MODELLING AND DESIGN OF CONTROL SYSTEMS BASED ON PETRI NETS MODELS

The synthesis of control systems for overall processes remains a challenge. Whilst a number of automated approaches have been explored academically, in practice systems are mainly synthesised using experience and intuition in conjunction with dynamic simulation software. An approach is presented in this paper for the systematic synthesis of overall process control systems which is simple, practical and appropriate for use at the undergraduate teaching level. Many potential problems can be identified and avoided in the synthesis of process control systems by ensuring that the control system can maintain a steady-state control of the overall mass, the mass of the individual components and, where necessary, multiple phases. Processes with recycles are vulnerable to process control problems when the overall mass balance of the system containing the recycle is not correctly managed. This can be overcome by self-regulation (perhaps involving process design changes) or by changing the structure of the control system. Achieving and maintaining the material balance are the main purposes of the majority of controllers in most chemical processes. Without robust delivery of material balance control, higher level control objectives (such as quality controls) are unlikely to be met reliably. This paper presents a step-wise approach to the synthesis of overall process control systems that avoids many potential problems by identifying which process parameters can be manipulated to achieve the intended process mass balance and designing the control structure accordingly.

The algorithm of structural and parametric synthesis of automatic control systems for limitedly uncertain non-linear objects with unstable balance status and right own values in their exit matrix is proposed. The pecu-liarity of the structural synthesis algorithm is that synthesized automatic control systems use differential com-pensating connection with two components. The signal of one of them is proportional to the signal of disa-greement between the required and measured values of the state vector of the system. A signal of another com-ponent is formed by the sign-operated integral feedback on the module of the control influence. The algorithm of parametric synthesis is reduced to solving the problem at a conditional minimum of integral regulatory error when limiting the characteristic frequency multi-member module to an algorithmically linearized system.

Computer-aided control system design (CACSD) encompasses a broad range of methods, tools, and technologies for system modelling, control system synthesis and tuning, dynamic system analysis and simulation, as well as validation and verification. The domain of CACSD enlarged progressively over decades from simple collections of algorithms and programs for control system analysis and synthesis to comprehensive tool sets and user-friendly environments supporting all aspects of developing and deploying advanced control systems in various application fields. This entry gives a brief introduction to CACSD and reviews the evolution of key concepts and technologies underlying the CACSD domain. Several cornerstone achievements in developing reliable numerical algorithms; implementing robust numerical software; and developing sophisticated integrated modelling, simulation, and design environments are highlighted.

This paper deals with the modeling and control of discrete event robotic manufacturing cells using Petri nets, and proposes a methodology of model based design and implementation of hierarchical and distributed control. Hierarchical Petri net models are adopted; conceptual Petri net model and detailed Petri net model. The overall detailed Petri net model is decomposed into local Petri net models which are used by the local machine controllers. The upper level station controller coordinates the distributed local controllers so that the aggregate behavior of decomposed subnets is the same as that of the original Petri net. The overall control system is implemented using multithreaded programming based on Petri net based multitask processing. Simulation experiments show that the distributed Petri net model based control system can perform the overall multitask processing control by coincidence of the behavior of the real system with the local Petri net models.

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

The problem of structural-parametric synthesis of automatic control systems (ACS) of technological objects is deter-mined by the multi-dimensionality, multi-connectedness and nonlinearity of their mathematical models. Despite the indicated properties of such objects, traditional linear systems based on PID-algorithms are still used for process control. Since the synthesis of linear systems using input-output models does not take into account the multi-dimensionality and mutual influence of state coordinates, such systems increase the influence of parametric and signal perturbations on the quality of control processes. The increasing requirements for the quality and efficiency of technological processes control made it expedient to apply the control principle by the state vector based on the use of uninertial state regulators or combined state regulators including flexible feedback on the derivative state coordinates or state coordinate integrals. The research uses methods of system analysis of technological processes as control objects, methods of automatic control theory, methods of control systems synthesis on the state regulators basis, meth-ods of computer simulation. The linearized mathematical model of liquid-phase chemical reactor in the state space has been obtained. It has been established that the investigated object has the property of free movement stability and it is fully controlled in the state space. The problem of synthesis of a single-channel concentration vector control system in a chemical reactor using state regulator has been solved. The parameters of state regulator settings have been determined using the method of modal control. The efficiency of the automatic control system on the basis of the state regulator with an integral component has been shown using the method of computer simulation of the ‘nonlinear object – linear control subsystem’ complex. It has been demonstrated that the absence of an integral component in the control algorithm structure leads to a great static error of regulation. To eliminate the static error of control and ensure the robustness of the control system, it is recommended to introduce an integral component into the structure of state controller. This ensures the efficiency of the control system both for the case of complete measurement of the state vector and for the case of measurement of the output controlled variable only.

A design method for control systems that minimizes the spectral bandwidth of the plant input signal is discussed. The plant input signal is minimized subject to the constraint that the integral square error for deterministic inputs or the mean square error for random inputs be limited to a known desired value. The control system transfer function that satisfies these requirements is derived, and the functions used in bandwidth shaping are discussed. An example of a system design using this technique is given.

