Lubos Spacek

Maze Navigation on Ball & Plate Model

Today’s CCD or CMOS image sensors are advanced enough to satisfy the need for accurate object detection and tracking. This leads to implementation of computer vision into industry, transportation, medicine, robotics and other sectors. The aim of this paper is to present steps needed to determine correct path through the maze constructed on a plate and navigate a ball along this path. Image processing techniques used here are simple enough to understand, so students can easily implement them to further extend educational capabilities of Ball & Plate model. The paper also shows the use of watershed transform, which can be extended for similar problems. The added maze thus provides excellent application for the model and simulates real-world issues in research and development.

MATLAB as a Tool for Modelling and Simulation of the Nonlinear System

This contribution describe the process that usually precedes the design of the controller - a modelling and a simulation of the observed technological system. Two types of models, physical and abstract, are discussed here. While physical model is usually small or simplified representation of the originally bigger system, the abstract (mathematical) model is description of the system in the form of linear or nonlinear ordinary or partial differential equations. Simulation of the mathematical model then means numerical solution of these equations using some mathematical software. The proposed modeling and simulation procedure is then applied on the real model of the water tank. The mathematical model was then derived and then subjected to the simulation of the steady-state and dynamic analysis.

Collaborative Robot YuMi in Ball and Plate Control Application: Pilot Study

Ball & Plate is a well-known concept and interesting example of an unstable process. Numerous types of Ball & Plate structure can be found and this paper tries to extend its potential of moving the whole plate in space by using an industrial robotic manipulator as the most flexible way to achieve this goal. The collaborative dual-arm robot YuMi from ABB is chosen for this task as the balance between precision and safety. The purpose of the paper is to investigate restrictions and boundaries of such solution, thus the model is identified and based on this identification is designed a controller, which is tested in a simulation environment.

Adaptive control of temperature inside plug-flow chemical reactor using 2DOF controller

The tubular chemical reactor is a industrial equipment widely used in the chemical or biochemical industry for production of various kinds of products. The mathematical model of such system is described by partial differential equations that are solved numerically. This article presents simulation results of the mean reactant’s temperature control inside the plug-flow tubular chemical reactor. The adaptive approach here is based on the recursive identification of the external linear model as a simplified mathematical representation of the originally nonlinear system. The control synthesis is based on the polynomial theory with the Pole-placement method and the spectral factorization. These methods are easily programmable and they also offers tuning of the controller. Used two degrees-of-freedom (2DOF) control structure divides the controller into two parts – the first in the feedback part and the second one in the feedforward part of the control loop.

Overview of Ball & Plate Application for Collaborative Robot YuMi

Most industrial robotic manipulators are used for specific type of operation with predefined movements. This is obvious because industrial robots are constructed to perform repetitive tasks with certain precision and cycle time. This paper introduces another way to exploit advantages of robots by changing their movement dynamically with reaction to external forces and environment. This is partially solved by integrated force control sensors for manipulator grippers, but this article deals with the extension to control of the unstable system with fast dynamics. The best representative of such a system is a Ball & Plate model. This paper deals with the overview of the designed structure of the project and testing the feasibility of solutions.

Ball & Plate Model For Robotic System.

There are many solutions to control Ball & Plate model, ranging from hobby projects to more advanced control. This paper brings a new idea of control using robotic manipulator. This is quite challenging because industrial robots are not originally designed as a motion system for relatively fast and unstable system, which the Ball & Plate certainly is. This paper compares 3 controller designs to better comprehend the situation a general LQR state-space control, LQ polynomial control and a basic PD controller. Results are also compared for a range of reference values to better understand advantages and disadvantages of chosen controllers, which will lead to future work and implementation for the real system. Data presented in this paper serve as a valuable background for next steps of the research and implementation.

Digital control of Ball & Plate model using LQ controller

This paper proposes the design of linear quadratic (LQ) digital controller in Ball & Plate model in experimental environment. The non-linear mathematical model of Ball & Plate structure is presented and adequately linearized. Polynomial approach to controller design for two degrees of freedom (2DOF) controller structure is introduced as the main tool for determination of unknown parameters. This method requires placing poles of characteristic polynomial, which are semi-optimally determined using minimization of linear quadratic criterion. This criterion is minimized by spectral factorization with the aid of the Polynomial Toolbox for MATLAB. Experiments have proved that this type of controller is able to stabilize the ball in desired position on the plate, reject external disturbances and follow reference path without much effort. In addition, a simple maze was created on the plate to extend possibilities of the choice of reference signal. The algorithm is able to determine correct path through the maze and navigate the ball along this path.

