Polynomial control design for polynomial systems: A non-iterative sum of squares approach

2018 ◽  
Vol 41 (7) ◽  
pp. 1993-2004
Author(s):  
Mohsen Rakhshan ◽  
Navid Vafamand ◽  
Mohammad Mehdi Mardani ◽  
Mohammad-Hassan Khooban ◽  
Tomislav Dragičević
Keyword(s):  
Controller Design ◽  
Time Derivative ◽  
Polynomial Systems ◽  
Sum Of Squares ◽  
Continuous Stirred Tank Reactor ◽  
Wide Range ◽  
Convex Problem ◽  
Lyapunov Matrix ◽  
Different Chaotic Systems ◽  
Real Time Simulations

This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum of squares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound on the time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computed through semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a wide range of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tank reactor, and power permanent magnet synchronous machine. Finally, software-in-the-loop (SiL) real-time simulations are presented to prove the practical application of the proposed approach.

scholarly journals Long-Time Average Cost Control of Polynomial Systems: A Sum-of-Squares-Based Small-Feedback Approach

2015 ◽  
Author(s):  
Deqing Huang ◽  
Sergei Chernyshenko
Keyword(s):  
Average Cost ◽  
Cost Control ◽  
Controller Design ◽  
Polynomial Systems ◽  
Sum Of Squares ◽  
Simultaneous Optimization ◽  
Control Law ◽  
Polynomial Coefficients ◽  
Long Time ◽  
Time Average

This paper provides a proof of concept of the recent novel idea in the area of long-time average cost control. Meanwhile, a new method of overcoming the well-known difficulty of nonconvexity of simultaneous optimization of a control law and an additional tunable function is given. First, a recently-proposed method of obtaining rigorous bounds of long-time average cost is outlined for the uncontrolled system with polynomials of system state on the right-hand side. In this method the polynomial constraints are relaxed to be sum-of-squares and formulated as semi-definite programs. It was proposed to use the upper bound of long-time average cost as the objective function instead of the time-average cost itself in controller design. In the present paper this suggestion is implemented for a particular system and is shown to give good results. Designing the optimal controller by this method requires optimising simultaneously both the control law and a tunable function similar to the Lyapunov function. The new approach proposed and implemented in this paper for overcoming the inherent non-convexity of this optimisation is based on a formal assumption that the amplitude of control is small. By expanding the tunable function and the bound in the small parameter, the long-time average cost is reduced by minimizing the respective bound in each term of the series. The derivation of all the polynomial coefficients in controller is given in terms of the solvability conditions of state-dependent linear and bilinear inequalities. The resultant sum-of-squares problems are solved in sequence, thus avoiding the non-convexity in optimization.

Single Crystal CVD Diamond Nuclear Detectors

2006 ◽  
Vol 48 ◽  
pp. 103-112 ◽  
Author(s):  
Claudio Manfredotti
Keyword(s):  
Single Crystal ◽  
Time Derivative ◽  
Diamond Films ◽  
Radiation Detectors ◽  
Cvd Diamond ◽  
High Energy ◽  
Neutron Spectrometry ◽  
Free Standing ◽  
Wide Range ◽  
Nuclear Detectors

CVD diamond films have reached in recent years superlative improvements in their “ detector grade “ quality, with a time derivative which was never registered for other similar frontier materials. The basic properties of high quality CVD diamond films make them very interesting for a wide range of radiation detectors : they provide fast signals with very low leakage currents, they are very radiation resistant, they have excellent thermal properties and they can be manufactured as free-standing detectors. The recent availability of single crystal CVD diamond samples of extreme good quality, suitable thickness and surface area has opened new application fields in nuclear detection and dosimetry, such as, for instance, hadron therapy and neutron spectrometry in fusion reactors. At the same time, strip and pixel detectors of unprecedented performances have been successfully realized and exploited in the framework of high energy physics experiments. The paper will review the more recent history of CVD diamond nuclear detectors with respect to material quality, with a particular emphasis on epitaxial single crystals diamond, and the achievements in terms of applications in some different fields.

Design of Dynamical Controllers for Linear Hamiltonian Systems

1999 ◽  
Author(s):  
Werner Haas ◽  
Michael Krommer ◽  
Hans Irschik
Keyword(s):  
Hamiltonian Systems ◽  
Controller Design ◽  
Time Derivative ◽  
Design Parameters ◽  
Internal Dynamics ◽  
Design Algorithm ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Linear Hamiltonian Systems ◽  
Frequency Domain Approach

Abstract Linear Hamiltonian control systems with collocation of sensor and actuator are considered. Based on a frequency domain approach a controller design algorithm is stated. The design leads to a controller with internal dynamics which uses the output of the system and its first time derivative. The presence of internal dynamics in the controller is an extension of the usual PD–control law and a main result of the work. The design is based on the special properties of the proposed class of systems. In particular, these Hamiltonian systems are passive. It is shown that the design leads to strictly passive controllers for a certain choice of the design parameters. This is another significant result and offers a way for robust ℒ2–stabilization even in the case of infinite dimensional systems. Some features of the controller design are discussed with respect to an application, the control of a composite circular plate.

