Robust and Optimal PID Controller Synthesis for Linear Time Invariant Systems

We dealt with new approaches to the design of Proportional-Integral-Derivative (PID) controllers and solved three important open problems: 1) Optimal design of H∞ continuous time controllers 2) Optimal design of H∞ discrete time controllers and 3) Design of PID controllers for prescribed settling time. We also deal with optimal Dynamic Compensator design for controllable and observable systems. The main result of the first problem is a constructive determination of the set Sγ of stabilizing continuous PI and PID controllers achieving an H∞ norm bound of γ on the error transfer function. This result utilizes the computation of the complete stabilizing set S. We also point out connections between this H∞ design and Gain and Phase Margin designs. The main result of the second problem is a constructive characterization of the set Sγ of stabilizing digital controllers achieving a prescribed bound γ on the error transfer function. This is accomplished by utilizing the computation of S, the set of all PID stabilizing controllers. The minimum achievable γ, denoted γ∗ is also determined. The main result of the third problem is a constructive determination of the set S(σ) of stabilizing PI and PID controllers with closed loop poles having real parts less than −σ. The signature method is applied to obtain the set S(σ) in the controller parameter space. The maximum achievable σ for a given plant is also determined. The main result of the last problem is a new approach to design an optimal dynamic compensator. The system is augmented with a proper number of integrators and the state feedback of the augmented system is considered with a design parameter. The dynamic compensator is then designed such that the eigenvalues of the augmented system is identical to the closed loop specboundtrum of the implemented system with the compensator. By sweeping over the design parameter, multiple design specifications are compared within achievable boundary of performances

Robust and Optimal PID Controller Synthesis for Linear Time Invariant Systems

We dealt with new approaches to the design of Proportional-Integral-Derivative (PID) controllers and solved three important open problems: 1) Optimal design of H∞ continuous time controllers 2) Optimal design of H∞ discrete time controllers and 3) Design of PID controllers for prescribed settling time. We also deal with optimal Dynamic Compensator design for controllable and observable systems. The main result of the first problem is a constructive determination of the set Sγ of stabilizing continuous PI and PID controllers achieving an H∞ norm bound of γ on the error transfer function. This result utilizes the computation of the complete stabilizing set S. We also point out connections between this H∞ design and Gain and Phase Margin designs. The main result of the second problem is a constructive characterization of the set Sγ of stabilizing digital controllers achieving a prescribed bound γ on the error transfer function. This is accomplished by utilizing the computation of S, the set of all PID stabilizing controllers. The minimum achievable γ, denoted γ∗ is also determined. The main result of the third problem is a constructive determination of the set S(σ) of stabilizing PI and PID controllers with closed loop poles having real parts less than −σ. The signature method is applied to obtain the set S(σ) in the controller parameter space. The maximum achievable σ for a given plant is also determined. The main result of the last problem is a new approach to design an optimal dynamic compensator. The system is augmented with a proper number of integrators and the state feedback of the augmented system is considered with a design parameter. The dynamic compensator is then designed such that the eigenvalues of the augmented system is identical to the closed loop specboundtrum of the implemented system with the compensator. By sweeping over the design parameter, multiple design specifications are compared within achievable boundary of performances

A graphical tuning method for fractional order controllers based on iso-slope phase curves

Fractional order controllers are widely used in the robust control field. As a generalization of the ubiquitous PID controllers, fractional order controllers are able to reach design specifications their integer counterparts cannot, and as a result they outperform them at particular situations. Their main drawback is that generalization of the design tools is not always evident, and therefore tuning this kind of controller is always a new and different challenge. Existing methods often use numerical computation to find the controller parameters that fit the specifications. This paper describes a graphical solution for fractional order controllers, which avoids the solution by nonlinear equations and helps designer to solve the control problem in a very intuitive way. This approach is tested in the servomotors of a real bio-inspired soft neck and results are compared with those obtained from other control strategies. The experiments show that the controller tuned by this method works as expected from a robust controller and that this approach is very competitive compared to other state of the art methods, while offering a more simplified and direct tuning process.Research leading to these results has received funding from HUMASOFT project, with reference DPI2016-75330-P, funded by the Spanish Ministry of Economy and Competitiveness, and from RoboCity2030-DIH-CM Madrid Robotics Digital Innovation Hub, S2018/NMT-4331, funded by "Programas de Actividades I+D en la Comunidad de Madrid" and cofunded by Structural Funds of the EU

