Downloads & Free Reading Options - Results

This thesis discusses application of a robust constrained optimization approach to control design to develop an Auto Balancing Controller (ABC) for a centrifuge rotor to be implemented on the International Space Station. The design goal is to minimize a performance objective of the system, while guaranteeing stability and proper performance for a range of uncertain plants. The Performance objective is to minimize the translational response of the centrifuge rotor due to a fixed worst-case rotor imbalance. The robustness constraints are posed with respect to parametric uncertainty in the plant. The proposed approach to control design allows for both of these objectives to be handled within the framework of constrained optimization. The resulting controller achieves acceptable performance and robustness characteristics.

In this research project, we have made significant progress in several fronts of modem control technology. Our major research results include: new model identification and validation techniques, new model uncertainty and robustness characterization methods using probabilistic approach, randomized control analysis and design methods, some advanced nonlinear control techniques including bifurcation stabilization and compressor stabilization techniques, model reduction techniques, fault detection and fault tolerant control methods, and several robust stability analysis algorithms.

In this paper, a new polynomial chaos based framework for analyzing linear systems with probabilistic parameters is presented. Stability analysis and synthesis of optimal quadratically stabilizing controllers for such systems are presented as convex optimization problems, with exponential mean square stability guarantees. A Monte-Carlo approach for analysis and synthesis is also presented, which is used to benchmark the polynomial chaos based approach. The computational advantage of the polynomial chaos approach is shown with an example based on the design of an optimal EMS-stabilizing controller, for an F-16 aircraft model.

A representation of controllable linear systems is introduced, which permits assigning poles or characteristic parameters to a state feedback system by a matrix multiplication. This is used as a link between state space and classical parameter plane methods. The system representation maps a point in a nxp dimensional parameter space of characteristic parameters into the nxp dimensional parameter space of state feedback gains, where p is the number of actuators. For p counts one the coordinates of the characteristic parameter space are the coefficients of the closed loop characteristic polynomial, for p greater than one they are coefficients in a characteristic polynomial matrix and its determinant is the characteristic polynomial. By this computationally simple mapping procedure it becomes feasible to map not only a fixed set of eigenvalues but also regions in the s or z plane, in which the eigenvalues shall be located. This relaxation of the dynamic specifications permits satisfying other typical design specifications like robustness with respect to sensor and actuator failures, large parameter variations, finite word length implementation, and actuator constraints. All tradeoffs between such requirements can be made in the feedback gain space. Three examples illustrate the variety of problems which can be tackled with this new tool. (Author)

Trade offs between stability margin and performance are considered in two and three degree of freedom multivariable control systems using a Wiener Hopf design approach. Maximum improvement in an approximate measure of stability margin is achieved at the expense of a prescribed increase in the quadratic cost functional measuring system performance. In order to attain an analytical solution to this fundamental trade off problem, the approximate measure of stability margin chosen is also a quadratic cost function. A novel approach is introduced which allows structured perturbations in the coprime polynomial matrix fraction description of the plant transfer matrix to be taken into account. As a consequence, it is believed that the use of an approximate measure of stability margin is mitigated. Moreover, if needed, the solution obtained could serve as a very good initial one from which to search for better solutions iteratively. The aforementioned control design methodology was implemented on the available testbeds for advanced weapon pointing systems at the Picatinny Army Arsenal in New Jersey.

