ACL

These laboratory reports were intended for internal use, although there are no restrictions to download them. They are brief studies, draft manuscripts and theses produced by the laboratory members. The abstracts summarize the scope of each report. To download any report, just click on the desired format (PS or PDF). Hard copies are available upon request. Please inquiry the technical publications administrator on their prices and availability, or write to:

Technical Reports (c/o Prof. Eduardo Misawa)
Advanced Controls Laboratory
Oklahoma State University
218 Engineering North
Stillwater, OK 74078-5016
USA

Questions should be addressed to technical publications administrator.

Note: Due to problems experienced with the server, we are in the process of recovering missing reports and re-upload them to the server as they are retrieved from backups and other sources.

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Reports Currently Available for

Electronic Distribution:

Years available: [1997] [1998] [1999] [2000] [2001] [2002] [2003] [2004] [2005] [2006] [2007]

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1997:

• ACL-97-001: Brian O'Dell, Fuzzy Sliding Mode Control: A Critical Review [PS (size: 1,133,594) / PDF (size: )].
  
  Abstract: The purpose of this project was to provide an unbiased, critical review of the literature available on the topic of fuzzy sliding mode control (FSMC). Towards this goal, several papers were selected on the topic and the approach advocated in each one reviewed. Ideally, the control law for each could be directly compared against a traditional sliding mode control (SMC) law. The inherent ``fuzzy'' nature of FSMC often prevented this, although reasonable simplifying assumptions could often be made to permit some comparison. Where possible, Matlab simulations were utilized to compare the performance of FSMC and SMC controllers.
  
  
• ACL-97-002: Brian O'Dell, A Study of Methods to Improve the Disturbance Rejection Properties of LQG/LTR [PS (size: 480,929) / PDF (size: )].
  
  Abstract: In a recent paper by Whiteley, et. al., it was noted that one shortcoming of the LQG/LTR controller proposed by O'Dell and Misawa was poor performance in response to disturbances. In the present note, we consider several possible methods for improving the disturbance rejection properties of the uniform singular value (USV) controller.
  

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1998:

• ACL-98-001: Prabhakar Pagilla, In Preparation (is not publicly available)
  
  
• ACL-98-002: Hanz Richter, Hyperplane Design in Observer-Based Discrete-Time Sliding Mode Control (M.S. Thesis) [PS (size:1,415,920 )/ PDF (size: )]
  
  Abstract: The design of digital control systems for practical applications demands the designer to spend a great amount of time and effort in trial-and-error procedures and computer simulations. The reason for this is that only a few works exist in the literature that address all the issues relevant to practical situations, like the effects of computational time delays, presence of disturbances and parametric uncertainties, and the use of state estimators. This is especially true in the case of Sliding Mode Control. This work presents a general method for the design of a central parameter in Observer-Based Discrete Sliding Mode Control: the sliding hyperplane. The technique is derived from the analysis of the tracking error dynamics inside the boundary layer. Investigation showed that the equivalent matrix and system dynamics can be decomposed into two subsystems, having one of them the same structure as a continuous sliding system. Also, the influence of the sliding gain and boundary layer thickness is linked to an eigenvalue of the equivalent matrix. Two ways of selecting hyperplane coefficients are developed: eigenvalue assignment and LQ-optimal poles. An application example -the control of a flexible beam- is used to show the usage of the method.
  
  
• ACL-98-003: Hanz Richter, Eduardo A. Misawa and Gary E. Young, Hyperplane Design in Observer-Based Discrete-Time Sliding Mode Control [PS (size: 658,305) / PDF (size: )]
  
  Abstract: A new result that allows the selection of sliding hyperplane coefficients in Observer-Based Discrete-Time Sliding Mode Control (OBDSMC) is presented. Selection of coefficients is done by analyzing the tracking error dynamics inside the boundary layer --- where the closed-loop system has a linear state feedback configuration --- rather than assuming that the sliding function has already converged to zero. The eigenvalue assignment problem is reduced to the continuous time case studied by Zinober and other researchers.
  
  
• ACL-98-004: Jorge Chiriboga, May-Win L. Thein and Eduardo A. Misawa, Input-Output Feedback Linearization Control of a Load-Sensing Hydraulic Servo System [PS (size: 689,383) / PDF (size: )]
  
  Abstract: The objective of this project is to analyze the feasibility of designing a non-linear controller for a load-sensing hydraulic servo system. The nonlinear controller is obtained using Input-Output Feedback Linearization. By using this technique, the system is not restricted to operate locally about a certain set of operating points. Hence, it shows improved performance over the system described by Kim, which uses a Taylor expansion linearization technique and, thus, is limited to operate about a chosen set of operating points.
  
