טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentPriziment Vladislav
SubjectNovel Structures and Tunings of Optimal Dead Time
Compensators for Low Order Time Delay systems
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Emeritus Zalman Palmor


Abstract

Delays are widespread in a wide variety of systems, like engineering systems, physical systems, biological systems etc. The existence of such delays affects the performance of the systems and makes them difficult to control. A conventional method to control such systems is via the dead-time-compensator, purpose of which is to pull the delay out of the feedback loop. Two main structures of the dead-time-compensator are used commonly. One is the classical Smith predictor and the other one is the modified Smith predictor. Both consist of a rational primary controller and an infinite dimensional predictor. The Smith Predictor can cope with stable systems only while the Modified Smith Predictor can be applied to both, stable and unstable systems. A limited number and typically ad-hoc structures and tuning methods for the primary controllers in the regular Smith Predictor were suggested in the literature. However, neither structures of the primary controller nor tuning methods were suggested in the literature for the modified Smith predictor.

The first H 2 solutions for systems with delays, developed about fifty years ago, were complicated and the structure of the resulting controllers wasn’t explicitly understood. Later on, analytical methods that justified the usage of the Smith predictor were developed. Just recently, the development of the “Loop Shifting” technique revealed that it is possible to convert a problem with a delay to an equivalent delay-free one. Consequently, it was found that the optimal controllers consist of a rational primary controller connected via feedback to a Modified Smith Predictor.

H 2 optimization minimizes the energy of the systems for impulse inputs. Such inputs do not represent adequately the engineering performance requirements which are typically represented by the responses to step inputs. To modify the problem to cope with more realistic requirements, the generalized plants should be expanded by including unstable dynamical weights.

In this work, H 2 optimal controllers with engineering-oriented performance criteria for low order processes with delays and for both command following as well as disturbance attenuation were derived and their properties investigated. It was concluded that in most cases, only two controller parameters are required to be tuned for first-order systems and three tuning parameters for second-order systems. Furthermore, there are cases where just one parameter is required for the optimal tuning.

One of the disadvantages of the H 2 optimization is that it does not guarantee any stability margins. To this end, an easy tuning tool, which is based on the H 2 optimization, has been developed. This tool deploys the closed-loop stability properties into simple graphs, and links between the closed-loop margins, and the primary controller's optimal parameters. As a result, an optimal controller can be obtained easily from the tuning graphs, with a full closed-loop stability indication, and without the need of performing the whole optimization machinery each time.

Nonetheless, it was also noted that unstable plants, with a relatively significant delay, have a narrow range of possible optimal performance and their robustness is barely satisfying. Hence in this circumstance, these controllers are not recommended for practical usage.