Rotorcraft flight control systems present design challenges which often exceed those associated with fixed-wing aircraft. First, large variations in the response characteristics of the rotorcraft result from the wide range of airspeeds of typical operation (hover to over 100 kts). Second, the assumption of vehicle rigidity often employed in the design of fixed-wing flight control systems is rarely justified in rotorcraft where rotor degrees of freedom can have a significant impact on the system performance and stability. This research was intended to develop a methodology for the design of robust rotorcraft flight control systems. Quantitative Feedback Theory (QFT) was chosen as the basis for the investigation. Quantitative Feedback Theory is a technique which accounts for variability in the dynamic response of the controlled element in the design robust control systems. It was developed to address a Multiple-Input Single-Output (MISO) design problem, and utilizes two degrees of freedom to satisfy the design criteria. Two techniques were examined for extending the QFT MISO technique to the design of a Multiple-Input-Multiple-Output (MIMO) flight control system (FCS) for a UH-60 Black Hawk Helicopter. In the first, a set of MISO systems, mathematically equivalent to the MIMO system, was determined. QFT was applied to each member of the set simultaneously. In the second, the same set of equivalent MISO systems were analyzed sequentially, with closed loop response information from each loop utilized in subsequent MISO designs. The results of each technique were compared, and the advantages of the second, termed Sequential Loop Closure, were clearly evident.

The long-range goal of this research program is to form a new system identification paradigm that fulfills all the requirements of robust control design, i.e., to produce from finite measured data a model which includes descriptors for both dynamic and disturbance uncertainty. Several directions were pursued during the reporting period: (1) least-squares related approaches (2) 'windsurfer' (learning) adaptation, and (3) uncertainty model unfalsification. The latter, together with some of the ideas in 'windsurfer' adaptation, marks a significant advance towards attaining the program objectives. The new idea is to replace identification of a single (transfer function) model with unfalsification of a family of uncertainty models and then to design a corresponding family of robust controllers to be tested on the actual system. (Both dynamic and noise uncertainty parameters are estimated along with the nominal transfer function).

Rotorcraft flight control systems present design challenges which often exceed those associated with fixed-wing aircraft. First, large variations in the response characteristics of the rotorcraft result from the wide range of airspeeds of typical operation (hover to over 100 kts). Second, the assumption of vehicle rigidity often employed in the design of fixed-wing flight control systems is rarely justified in rotorcraft where rotor degrees of freedom can have a significant impact on the system performance and stability. This research was intended to develop a methodology for the design of robust rotorcraft flight control systems. Quantitative Feedback Theory (QFT) was chosen as the basis for the investigation. Quantitative Feedback Theory is a technique which accounts for variability in the dynamic response of the controlled element in the design robust control systems. It was developed to address a Multiple-Input Single-Output (MISO) design problem, and utilizes two degrees of freedom to satisfy the design criteria. Two techniques were examined for extending the QFT MISO technique to the design of a Multiple-Input-Multiple-Output (MIMO) flight control system (FCS) for a UH-60 Black Hawk Helicopter. In the first, a set of MISO systems, mathematically equivalent to the MIMO system, was determined. QFT was applied to each member of the set simultaneously. In the second, the same set of equivalent MISO systems were analyzed sequentially, with closed loop response information from each loop utilized in subsequent MISO designs. The results of each technique were compared, and the advantages of the second, termed Sequential Loop Closure, were clearly evident.

The complexity of large-scale dynamic systems provides a challenging proving ground for modern control system analysis and design techniques. High plant dimensionality inherent in large-scale systems can lead to breakdowns in numerics of state-space algorithms or intolerably long computational times, necessitating use of model reduction techniques. Reducing plant order consequently introduces unmodeled dynamics into the system, which must then be accounted for via stability and performance robustness considerations. A design framework is adopted herein which allows stability robustness to be guaranteed via unstructured uncertainty representation and the Small Gain Theorem, and performance robustness to be independently verified. The applicability of modern multivariable controller design techniques to large-scale systems is demonstrated by synthesis of robustly stable H2 optimal, H at infinity optimal, and H2/H at infinity loop-shaped compensators for a space-based laser forebody using reduced order models. Performance goals are expressed in terms of both allowable 2-norms and root-mean-square valves of line-of-sight and segment phasing errors, and an evolutionary process leads to a final controller design. First, ideally performing but non-robust unconstrained bandwidth H2 and H at infinity designs are presented which illustrate the danger of ignoring unmodeled high-frequency dynamics. Then robustly stable but poorly performing reduced bandwidth H2 and H at infinity designs are derived, achieved via constant penalizing of the system control at all frequencies.