Verification Of Robust Properties Of Digital Control Closed-Loop Systems.

Robustness is specific property of closed-loop systems when the designed controller guarantees control not only for one nominal controlled system but also for all predefined class of systems (perturbed models). The robust theory is mainly exploited for design of the continuous-time systems. This paper deals with an experimental simulation investigation of robust properties of digital control closed-loop systems. Minimization of the Linear Quadratic (LQ) criterion was used for the design of control algorithm. Polynomial approach is based on the structure of the controller with two degrees of freedom (2DOF). Four types of process models (stable, non-minimum phase, unstable and integrating) were used for controller design. The Nyquist plot based characteristics of the open-loop transfer function (gain margin, phase margin and modulus margin) served as robustness indicators. The influence of change of process gain was chosen as a parametric uncertainty. The experimental results demonstrated that a robustness of examined digital control closed-loop systems could be improved by addition of user-defined poles (UDP). INTRODUCTION One of possible approaches to digital control systems is the polynomial theory. Polynomial methods are design techniques for complex systems (including multivariable), signals and processes encountered in control, communications and computing that are based on manipulations and equations with polynomials, polynomial matrices and similar objects. Systems are described by input-output relations in fractional form and processed using algebraic methodology and tools (Šebek and Hromčík 2007). The design procedure is thus reduced to algebraic polynomial equations. Controller design consists of solving polynomial (Diophantine) equations. The Diophantine equations can be solved using the uncertain coefficient method – which is based on comparing coefficients of the same power. This is transformed into a system of linear algebraic equations (Kučera 1997). It is obvious that the majority processes met in industrial practice are influenced by uncertainties. The uncertainties suppression can be solved by implementation of either adaptive control or robust control. The robust control and the adaptive control are viewed as two control techniques, which are used for controller design in the presence of process model uncertainty process model variations (Landau 1999; Landau et al. 2011). The design of a robust controller deals in general with designing the controller in the presence of process uncertainties. This can be simultaneously: parameter variations (affecting lowand medium-frequency ranges) and unstructured model uncertainties (often located in high-frequency range). The aim of this paper is the experimental examination of the robustness of digital controllers based on LQ method. Robustness is the property when the dynamic response of control closed loop (including stability of course) is satisfactory not only for the nominal process transfer function used for the design but also for the entire (perturbed) class of transfer functions that expresses uncertainty of the designer in dynamic environment in which a real controller is expected to operate. The design of a robust digital pole assignment controller is investigated in (Landau and Zito 2006), the robust stability of discrete-time systems with parametric uncertainty is analysed in (Matušů 2014). A more comprehensive discussion of robustness is taken when the design based on frequency methods is considered. One can readily compare the system gain at the desired operating point and the point(s) of onset of instability to determine how much gain change is acceptable. Only this method will be used for investigation of the robustness of digital control stable, unstable, non-minimum phase and integrating processes. The paper is organized in the following way. The fundamental principle of the robustness of digital Proceedings 31st European Conference on Modelling and Simulation ©ECMS Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics (Editors) ISBN: 978-0-9932440-4-9/ ISBN: 978-0-9932440-5-6 (CD) control-loop in Section 2. presented in robust prope their results concludes thi ROBUSTNE CONCEPTS Digital Cont The “degrees the develop system desig system is def functions th design of con so a Two-D naturally ha Freedom (ab fact was alre structure of modification

Simulation Study Of 1DOF Hybrid Adaptive Control Applied On Isothermal Continuous Stirred-Tank Reactor.

