Matching Items (3)
Filtering by
- All Subjects: Robust control
- Creators: Rodriguez, Armando A.
- Creators: Korad, Akshay Shashikumar
Description
Proportional-Integral-Derivative (PID) controllers are a versatile category of controllers that are commonly used in the industry as control systems due to the ease of their implementation and low cost. One problem that continues to intrigue control designers is the matter of finding a good combination of the three parameters - P, I and D of these controllers so that system stability and optimum performance is achieved. Also, a certain amount of robustness to the process is expected from the PID controllers. In the past, many different methods for tuning PID parameters have been developed. Some notable techniques are the Ziegler-Nichols, Cohen-Coon, Astrom methods etc. For all these techniques, a simple limitation remained with the fact that for a particular system, there can be only one set of tuned parameters; i.e. there are no degrees of freedom involved to readjust the parameters for a given system to achieve, for instance, higher bandwidth. Another limitation in most cases is where a controller is designed in continuous time then converted into discrete-time for computer implementation. The drawback of this method is that some robustness due to phase and gain margin is lost in the process. In this work a method of tuning PID controllers using a loop-shaping approach has been developed where the bandwidth of the system can be chosen within an acceptable range. The loop-shaping is done against a Glover-McFarlane type ℋ∞ controller which is widely accepted as a robust control design method. The numerical computations are carried out entirely in discrete-time so there is no loss of robustness due to conversion and approximations near Nyquist frequencies. Some extra degrees of freedom owing to choice of bandwidth and capability of choosing loop-shapes are also involved and are discussed in detail. Finally, comparisons of this method against existing techniques for tuning PID controllers both in continuous and in discrete-time are shown. The results tell us that our design performs well for loop-shapes that are achievable through a PID controller.
ContributorsShafique, Md. Ashfaque Bin (Author) / Tsakalis, Konstantinos S. (Thesis advisor) / Rodriguez, Armando A. (Committee member) / Si, Jennie (Committee member) / Arizona State University (Publisher)
Created2011
Description
Corrective transmission topology control schemes are an essential part of grid operations and are used to improve the reliability of the grid as well as the operational efficiency. However, topology control schemes are frequently established based on the operator's past knowledge of the system as well as other ad-hoc methods. This research presents robust corrective topology control, which is a transmission switching methodology used for system reliability as well as to facilitate renewable integration.
This research presents three topology control (corrective transmission switching) methodologies along with the detailed formulation of robust corrective switching. The robust model can be solved off-line to suggest switching actions that can be used in a dynamic security assessment tool in real-time. The proposed robust topology control algorithm can also generate multiple corrective switching actions for a particular contingency. The solution obtained from the robust topology control algorithm is guaranteed to be feasible for the entire uncertainty set, i.e., a range of system operating states.
Furthermore, this research extends the benefits of robust corrective topology control to renewable resource integration. In recent years, the penetration of renewable resources in electrical power systems has increased. These renewable resources add more complexities to power system operations, due to their intermittent nature. This research presents robust corrective topology control as a congestion management tool to manage power flows and the associated renewable uncertainty. The proposed day-ahead method determines the maximum uncertainty in renewable resources in terms of do-not-exceed limits combined with corrective topology control. The results obtained from the topology control algorithm are tested for system stability and AC feasibility.
The scalability of do-not-exceed limits problem, from a smaller test case to a realistic test case, is also addressed in this research. The do-not-exceed limit problem is simplified by proposing a zonal do-not-exceed limit formulation over a detailed nodal do-not-exceed limit formulation. The simulation results show that the zonal approach is capable of addressing scalability of the do-not-exceed limit problem for a realistic test case.
This research presents three topology control (corrective transmission switching) methodologies along with the detailed formulation of robust corrective switching. The robust model can be solved off-line to suggest switching actions that can be used in a dynamic security assessment tool in real-time. The proposed robust topology control algorithm can also generate multiple corrective switching actions for a particular contingency. The solution obtained from the robust topology control algorithm is guaranteed to be feasible for the entire uncertainty set, i.e., a range of system operating states.
