Frank Schrödel

Lyapunov stability bounds in the controller parameter space

A novel Lyapunov stability based method for the parameter space design of linear time invariant control systems is proposed in this paper. The basic idea lies in utilizing the Lyapunov equation as the basic vehicle for mapping the stability bounds into the control parameter space. In comparison to the existing parameter space methods in the literature, the new technique provides two computationally critical advantages. First, it avoids the necessity for the frequency gridding which has been almost traditional and a source of an inherent computational complexity. Second, the proposed design method provides directly the bounds in the multi-dimensional control parameter space, thereby dropping the limitation of most related design techniques that take place on a parameter plane. The usage of the proposed method is demonstrated in the prominent case study of a PID control.

PIDrobust Toolbox - Performance Tuning for PID Controlled Time Delay Systems with Parameter Uncertainties

Abstract Most of the PID controller tuning rules for time delay LTI systems existing today use only time delay approximations and ignore parameter uncertainties in the modeled system. This article presents a toolbox for parameter optimization and loop shaping for PID parameter tuning with explicit consideration of the time delay and the parameter uncertainties of the system. In addition a root locus method for time delay systems is implemented. All tuning methods use the nominal model to formulate the performance requirements. During the subsequent optimization, the parameter uncertainties are included through limitation of the PID parameter space. This parameter space is calculated by the parameter space approach and serves as the basis of the presented tuning methods. Hence, all tuning methods guarantee robust stability.

Parameter space approach based state feedback control of LTV systems

The calculation of all stabilizing controller parameters with the parameter space approach is a well-known method. Based on the determined stabilizing parameter space, there exist various analysis and fine-tuning tools for the design of controllers. Unfortunately, only for PID controller (of LTI systems) the parameter space approach is developed and implemented systematically now a days. This work expands the syntheses step of the classical parameter space approach to the LTV system class. It is realized by using a transformation method to bring a LTV system into a LTI system description as well as a frozen time eigenvalue based method. Therefore, this paper presents an overview of the parameter space method to design LTI state feedback controllers. After that, a short survey of LTV stability analyse methods and the transformation based method to extend the parameter space approach to LTV is given.

An approach for calculating all stable PID parameters for time delay systems with uncertain parameters

Abstract There exists a large number of PID tuning rules for LTI systems. However, these rules often use time delay approximations and ignore parameter uncertainties. This work updates the classical parameter space approach to an one step PID tuning approach to guarantee robust stability for LTI time delay systems with explicit consideration of uncertainties in the plant parameters and the time delay. The basic idea is to calculate how the root boundaries changes due variation of system parameters. Bands of root boundaries are determined by this analysis. The challenging task of robust stability of time delay systems is converted to an easier minimum/maximum search to estimate the borders of the root boundary bands. The presented method satisfies robust stability with only small conservatism.

Lyapunov stability bounds mapping for descriptor and switching systems

Calculating the stabilising parameter space of descriptor and switching systems is non-trivial. In this paper a new approach for the stability region calculation for descriptor and switching systems is presented by using a Lyapunov stability mapping method. This method has several advantages over the existing parameter space approaches. Currently, the calculation of the complex root boundaries relies on frequency sweeping or decoupling at singular frequencies. The new proposed method avoids this while reducing the computational complexity and increasing the practicality of the method at the same time.

Expanding the parameter space approach to multi loop control with multi time delays

The calculation of all stabilizing controller parameters with the parameter space approach is a well-known method. Based on the determined stabilizing parameter space, there exist various analysis and fine-tuning tools for controller design. Unfortunately, the parameter space approach is currently only systematically developed and implemented for the PID controller tuning. This work presents an easy way to expand the syntheses step of the classical parameter space approach to time delay multi loop control loops. The paper illustrates a method for determining controller parameter space boundaries (RRB, IRB and CRB) analogously to the classical PID controller parameter space approach. A major advantage of the proposed method is the great transparency and simplicity.

Parameter space mapping for linear discrete-time systems with parametric uncertainties

Many Parameter Space Approach (PSA) based methods have been proposed previously to determine the stabilizing controller parameter spaces for discrete-time systems. The PSA approach is based on sweeping over the whole range of singular frequencies which leads to an expensive numerical computation to find the boundaries of the stability region. These PSA based methods were used for obtaining the stability boundaries for parameter uncertain discrete-time systems as well. However, this results in extremely high computational complexity in addition to other drawbacks. In this study, an approach to determine the stabilizing controller parameter regions of linear discrete-time systems with uncertain parameters is proposed. This novel procedure makes use of the Strong Kharitonov theorem for getting over the high computational complexity resulted due to the uncertainty of the system. Moreover, the asserted approach utilizes a novel Lyapunov based mapping technique for avoiding the drawbacks accompanied with the previously presented PSA based methods in literature. Two different case studies are included in the paper to illustrate the advantages and effectiveness of the proposed method.

Parameter space approach based robust MIMO controller tuning for a vacuum thermal evaporation process

The parameter space approach method for stability chart calculation is a well-known method. There are various analysis and fine-tuning tools available for controller design which are based on the determined stabilizing controller parameter space. Unfortunately the parameter space approach is currently only systematically developed and implemented for single loop PID controller tuning. This work presents an easy way (based on decoupling techniques) to expand the synthesis step of the classical parameter space approach to MIMO systems (with multiple time delay). The developed method is illustrated on the application example of a vacuum thermal evaporation process (VTA). Regarding this example, the presented approach is used to tune the parameters of the internal PID heat controllers. The VTA-process is characterized in detail before the controller design starts. Furthermore a physical model which describes the heat transfer in the process is obtained.

Improvement of Practical Orientation in Teaching by Introduction of an Innovative Laboratory and Competition

Abstract In this paper, an innovative concept for a laboratory and a student competition for the improvement of practical orientation of control engineering teaching are presented. The overall goals of the new teaching concepts are to consolidate the students control theory knowledge, to establish practical relevance of the lectures, to gain experience and to develop creativity as well as team-working skills. A laboratory is planned as an introduction to automatic control for students with no engineering background. The goal is to give the students a practical and basic overview of control theory. In addition, a student contest is introduced, which is focused on autonomous vehicle control problems such as path following and advanced cruise control.

Parameter space approach for large scale systems

The computational costs of the parameter space approach, which is used to calculate the stability boundaries for linear time-invariant systems (LTI), increase fast with the dimension of the investigated system. In this paper, the authors present a successive approximation of the stability boundaries for large scale systems. The approximation provides a fast and accurate estimation of the stability boundaries. Furthermore, the approximation converges to the stability boundaries of the large scale system and points, that are not stable, are never classified as stable during approximation. Thus, the new method enables the applicability of the parameter space approach to large scale systems by greatly reducing the computational costs.