This thesis applied modern, multi-variable control design techniques, via a FORTRAN computer algorithm, to U.S. Army helicopter models in hovering flight conditions. Eigenstructure assignment and Linear Quadratic Regulator (LQR) theory are used to achieve enhanced closed loop performance and stability characteristics with full state feedback. The addition of cross coupling weights to the standard LQR performance index is specifically addressed. A desired eigenstructure is chosen with a goal of reduced pilot workload via performance qualities requirements. Cross coupling weighting is shown to provide greater flexibility in achieving a desired closed loop eigenstructure. While the addition of cross coupling weighting is shown to eliminate stability margin guarantees associated with LQR methods, the modified algorithm can achieve a closer match to a desired eigenstructure than previous versions of the program while maintaining acceptable stability characteristics.

The importance of designing control systems which are robust or insensitive to variations in the plant parameters has long been appreciated. However, the rapid advances in design techniques for multivariable systems has heightened interest in the study and design of robust systems. The purpose of this report is to provide an up to date survey of the work in this field and summarize the results of research in this area conducted at the Coordinated Science Laboratory. The report begins in Chapter 2 with a description and examples of the robust control problem. Chapter 3 provides a survey of research in the field of robust control. It is apparent from this survey that the work can be divided into two areas. The first assumes unstructured perturbations and analyzes worst case effects. The second considers large, structured perturbations. The parameter space design method presented in Chapter 4 is directed at the second area. The tools of Chapter 4 are applied to a fighter aircraft example in Chapter 5. Chapter 6 presents an optimization approach to the same problem. Finally, Chapter 7 summarizes the report and presents several directions for future research. (Author)

In the design and analysis of robust control systems for uncertain plants, the technique of formulating what is termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents the transfer function matrix M(s) of the nominal system, and delta represents an uncertainty matrix acting on M(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unstructured uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, and for real parameter variations the diagonal elements are real. As stated in the literature, this structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the literature addresses methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty. Since have a delta matrix of minimum order would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta model would be useful. A generalized method of obtaining a minimal M-delta structure for systems with real parameter variations is given.

Classical stability analysis consists of breaking the feedback loops one at a time and determining separately how much gain or phase variations would destabilize the stable nominal feedback system. For typical launch vehicle control design, classical control techniques are generally employed. In addition to stability margins, frequency domain Monte Carlo methods are used to evaluate the robustness of the design. However, such techniques were developed for Single-Input-Single-Output (SISO) systems and do not take into consideration the off-diagonal terms in the transfer function matrix of Multi-Input-Multi-Output (MIMO) systems. Robust stability analysis techniques such as H(sub infinity) and mu are applicable to MIMO systems but have not been adopted as standard practices within the launch vehicle controls community. This paper took advantage of a simple singular-value-based MIMO stability margin evaluation method based on work done by Mukhopadhyay and Newsom and applied it to the SLS high-fidelity dynamics model. The method computes a simultaneous multi-loop gain and phase margin that could be related back to classical margins. The results presented in this paper suggest that for the SLS system, traditional SISO stability margins are similar to the MIMO margins. This additional level of verification provides confidence in the robustness of the control design.

The analysis and design of robust controllers for multivariable discrete-time feedback systems in the frequency domain are studied. The robustness stability conditions for discrete-time systems with additive alteration, and with multiplicative alteration are developed. The robust LQG/LTR method has been extended from the continuous-time system to the discrete-time system. It has been proven that the LQG/LTR method is also valid for the LQG control of the discrete-time system with the filtering observer. As an application of the LQG/LTR technique for discrete-time systems, the design of reduced order optimal digital LQG controllers for the orbiting flexible shallow spherical shell system is considered. The comparison between the digital optimal LQG controller with the filtering observer and with the predicting observer for the orbiting flexible shallow spherical shell has been made.... Digital control, Large space structures, LQG/LTR method for discrete-time system, Robust controller design, Design of reduced order LQG controller.