State Feedback Controller Design for CSTR Based on Kalman Filter

2013 ◽  
Vol 404 ◽  
pp. 657-662 ◽  
Author(s):  
Hao Wu ◽  
Ze Biao Shan ◽  
Yao Wu Shi
Keyword(s):  
Kalman Filter ◽  
State Feedback ◽  
Controller Design ◽  
Dynamic Performance ◽  
Chemical Species ◽  
Operating Conditions ◽  
Feedback Controller ◽  
Continuous Stirred Tank Reactor ◽  
State Feedback Controller ◽  
Cstr System

Due to operating conditions and economic factors, it may be either practical or feasible to measuring the chemical species directly in the continuous stirred tank reactor (CSTR) system which is a typical nonlinear, multi-variables, time-varying system. So, a concentration estimate strategy of components based on Kalman filter is proposed, with which the measurement of temperature conversion can be reconstructed. Then the state feedback controller is designed based on the estimated strategy. Simulation results show that the proposed control scheme is efficient and the system contains good dynamic performance.

Automatic Transmission Shift Calibration Based on Parallel-Modulated Neural Network (PMNN) Friction Component Model

2004 ◽  
Author(s):  
M. Cao ◽  
K. W. Wang ◽  
Y. Fujii ◽  
W. E. Tobler
Keyword(s):  
Neural Network ◽  
Controller Design ◽  
Automatic Transmission ◽  
Applied Pressure ◽  
Operating Conditions ◽  
Component Model ◽  
Powertrain System ◽  
Friction Component ◽  
Wide Range ◽  
Shift Dynamics

The parallel-modulated-neural-network (PMNN) -based friction component model [19] provides a simple pressure-torque formula, which possesses much improved scalability with respect to the applied pressure. In this paper, the PMNN friction component model is implemented within a comprehensive powertrain model, to simulate the shifting process of an automatic transmission (AT) system under various operating conditions. Simulation results demonstrate that the PMNN model can be effectively applied as a part of powertrain system model to accurately predict transmission shift dynamics. A pressure-profiling scheme through a quadratic polynomial pressure-torque relationship from the PMNN model is developed for the transmission shifting optimization. This scheme is implemented to improve the transmission shifting quality under certain operating conditions. The pressure profiling results illustrate that the proposed pressure profiling technique can be potentially applied to a wide range of operating conditions. This study demonstrates that the PMNN architecture not only outperforms the conventional network modeling techniques in accuracy and numerical efficiency, but is also a new tool for AT controller design.

Modified Nernst-Plank-Poisson Model for IPMC With Back-Relaxation Effects

2019 ◽  
Author(s):  
Aiman Al-Allaq ◽  
Nebojsa Jaksic ◽  
Bahaa Ansaf ◽  
Jude DePalma ◽  
Trung Duong
Keyword(s):  
Controller Design ◽  
Real Life ◽  
Poisson Model ◽  
Great Accuracy ◽  
Metal Composite ◽  
New Model ◽  
Relaxation Effects ◽  
Wide Range ◽  
Polymer Metal ◽  
Robotic Applications

Abstract The ionic polymer–metal composite (IPMC) is a new practical engineering material that, it has a wide range of capabilities in both dry and liquid environments. IPMC is a new candidate for diaphragms in micropump devices, micro and Nano robotic applications. IPMCs are regarded as a capable actuator for transportable applications, however, the unique combination of electrochemical and mechanical properties that they possess, such as back-relaxation, restraint their use in real-life applications. There have a lot of attempts to understand and model the IPMCs properties and build a whole prototype that can be used, with certainty, in different robotic, control, and medical applications, yet, till now, it seems that the dehydration and back-relaxation are still not modeled properly. The Nernst-Plank-Poisson was chosen to be the base model for the IPMC behavior, we were able to create a new model that truly represent the back-relaxation effects that occur in IPMCs, we’ve called the new model as modified NPP model. The modification used captured data from our experimental work Our modified analytical NPP (Nernst-Plank-Poisson) model was the verified using MATLAB & Simulink, which showed that the model, and the controller design for it was able to first compensate the loss of position of the IPMC due to back-relaxation, and then track the desired position input signals with great accuracy. The model and designed controller can be utilized in verity of robotic applications.

A Robust Pressure Controller for a Variable Speed AC Motor Pump: Application to Aircraft Hydraulic Power Packages

2018 ◽  
Author(s):  
Nils Trochelmann ◽  
Phillip Bischof Stump ◽  
Frank Thielecke ◽  
Dirk Metzler ◽  
Stefan Bassett
Keyword(s):  
Distribution Systems ◽  
Controller Design ◽  
Dynamic Performance ◽  
Operating Conditions ◽  
Gear Pump ◽  
Variable Speed ◽  
Hydraulic Power ◽  
Worst Case ◽  
Wide Range ◽  
Pressure Controller

Highly integrated electro-hydraulic power packages with electric motor-driven pumps (EMP) are a key technology for future aircraft with electric distribution systems. State of the art aircraft EMPs are robust but lack efficiency, availability, and have high noise emissions. Variable speed fixed displacement (VSFD-) EMPs, combining a permanent magnet synchronous motor and an internal gear pump, show promising properties regarding noise reduction and energy efficiency. Though, meeting the strict dynamic requirements is tough with this EMP-concept. Speed limitations and inertia impose strong restrictions on the achievable dynamic performance. Moreover, the requirements must be met under a wide range of operating conditions. For a prototype aircraft VSFD-EMP a robust pressure controller design is proposed in this paper. In a first step the operating conditions of the EMP are defined, analyzing environmental conditions and impacts of the interfacing aircraft systems. Nonlinear and linear control design models are developed and validated by measurements at an EMP test rig built for this project. A conventional cascade pressure control concept is selected. This is motivated by the demand for simple, reliable, and proven solutions in aerospace applications. A controller is designed by applying classical loop shaping techniques. Robust stability and performance of the system are investigated through a subsequent μ-analysis. Finally, the controller is tested under nominal and worst case conditions in nonlinear simulations.

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