Furthermore, this research extends the benefits of robust corrective topology control to renewable resource integration. In recent years, the penetration of renewable resources in electrical power systems has increased. These renewable resources add more complexities to power system operations, due to their intermittent nature. This research presents robust corrective topology control as a congestion management tool to manage power flows and the associated renewable uncertainty. The proposed day-ahead method determines the maximum uncertainty in renewable resources in terms of do-not-exceed limits combined with corrective topology control. The results obtained from the topology control algorithm are tested for system stability and AC feasibility.
The scalability of do-not-exceed limits problem, from a smaller test case to a realistic test case, is also addressed in this research. The do-not-exceed limit problem is simplified by proposing a zonal do-not-exceed limit formulation over a detailed nodal do-not-exceed limit formulation. The simulation results show that the zonal approach is capable of addressing scalability of the do-not-exceed limit problem for a realistic test case.
ContributorsKorad, Akshay Shashikumar (Author) / Hedman, Kory W (Thesis advisor) / Ayyanar, Raja (Committee member) / Vittal, Vijay (Committee member) / Zhang, Muhong (Committee member) / Arizona State University (Publisher)
Created2015
Description
In this dissertation, we present a H-infinity based multivariable control design methodology that can be used to systematically address design specifications at distinct feedback loop-breaking points. It is well understood that for multivariable systems, obtaining good/acceptable closed loop properties at one loop-breaking point does not mean the same at another. This is especially true for multivariable systems that are ill-conditioned (having high condition number and/or relative gain array and/or scaled condition number). We analyze the tradeoffs involved in shaping closed loop properties at these distinct loop-breaking points and illustrate through examples the existence of pareto optimal points associated with them. Further, we study the limitations and tradeoffs associated with shaping the properties in the presence of right half plane poles/zeros, limited available bandwidth and peak time-domain constraints. To address the above tradeoffs, we present a methodology for designing multiobjective constrained H-infinity based controllers, called Generalized Mixed Sensitivity (GMS), to effectively and efficiently shape properties at distinct loop-breaking points. The methodology accommodates a broad class of convex frequency- and time-domain design specifications. This is accomplished by exploiting the Youla-Jabr-Bongiorno-Kucera parameterization that transforms the nonlinear problem in the controller to an affine one in the Youla et al. parameter. Basis parameters that result in efficient approximation (using lesser number of basis terms) of the infinite-dimensional parameter are studied. Three state-of-the-art subgradient-based non-differentiable constrained convex optimization solvers, namely Analytic Center Cutting Plane Method (ACCPM), Kelley's CPM and SolvOpt are implemented and compared.
The above approach is used to design controllers for and tradeoff between several control properties of longitudinal dynamics of 3-DOF Hypersonic vehicle model -– one that is unstable, non-minimum phase and possesses significant coupling between channels. A hierarchical inner-outer loop control architecture is used to exploit additional feedback information in order to significantly help in making reasonable tradeoffs between properties at distinct loop-breaking points. The methodology is shown to generate very good designs –- designs that would be difficult to obtain without our presented methodology. Critical control tradeoffs associated are studied and compared with other design methods (e.g., classically motivated, standard mixed sensitivity) to further illustrate its power and transparency.
The above approach is used to design controllers for and tradeoff between several control properties of longitudinal dynamics of 3-DOF Hypersonic vehicle model -– one that is unstable, non-minimum phase and possesses significant coupling between channels. A hierarchical inner-outer loop control architecture is used to exploit additional feedback information in order to significantly help in making reasonable tradeoffs between properties at distinct loop-breaking points. The methodology is shown to generate very good designs –- designs that would be difficult to obtain without our presented methodology. Critical control tradeoffs associated are studied and compared with other design methods (e.g., classically motivated, standard mixed sensitivity) to further illustrate its power and transparency.
ContributorsPuttannaiah, Karan (Author) / Rodriguez, Armando A. (Thesis advisor) / Berman, Spring M. (Committee member) / Mittelmann, Hans D. (Committee member) / Tsakalis, Konstantinos (Committee member) / Arizona State University (Publisher)
Created2018