  
• ACL-98-005: May-Win L. Thein, Eduardo A. Misawa, Comparison of the Sliding Observers to Several State Estimators using a Rotational Inverted Pendulum [PS (size: 692,750) / PDF (size: )]
  
  Abstract: Because of the inherent characteristics of nonlinear systems, state estimation of these systems continues to pose difficult problems. The objective of this paper is to test the Sliding Mode Observer technique on a highly nonlinear non-minimum phase system. The chosen system is the rotational inverted pendulum system of Misawa, Arrington, and Ledgerwood . In addition, the observer technique is compared to that of other techniques: the Linear Kalman Filter, Thau's Method, the Adaptive Observer, the High Gain Observer, the Multistage Nonlinear Observer, and the Equivalent Control-Based Sliding Mode Observer. The bases of comparison is performance, robustness against disturbances and modeling errors, stability, and ease of application.
  
  
• ACL-98-006: Choon Yik Tang, Discrete Variable Structure Control for Uncertain Linear Multivariable Systems (M.S. Thesis) [PS (size: 1,499,386) / PDF (size: )]
  
  Abstract: The methodology of variable structure with sliding mode is proven to be very successful in controlling uncertain continuous-time dynamical systems. When the system is sampled or purely discrete, the invariance property of sliding mode, which is originally a continuous-time concept, no longer holds and the reaching condition has to be modified to allow a pseudo-sliding mode. Moreover, the state dependency of parametric uncertainties makes the satisfaction of reaching conditions considerably more difficult especially in multivariable systems. These difficulties have offered challenges that attracted a great deal of research interests. This thesis presents theoretical results on the discrete variable structure control of uncertain linear multivariable systems using the concepts of sliding mode and switching sector. It considers both the state and output feedback cases for systems with additive uncertainties and the state feedback case for systems with parametric uncertainties. The thesis also presents a sliding surface design procedure for single-input systems based on the version of discrete variable structure control developed by the ACL research group.
  
  
• ACL-98-007: Choon Yik Tang, Eduardo A. Misawa, Discrete Variable Structure Control for Linear Multivariable Systems: The State Feedback Case [PS (size: 536,106) / PDF (size: )]
  
  Abstract: This paper presents a state feedback sidcrete variable structure controller for linear multivariable systems with unmatched additive uncertainties, a generalization of the controller for single-input systems by Misawa (1997). It is shown that the controller guarantees the attractiveness and invariance of the boundary layer. In contrast to existing schemes, it utilizes one sliding hyperplane regardless of the number of inputs. This attribute enhances the design freedoms of tracking error dynamics inside the boundary layer while preserving robustness. It allows the use of well-established linear control design strategies under an eigenvalue constraint. A numerical example is used to illustrate the proposed technique.
  
  
• ACL-98-008: Choon Yik Tang, Eduardo A. Misawa, Discrete Variable Structure Control for Linear Multivariable Systems: The Output Feedback Case [PS (size: 547,563) / PDF (size: )]
  
  Abstract: This paper presents an observer-based discrete variable structure controller for linear multivariable systems with unmatched additive uncertainties, an extension of the results reported in Tang and Misawa (1998) to the output feedback case. It is shown that the incorporation of a prediction observer with uncertainty estimation into the controller guarantees the attractiveness and invariance of the estimated boundary layer, which is dynamic and parallel to the sliding hyperplane, after a transient. As in the state feedback case, linear control design strategies are applicable to the tracking error dynamics design inside the estimated boundary layer under an eigenvalue constraint. A numerical example is used to illustrate the proposed technique.
  
  
• ACL-98-009: Choon Yik Tang, Eduardo A. Misawa, On Discrete Variable Structure Control with Switching Sector [PS (size: 735,960) / PDF (size: )]
  
  Abstract:

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1999:

• ACL-1999-001: Brian D. O’Dell, Ellipsoidal and Semi-Ellipsoidal Controlled Invariant Sets for Constrained Linear Systems [PS (size: ) / PDF (size: )]
  
  Abstract:
  

2000:

2001:

• ACL-2001-001: Hanz Richter, Stability and Equilibria of Linear Control Systems Under Input and Measurement Quantization [PS (size: ) / PDF (size: 1,834,639)]
  
  Abstract: The problems of characterization of equilibria and stability analysis of a class of systems with quantization are treated in this work. System configurations considered include the main cases of open-loop stable linear plants under full state feedback, and under output feedback with dynamic compensation. The state feedback case is divided into sub-cases according to the type of quantization present in the system. The theoretical tools most predominatly used are those of Absolute Stability and Discrete Positive Real Theory. Standard results from these theories are expanded and modified to suit the needs of the
  particular problems. Standing assumptions include the open-loop stability of the plant and controller, in addition with properness conditions in specific cases.
  