A Continuous Stirred-Tank Reactor is typical system with nonlinear behavior and lumped parameters. The mathematical model of this type of reactor is described by the set of nonlinear ordinary differential equations that are easily solvable with the use of numerical methods. The big advantage of the computer simulation is that once we have reliable mathematical model of the system we can do thousands of simulation experiments that are quicker, cheaper and safer then examination on the real system. The control approach used in this work is a hybrid adaptive control where an adaptation process is satisfied by the on-line recursive identification of the External Linear Model as a linear representation of the originally nonlinear system. The polynomial approach together with the Pole-placement method and spectral factorization satisfies basic control requirements such as a stability, a reference signal tracking and a disturbance attenuation. Moreover, these methods produce also relations for computing of controller’s parameters. As a bonus, the controlled output could be affected by the choice of the root position in the Pole-placement method. The goal of this contribution is to show that proposed controller could be used for various outputs as this system provides five possible options. INTRODUCTION The mathematical modelling and the computer simulation is a great tool for control engineering that helps with the understanding of the system’s behavior without exanimation on a real equipment or a real model of the system (Honc et al. 2014), (Ingham et al. 2000). The benefits of the computer simulation are clear – it is quick, safe and of course much cheaper method than real experiments which, especially in chemical industry, could consume a lot of chemicals without a clear result. Even more, a lot of chemical experiments produce an exothermic reaction and wrong settings of the controller could end with the dangerous explosion. This paper presents the simulation study from the initial steady-state and dynamic analyses to the hybrid adaptive control of the system. The steady-state and dynamic analyses observes the nonlinear behavior of the system and help us with the choice of the optimal control strategy. The system under the consideration is an isothermal Continuous Stirred-Tank Reactor (CSTR) the mathematical model of which is described by the set of five nonlinear ordinary differential equations (ODE) as there are five state variables – concentrations (Russell and Denn 1972). There were used Simple iteration method for the solving of the steady-state of this system which is, in fact, the numerical solution of the set of nonlinear algebraic equations that are transformed from the set of ODE with the condition that the derivative with respect to the time are equal to the zero in the steady-state. The dynamic analysis then employs the Standard Runge-Kutta’s method for numerical solution of the set of ODE. Both methods are simple but accurate enough. Moreover, they are easily programmable and Runge-Kutta’s methods are even build-in functions in the mathematical software Matlab (Vojtesek 2014) which was used as a simulation program in this work. The control method here is based on the idea of the adaptive control (Åström and Wittenmark, 1989) where parameters of the controller are restored during the control according to the actual needs and state of the controlled system. The core function of this adaptive approach is the recursive identification of the External Linear Model (ELM) as a linear representation of the nonlinear system (Bobal et al., 2005). Parameters of the controller than depends on the identified ELM and they are computed with the use the Polynomial method, the Pole-placement method and the Spectral factorization. As a result, this approach produces not only the controller that satisfies basic control requirements but also easily programmable relations for computing of controller’s parameters which helps with the implementation inside the industrial controllers. We call this approach the “hybrid” adaptive control because the polynomial approach used here is defined in the continuous-time which is more accurate but problematic for the on-line identification. Because of this, the special type of the discrete-time identification was used. This method is called the Delta-models (Middleton and Goodwin 2004) that belongs to the class of discrete-time models but its parameters approaches to the continuous-time ones for sufficiently small sampling Proceedings 31st European Conference on Modelling and Simulation ©ECMS Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics (Editors) ISBN: 978-0-9932440-4-9/ ISBN: 978-0-9932440-5-6 (CD) period (Stericker and Sinha 1993) as there are both input and output variables related to the sampling period. The control strategy was applied on the control of two different outputs which shows that it could be also successfully applicable to similar types of processes. ADAPTIVE CONTROL The control approach used in this work is an adaptive control. The philosophy of this control method comes from the nature, where plants, animals and even human beings “adopt” their behavior to the actual conditions and an environment. This could be done, from the control point of the view, for example by the change of the controller’s parameters, structure etc. (Bobal et al., 2005). External Linear Model The approach used here starts with the dynamic analysis of the system that help us with the understanding of the system’s behavior. Resulted step responses are then used for the choice of the External Linear Model (ELM) as a linear representation of usually nonlinear system. This ELM could be in the form of the polynomial transfer function and the adaptivity is then satisfied by on-line recursive identification that estimates parameters of the ELM in every moment. This procedure guarantees that this ELM describes the system accurately to the relative state of the system. The general form of the ELM’s transfer function is ( ) ( ) ( ) b s G s a s = (1) where parameters of polynomials a(s) and b(s) are computed from the recursive identification and both polynomials holds the feasibility condition for ( ) ( ) deg deg a s b s ≥ . Design of Controller Now we know, that the controlled nonlinear system is described by the polynomial transfer function (1) and we can describe the controller also by the transfer function ( ) ( ) ( ) q s Q s p s = (2) where q(s) and p(s) are again commensurable polynomials with the properness condition ( ) ( ) deg deg p s q s ≥ . Figure 1: 1DOF control scheme If we put this controller’s transfer function in the feedback part of the closed-loop scheme displayed in Figure 1, the Laplace transform of the transfer function G(s) in (1) is then ( ) ( ) ( ) ( ) ( ) ( ) Y s G s Y s G s U s U s = ⇒ = ⋅ (3) where Laplace transform of the input signal u is from Figure 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) U s Q s E s V s Q s W s Y s V s = ⋅ + = ⋅ − + ⎡ ⎤ ⎣ ⎦ (4) Then, if we put polynomials a(s), b(s), p(s) and q(s) from (1) and (2), the equation (3) has form ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) b s q s Y s W s a s p s b s q s a s p s V s a s p s b s q s = ⋅ + +