A multiple input-multiple output flight control design on the KC-135 aircraft is completed using Quantitative Feedback Theory (QFT). The three degrees-of-freedom model for the lateral mode is reduced to a two degrees-of- freedom model. From this model a robust controller is developed to perform two maneuvers over a wide range of the aircraft flight envelope. The three degrees- of-freedom for the longitudinal mode is then used to develop a robust controller to perform one maneuver. The first and second body bending modes are then added to remove the rigid bosy constraint and a robust control is developed for the non-rigid aircraft. The robust controllers developed for the lateral and longitudinal modes are simulated over a large range of the aircraft's flight envelope. The conclusion drawn from the research is that this method is very effective in designing multiple input-multiple output systems with plant uncertainty. Keywords: Multivariable control, Flight control, Laternal controllers, Longitudinal controllers, Uncertain plants, and Robustness.

This research was concerned with the robust optimal control of systems subjected to structured uncertainty. The design objective was to minimize the induced system norm (i.e. maximum gain) in the cases of l2/L2 and l(inf)/L(inf) inputs. Major results were obtained in the case of linear discrete-time systems with nonlinear/time-varying uncertainty and for continuous systems controlled by digital computers (sampled-data systems). The sampled-data results are now a part of the MATLAB u-tools toolbox and the structured uncertainty results for discrete-time systems has led to an efficient 'D-K-type' synthesis procedure for minimizing the l(inf) induced system norm. (AN)

This thesis discusses application of a robust constrained optimization approach to control design to develop an Auto Balancing Controller (ABC) for a centrifuge rotor to be implemented on the International Space Station. The design goal is to minimize a performance objective of the system, while guaranteeing stability and proper performance for a range of uncertain plants. The performance objective is to minimize the translational response of the centrifuge rotor due to a fixed worst-case rotor imbalance. The robustness constraints are posed with respect to parametric uncertainty in the plant. The proposed approach to control design allows for both of these objectives to be handled within the framework of constrained optimization. The resulting controller achieves acceptable performance and robustness characteristics.

Abstract: This paper provides further advancement of the D-Partitioning analysis applied to nonlinear digital control system with variable parameters. As a case study, a nonlinear control system for accurate speed control of a dc motor is considered. The Bilinear Tustin Transform method is employed as one of the most precise facilities for systems discretization, where also the Euler's approximation is taken into account. A robust controller design is accomplished by a number of successive steps. Based on the difference equations of its stages, the robust controller can be realized by microcontrollers. The research is a further development of the author’s work on the D-Partitioning analysis and design of nonlinear digital control systems with variable parameters. The suggested tool for analysis is essential and beneficial for the further development of control theory in this area. Keywords: Wheatstone Speed-to-Voltage Converter, Speed Control, Nonlinear, Bilinear approximation, Discretization, D-Partitioning Stability Analysis, Digital Control Systems; http://www.icgst.com/paper.aspx?pid=P1111610484 @ARTICLE { P1111610484, author= "Prof. Kamen M. Yanev", title= "Design and Analysis of a Robust Accurate Speed Control System by Applying a Digital Compensator", journal= "Automatic Control and System Engineering  ACSE", year= "2016", month= "4", volume= "16", number= "1", pages= "27--36" }

This paper is interested to study power system stability in smart grid power system using wind characteristic in south of Yogyakarta, Indonesia. To overcome the intermittent of wind characteristics, this paper presents adaptive robust control design to enhance power system stabilization. The online identification system is used in this research, which updated whenever the estimated model mismatch exceeds predetermined bounds. Then genetic algorithm (GA) is applied to re-tune parameters controller based on the estimated model. The structure of controller is proportional integral (PI) controller due to the most applicable in industry, simple structure, low cost and high reliability. Robustness of controller is guaranteed by taking system uncertainties into consideration. The performance of the proposed controller has been carried out in a hybrid wind-diesel power system in comparison with previous work controller. Simulation results confirm that damping effect of the proposed controllers are much better that of the conventional controllers against various operating.