Self-tuning run-time reconfigurable PID controller

Digital PID control algorithm is one of the most commonly used algorithms in the control systems area. This algorithm is very well known, it is simple, easily implementable in the computer control systems and most of all its operation is very predictable. Thus PID control has got well known impact on the control system behavior. However, in its simple form the controller have no reconfiguration support. In a case of the controlled system substantial changes (or the whole control environment, in the wider aspect, for example if the disturbances characteristics would change) it is not possible to make the PID controller robust enough. In this paper a new structure of digital PID controller is proposed, where the policy-based computing is used to equip the controller with the ability to adjust it's behavior according to the environmental changes. Application to the electro-oil evaporator which is a part of distillation installation is used to show the new controller structure in operation

A comparative study of several control techniques applied to a boost converter

In this paper a comparison among three control strategies is presented, with application to a boost DC-DC converter. The control strategies are developed on the switched boost circuit model and validated on the nonlinear model by use of simulations. The classical PID, a 2dof-IMC (two degree of freedom internal model controller) and an alternative controller - MAC (uprocessor advanced control) are applied, tested and compared on the nonlinear system. Additional tests show the robustness of the controllers on the highly nonlinear circuit

Reinforcement Learning for UAV Attitude Control

Autopilot systems are typically composed of an "inner loop" providing stability and control, while an "outer loop" is responsible for mission-level objectives, e.g. way-point navigation. Autopilot systems for UAVs are predominately implemented using Proportional, Integral Derivative (PID) control systems, which have demonstrated exceptional performance in stable environments. However more sophisticated control is required to operate in unpredictable, and harsh environments. Intelligent flight control systems is an active area of research addressing limitations of PID control most recently through the use of reinforcement learning (RL) which has had success in other applications such as robotics. However previous work has focused primarily on using RL at the mission-level controller. In this work, we investigate the performance and accuracy of the inner control loop providing attitude control when using intelligent flight control systems trained with the state-of-the-art RL algorithms, Deep Deterministic Gradient Policy (DDGP), Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO). To investigate these unknowns we first developed an open-source high-fidelity simulation environment to train a flight controller attitude control of a quadrotor through RL. We then use our environment to compare their performance to that of a PID controller to identify if using RL is appropriate in high-precision, time-critical flight control.Comment: 13 pages, 9 figure

PID control system analysis, design, and technology

Designing and tuning a proportional-integral-derivative (PID) controller appears to be conceptually intuitive, but can be hard in practice, if multiple (and often conflicting) objectives such as short transient and high stability are to be achieved. Usually, initial designs obtained by all means need to be adjusted repeatedly through computer simulations until the closed-loop system performs or compromises as desired. This stimulates the development of "intelligent" tools that can assist engineers to achieve the best overall PID control for the entire operating envelope. This development has further led to the incorporation of some advanced tuning algorithms into PID hardware modules. Corresponding to these developments, this paper presents a modern overview of functionalities and tuning methods in patents, software packages and commercial hardware modules. It is seen that many PID variants have been developed in order to improve transient performance, but standardising and modularising PID control are desired, although challenging. The inclusion of system identification and "intelligent" techniques in software based PID systems helps automate the entire design and tuning process to a useful degree. This should also assist future development of "plug-and-play" PID controllers that are widely applicable and can be set up easily and operate optimally for enhanced productivity, improved quality and reduced maintenance requirements

Development of a MATLAB/Simulink - Arduino environment for experimental practices in control engineering teaching

This project presents the steps followed when implementing a platform based on MATLAB/Simulink and Arduino for the restoration of digital control practices. During this project, an Arduino shield has being designed. Along with this, a web page has also been created where all the material done during all this project is available and can be freely used. So anyone interested on doing a project can have a starting point instead of starting a project from scratch, which most of times this results hard to implement. Taking all this into account, the document is structured in the following manner. The first chapter talks about the hardware used and designed. The second one explains the software used and the configurations done on the laboratory’s PCs. After that, the web page Duino-Based Learning is explained, where you can find the five projects carried out in the "Control Automàtic" subject with their corresponding results. In this section too, as an additional research, the implemented indirect adaptive control will be explained, where the parameter estimation has been done by the Recursive Least Square algorithm. The last four sections before presenting the conclusions of the work, correspond to a satisfaction questionnaire done to the teachers that have used the setup, the costs and saves of the project, the environmental impact and the planning of the project respectively