Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThis paper derives new formulations for designing dominant pole placement based proportionalintegral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for pole placement in delay-free systems. The presence of the time delay term manifests itself as a higher order system with variable number of interlaced poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement control. We here report the analytical expressions to constrain the closed loop dominant and nondominant poles at the desired locations in the complex s-plane, using a third order Pade approximation for the delay term. However, invariance of the closed loop performance with different time delay approximation has also been verified using increasing order of Pade, representing a closed to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being complex, real or a combination of them modifies the characteristic equation and influences the achievable stability regions. The effect of different types of non-dominant poles and the corresponding stability regions are obtained for nine test-bench processes indicating different levels of open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider stability region in the design parameter space by using Monte Carlo simulations while uniformly sampling a chosen design parameter space. The accepted data-points from the stabilizing region in the design parameter space can then be mapped on to the PID controller parameter space, relating these two sets of parameters. The widest stability region is then used to find out the most robust solution which are investigated using an unsupervised data clustering algorithm yielding the optimal centroid location of the arbitrary shaped stability regions. Various time and frequency domain control performance parameters are investigated next, as well as their deviations with uncertain process parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of the nine test-bench processes. We also report, PID controller tuning rules for the robust stable solutions using the test-bench processes while also providing computational complexity analysis of the algorithm and carry out hypothesis testing for the distribution of sampled data-points for different classes of process dynamics and non-dominant pole types.KH acknowledges the support from the University Grants Commission (UGC), Govt. of India under its Basic Scientific Research (BSR) schem

Interactive Tool for Frequency Domain Tuning of PID Controllers

This paper presents an interactive tool focused on the study of proportional-integral-derivative (PID) controllers. Nowadays, PID control loops are extensively used in industrial applications. However, it is reported that many of them are badly tuned. From an educational point of view, it is essential for undergraduate students in control engineering to understand the importance of tuning a control loop correctly. For this reason, the tool provides different PID tuning methods in the frequency domain for stable open-loop time-delay-free processes. The different designs can be compared interactively by the user, allowing them to understand concepts about stability, robustness, and performance in PID control loops. A survey and a comparative study were performed to evaluate the effectiveness of the proposed tool

Complete stability region of PD controllers for TCP/AQM networks

"This paper addresses the stabilization problem of delay models of Transmission Control Protocol/Active Queue Management (TCP/AQM) by using a Proportional- Derivative (PD) controller as AQM strategy. The complete set of PD controllers that exponentially stabilizes the linearization is determined in counterpart with the existing works in the literature which only give an estimate of it. Additionally, a simple procedure for determining a non-fragile PD controller that admits controller coefficient perturbations is provided.

Comparison of analytical predictions of longitudinal short period pilot-induced oscillations with results from a simulation study of the space shuttle orbiter

An analytical analysis of conditions producing pilot induced oscillations (PIO's) was made for the space shuttle orbiter in a landing approach configuration for the task of milling the elevation angle of the line of sight to a target vehicle. The analysis yielded a value of PIO frequency and a value for the amount of total system time delay (pilot + control system) that can be tolerated before instability results. Calculations were performed showing the effect of varying the range to the target and of varying the handling qualities of the orbiter vehicle. Analytical predictions were compared with simulation results obtained using a visual motion simulator

Robot Impedance Control and Passivity Analysis with Inner Torque and Velocity Feedback Loops

Impedance control is a well-established technique to control interaction forces in robotics. However, real implementations of impedance control with an inner loop may suffer from several limitations. Although common practice in designing nested control systems is to maximize the bandwidth of the inner loop to improve tracking performance, it may not be the most suitable approach when a certain range of impedance parameters has to be rendered. In particular, it turns out that the viable range of stable stiffness and damping values can be strongly affected by the bandwidth of the inner control loops (e.g. a torque loop) as well as by the filtering and sampling frequency. This paper provides an extensive analysis on how these aspects influence the stability region of impedance parameters as well as the passivity of the system. This will be supported by both simulations and experimental data. Moreover, a methodology for designing joint impedance controllers based on an inner torque loop and a positive velocity feedback loop will be presented. The goal of the velocity feedback is to increase (given the constraints to preserve stability) the bandwidth of the torque loop without the need of a complex controller.Comment: 14 pages in Control Theory and Technology (2016

Robust PI control of interval plants with gain and phase margin specifications: Application to a continuous stirred tank reactor

The paper is focused on robust Proportional-Integral (PI) control of interval plants with gain and phase margin specifications and on the application of this approach to a Continuous Stirred Tank Reactor (CSTR). More specifically, the work aims at the determination of PI controller parameter regions, for which not only robust stability but also some level of robust performance of the closed-loop control system is guaranteed, and this robust performance is represented by the required gain and phase margin that has to be ensured for all potential members of the interval family of controlled plants, even for the worst case. The applied technique is based on the combination of the previously published generalization of stability boundary locus method (for specified gain and phase margin under the assumption of fixed-parameter plants) with the sixteen plant theorem. This extension enables the direct application of the method to design the robustly performing PI controllers for interval plants. The effectiveness of the improved method is demonstrated on a CSTR, modeled as the interval plant, for which the robust stability and robust performance regions are obtained. © 2013 IEEE.CEBIA-Tech Instrumentation Project through the European Regional Development Fund [CZ.1.05/2.1.00/19.0376]; National Sustainability Programme of Ministry of Education, Youth, and Sports, Czech Republic [LO1303 (MSMT-7778/2014)

Controller design for haptic systems under delayed position and velocity feedback

Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Sciences of Bilkent University, 2012.Thesis (Master's) -- Bilkent University, 2012.Includes bibliographical refences.This thesis considers controller design for haptic systems under delayed position and velocity feedback. More precisely, a complete stability analysis of a haptic system, where local dynamics are described by some second-order mechanical dynamics, is presented. Characteristic equation of this system with time delays involves quasipolynomials. By a change of variables in the characteristic equation, stability conditions are obtained analytically and regions are plotted by using Matlab. Next, using two optimization techniques (H∞ and stability margin optimization) optimal choice for the controller gains is proposed. H∞ optimization minimizes tracking error between devices while avoiding large control action inputs. H∞ analysis requires high computational cost for accurate results due to its dependency to frequency domain. On the other hand, stability margin optimization defines a cost function that expresses the trade-off between system bandwidth and robustness with low computational cost. The derived results are tested on a three degree of freedom real-time experimental platform to illustrate the theoretical results. Finally robustness analysis is performed for optimal parameters to find allowable delay perturbationsKoru, Ahmet TahaM.S