  The sub-case of quantized input with precise state measurements, termed QI case, is amenable to explicit solution of the equilibrium equations. This knowledge is used in obtaining a necessary and sufficient condition for the origin to be the only equilibrium point. The stability problem in QI systems is analyzed directly using available tools of Absolute Stability and Discrete Positive Real theory. The main contribution to the stability analysis of QI systems is a parameterization of stabilizing feedback gains. For unstable continuous-time systems, a modified quantized feedback law is considered that can stabilize the system at the expense of chattering control. The equilibrium equations for the sub-case of quantization at the input and the state measurements, denoted QIQM, do not have a closed-form solution. A graphical construction is proposed that can be used in finding all equilibrium solutions of a QIQM system of arbitrary order. The stability problem cannot be directly analyzed using the standard tools of DPR theory or Absolute Stability. A system transformation is introduced that puts the system in a form similar to the Lur´e problem, where the sector nonlinearity is multiplicatively perturbed by a bounded function of the state. A result stating conditions for the stability of such systems is developed, and its use is not limited to systems with quantization. The stability analysis of QIQM systems culminates in a simple stability test in the frequency domain. The design problem in QIQM systems remains difficult, and only a method of gain scaling is presented. It is also shown that the parametric behavior of the system with
  respect to changes in gain scaling displays bifurcations. The sub-case of quantized input with precise output measurement and dynamic compensation, called QI0, reduces to its state-space counterpart, QI. The same is true for systems with no input quantization and quantized output feedback, termed IQO. The case of quantization at plant input and output, called QIQO, is more difficult to analyze. The equilibrium equations do not have a closed-form solution, thus only an upper bound on the number of solutions is given, along with a sufficient condition for the origin to be only equilibrim point is given. The stability analysis has been carried out by means of the Small Gain Theorem.
  
  
• ACL-2001-002: Hanz Richter and Eduardo A. Misawa, Stability and Equilibria of Discrete-time Linear Systems under Input and Measurement Quantization [PS (size: ) / PDF (size: 242,256)]
  
  Abstract: This article focuses on linear discrete-time systems controlled using a quantized input computed from quantized measurements. Nominally stabilizing, but otherwise arbitrary, state feedback gains may result in either limit cycling or nonzero equilibrium points. Although a single quantizer is a sector nonlinearity, the presence of a quantizer at each state measurement channel makes traditional Absolute Stability theory not applicable in a direct way. A global asymptotic stability condition is obtained by means of a result which allows to apply Discrete Positive Real theory to systems with a sector nonlinearity which is multiplicatively perturbed by a bounded function of the state. The stability result is readily applicable by evaluating the location of the polar plot of a system transfer function relative to a vertical line whose abcissa depends on the 1-norm of the feedback gain. A graphical method is also described that can be used to determine the equilibrium points of the closed-loop system for any given feedback gain.

2002:

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2003:

2004:

• ACL-2004-001: Hanz Richter and Eduardo A. Misawa, Boundary Layer Eigenvalues in SISO Discrete-Time Sliding Mode Control with Observer [PS (size: ) / PDF (size: 86,451 )]
  
  Abstract: A result that allows to specify the sliding manifold in Observer-Based Discrete-Time Sliding Mode Control is presented. Selection of coefficients is done by analyzing the tracking error dynamics inside the boundary layer, where the closed-loop system has a linear state feedback configuration, rather than
  assuming that ideal sliding occurs. The result facilitates assignment of eigenvalues for the system matrix which defines such linear dynamics.
  

2005:

2006:

• ACL-2006-001: Hanz Richter, Brian D. O’Dell and Eduardo A. Misawa, Robust Positively Invariant Cylinders in Constrained Variable Structure Control [PS (size:) / PDF (size: 254,866 )]
  
  Abstract: The paper proposes the use of cylinders as primary invariant sets to be used in certain stateconstrained control designs. Following the idea originally introduced by O’Dell, the primary invariant set is intersected with the state constraints to yield sets which retain the invariance under some conditions.
  Although several results presented here apply to fairly general nonlinear systems and primary invariant sets of any shape, the focus is on constrained sliding mode control using infinite cylinders as the primary invariant set. Their use is motivated by a coordinate transformation where the sliding motion is decoupled from the overall convergence to the origin. Robust positive invariance conditions are given for cylinders having convex and compact cross sections. For the case of cylinders with ellipsoidal cross sections, the invariance condition is given in the form of a linear matrix inequality. Further, a decision procedure to qualify each state constraint is given as a tool for the selection of the switching gain. A
  numerical example for a third-order plant illustrates the method.
  

2007:

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