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- All Subjects: Robust control
- Creators: Berman, Spring
- Creators: Rodriguez, Armando A.
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
Wearable robotics is a growing sector in the robotics industry, they can increase the productivity of workers and soldiers and can restore some of the lost function to people with disabilities. Wearable robots should be comfortable, easy to use, and intuitive. Robust control methods are needed for wearable robots that assist periodic motion.
This dissertation studies a phase based oscillator constructed with a second order dynamic system and a forcing function based on the phase angle of the system. This produces a bounded control signal that can alter the damping and stiffens properties of the dynamic system. It is shown analytically and experimentally that it is stable and robust. It can handle perturbations remarkably well. The forcing function uses the states of the system to produces stable oscillations. Also, this work shows the use of the phase based oscillator in wearable robots to assist periodic human motion focusing on assisting the hip motion. One of the main problems to assist periodic motion properly is to determine the frequency of the signal. The phase oscillator eliminates this problem because the signal always has the correct frequency. The input requires the position and velocity of the system. Additionally, the simplicity of the controller allows for simple implementation.
This dissertation studies a phase based oscillator constructed with a second order dynamic system and a forcing function based on the phase angle of the system. This produces a bounded control signal that can alter the damping and stiffens properties of the dynamic system. It is shown analytically and experimentally that it is stable and robust. It can handle perturbations remarkably well. The forcing function uses the states of the system to produces stable oscillations. Also, this work shows the use of the phase based oscillator in wearable robots to assist periodic human motion focusing on assisting the hip motion. One of the main problems to assist periodic motion properly is to determine the frequency of the signal. The phase oscillator eliminates this problem because the signal always has the correct frequency. The input requires the position and velocity of the system. Additionally, the simplicity of the controller allows for simple implementation.
ContributorsDe la Fuente Valadez, Juan Oziel (Author) / Sugar, Thomas G. (Committee member) / Redkar, Sangram (Committee member) / Berman, Spring (Committee member) / Artemiadis, Panagiotis (Committee member) / Schroeder, Kyle A (Committee member) / Arizona State University (Publisher)
Created2016
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
Description
The introduction of assistive/autonomous features in cyber-physical systems, e.g., self-driving vehicles, have paved the way to a relatively new field of system analysis for safety-critical applications, along with the topic of controlling systems with performance and safety guarantees. The different works in this thesis explore and design methodologies that focus on the analysis of nonlinear dynamical systems via set-membership approximations, as well as the development of controllers and estimators that can give worst-case performance guarantees, especially when the sensor data containing information on system outputs is prone to data drops and delays. For analyzing the distinguishability of nonlinear systems, building upon the idea of set membership over-approximation of the nonlinear systems, a novel optimization-based method for multi-model affine abstraction (i.e., simultaneous set-membership over-approximation of multiple models) is designed. This work solves for the existence of set-membership over-approximations of a pair of different nonlinear models such that the different systems can be distinguished/discriminated within a guaranteed detection time under worst-case uncertainties and approximation errors. Specifically, by combining mesh-based affine abstraction methods with T-distinguishability analysis in the literature yields a bilevel bilinear optimization problem, whereby leveraging robust optimization techniques and a suitable change of variables result in a sufficient linear program that can obtain a tractable solution with T-distinguishability guarantees. Moreover, the thesis studied the designs of controllers and estimators with performance guarantees, and specifically, path-dependent feedback controllers and bounded-error estimators for time-varying affine systems are proposed that are subject to delayed observations or missing data. To model the delayed/missing data, two approaches are explored; a fixed-length language and an automaton-based model. Furthermore, controllers/estimators that satisfy the equalized recovery property (a weaker form of invariance with time-varying finite bounds) are synthesized whose feedback gains can be adapted based on the observed path, i.e., the history of observed data patterns up to the latest available time step. Finally, a robust kinodynamic motion planning algorithm is also developed with collision avoidance and probabilistic completeness guarantees. In particular, methods based on fixed and flexible invariant tubes are designed such that the planned motion/trajectories can reject bounded disturbances using noisy observations.
ContributorsHassaan, Syed Muhammad (Author) / Yong, Sze Zheng (Thesis advisor) / Rivera, Daniel (Committee member) / Marvi, Hamidreza (Committee member) / Lee, Hyunglae (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2023
Description
Soft robotics has garnered attention for its substantial prospective in various domains, such as manipulation and interactions with humans, by offering competitive advantages against rigid robotic systems, including inherent compliance and variable stiffness. Despite these benefits, their theoretically infinite degrees of freedom and prominent nonlinearities pose significant challenges in developing dynamic models and guiding the robots along desired paths. Additionally, soft robots may exhibit rigid behaviors and potentially collide with their surroundings during path tracking tasks, particularly when possible contact points are unknown. In this dissertation, reduced-order models are used to describe the behaviors of three different soft robot designs, including both linear parameter varying (LPV) and augmented rigid robot (ARR) models. While the reduced-order model captures the majority of the soft robot's dynamics, modeling uncertainties notably remain. Non-repeated modeling uncertainties are addressed by categorizing them as a lumped disturbance, employing two methodologies, $H_\infty$ method and nonlinear disturbance observer (NDOB) based sliding mode control, for its rejection. For repeated disturbances, an iterative learning control (ILC) with a P-type learning function is implemented to enhance trajectory tracking efficacy. Furthermore,for non-repeated disturbances, the NDOB facilitates the contact estimation, and its results are jointly used with a switching algorithm to modify the robot trajectories. The stability proof of all controllers and corresponding simulation and experimental results are provided. For a path tracking task of a soft robot with multi-segments, a robust control strategy that combines a LPV model with an innovative improved nonlinear disturbance observer-based adaptive sliding mode control (INASMC). The control framework employs a first-order LPV model for dynamic representation, leverages an improved disturbance observer for accurate disturbance forecasting, and utilizes adaptive sliding mode control to effectively counteract uncertainties. The tracking error under the proposed controller is proven to be asymptotically stable, and the controller's effectiveness is is validated with simulation and experimental results. Ultimately, this research mitigates the inherent uncertainty in soft robot modeling, thereby enhancing their functionality in contact-intensive tasks.
ContributorsQIAO, ZHI (Author) / Zhang, Wenlong (Thesis advisor) / Marvi, Hamidreza (Committee member) / Lee, Hyunglae (Committee member) / Berman, Spring (Committee member) / Sugar, Thomas (Committee member) / Arizona State University (Publisher)
Created2023