduced analytic model in order to use feedback linearization techniques to design the controller. Since we neglect some of the aerodynamic terms, the controller is then modified so that stability robustness to modeling errors can be achieved. In addition, we modify the robust control method to add integral action to enable the controller to reduce steady state errors and to lower the control rates.
Item Robust H∞ Output Feedback Control of Bilinear Systems(1996) Teolis, C.A.; Yuliar, S.; James, Matthew R.; Baras, John S.; ISRThe study of robust nonlinear control has attracted increasing interest over the last few years. Progress has been aided by the recent entension [FM91, Jam92] of the linear quadratic results [Jac73, Whi81] linking the theories of L2 gain control (nonlinear H∞ control), different games, and the stochastic risk sensitive control. Most of the previous research conducted in the area of robust nonlinear control has focused on the case where full state information is available. Thus, previously little attention has been given to the problem of robust nonlinear control via output feedback. In this paper we address the problem of robust H∞ output feedback control for the special case of bilinear systems.