The subject matter of the article is an air pollution control process. The aim is development of proposals for the synthesis of the air pollution control system based on hyperconvergent infrastructures. The objectives are: the development of a mathematical model for constructing pollutants concentration fields; substantiation and development of a conceptual model of the geoinformation system for air pollution control, justification and selection of the basic infrastructure of the control system. The methods used are: system analysis of risks, cause-and-effect analysis, statistical methods. The following results are obtained: The basic influencing on character of dispersion and distribution of harmful substances factors in atmosphere are allocated. A multifactorial mathematical model has been developed for constructing fields of concentration of pollutants, which is based on two types of distribution-the normal and S L -distribution of Johnson. The geoinformation technology (GIT) structure components are determined. A program for determining the stability class of the atmosphere has been developed. A model of the process under investigation on a cartographic basis was developed with the presentation of the results in the form of a concentration isotype. The structure of the database of the parameters of sources and characteristics of sources of air pollution, which is part of the serving hyperconvergent infrastructure, has been developed. Conclusion . The synthesized air pollution control system will allow to solve such tasks: collection of primary information, its systematization, analysis and formation of a data bank; processing and presentation of data in the form of thematic pollution maps; Assessment of the current state of the environment and forecast; analysis of the causes of observed and probable changes in the state; prompt provision of necessary information to all stakeholders.

Optics swing mirror is a core module with special requirements of high precision and fast response in target simulator of infrared interference.In order to achieve theses pecial requirements,a design method of servo control system is proposed.The high-precision control system which adopts angle feedback and velocity feedback by PID algorithm is built with DSP,brushless resolvers and limited angle brushless torque motor.The experimental result indicates that the system can make the swing mirror achieve precise movement control and fast response.The design method of the servo control system can be widely used in the area of high-precision scanning control systems and has good application prospect in engineering.

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

A robust automatic flight control system is designed for an extra-atmospheric aircraft. The control systems consist of attitude control system used modified -infinity loop shaping method and the navigation system used Modified Augmented Proportional Navigation (MAPN) guidance law. In the inner-loop design, using the H-infinity loop shaping method to transfer the transfer function matrix from the real system to the target system, which is a very useful way to solve the difficulties in choosing a proper weighting matrix in the loop shaping. In the outer-loop design, the MAPNG law is derived by adding the line-of-sight into the Augmented Proportional Navigation (APN) law in order to improve the observability of the system. Compared with the traditional method, the system using the new methods in control system design have a larger robust stability margin, the decoupling and the bandwidth of the system also improve a lot, the guidance accuracy and the miss distance accuracy is higher, furthermore, it reduces the complexity and blindness for the designer to find the proper weighting matrix. The simulation results proved the control performance of the unmanned aircraft system achieves a top level performance.

Modelling and analysis of kanban-controlled (just-in-time) production systems under realistic assumptions presents a number of challenges, including the ability to conduct both qualitative and quantitative analysis, and the ability to model control policies. These challenges are due, in part, to station interdependence, blocking and starvation due to limited buffer spaces, and the necessity of modelling both material and kanban flows. Petri nets (PNs) have recently emerged as a promising approach for modelling manufacturing systems. PNs are a graphical and mathematical technique useful for modelling concurrent, asynchronous, distributed, parallel, non-deterministic and stochastic systems. PN models can be analysed to determine both their qualitative and quantitative properties. In this paper, we develop stochastic, coloured PN (SCPN) models of a JIT system utilizing two different kanban control policies: a traditional kanban system (TKS) policy and a flexible kanban system (FKS) policy. The resulting models can be used to represent JIT systems of arbitrary size, producing single or multiple types of products, with fixed order points 1. The models are shown to be live and bounded, and can be simulated to produce quantitative results. Sample simulation results are presented to illustrate the models' capabilities.

The present article proposes a simple tuning technique aimed to produce a robust non-integer order PID controller exhibiting iso-damping property during reparameterization of a plant. The required robustness property is achieved by letting the fractional PID control system to imitate the dynamics of a reference system having Bode’s ideal transfer function in its forward path. The objective of designing robust controller by tracking the dynamics of reference control system is defined mathematically as an H∞- optimal control problem. Fractional differential systems are transformed into algebraic equations by the use of triangular strip operational matrices. The H∞-optimal control problem is then changed to an ∞-norm minimization of a parameter (Kc,KI,Kd, λ, μ) varying square matrix. Global optimization techniques, Luus-Jaakola direct search and particle swarm optimization are employed to find the optimum values of fractional PID controller parameters. The proposed method of control system design is implemented in heating furnace temperature control, automatic voltage regulator system and some integer and fractional order process models. Fractional PI, fractional PD and various versions of fractional PID controllers are designed as optimal controllers using the triangular strip operational matrix based control design method.

To simulate and debug or diagnose manufacturing systems is always challenging. This paper presents a hybrid PLC-controlled and PC Visual Basic (VB)-based Human-Machine Interface (HMI) platform based on Petri net (PN) theory for Manufacturing Systems. An augmented PN model was adopted to design and simulate the operational sequence of the Flexible Manufacturing System (FMS) at the National Kaohsiung First University of Science and Technology (NKFUST). With the simulated PN model, the control sequences were quickly translated into PLC programs. A PC-based HMI monitoring system based on the PN model was developed to provide an intuitive offline simulation and online diagnostic tools for the FMS. This hybrid system shows many of advantages by using the economical discrete control unit with PLC, and PC-based HMI using PN model as a base. The discrete event control sequence of an FMS can be easily modeled and evaluated before its build-up. More importantly, it can be diagnosed online when the system is malfunctioning. That is, the presented system provides an adequate means for offline system design, simulation, performance evaluation, and quick online system diagnostic.

One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions and gradient-speed dynamic control systems. The basic statements of Lyapunov's theorem about asymptotic stability and notions of stability of dynamic systems are used. The representation of control systems as gradient systems and Lyapunov functions as potential functions of gradient systems from the catastrophe theory allow to construct the full-time derivative of Lyapunov vector functions always as a sign-negative function equal to the scalar product of the velocity vector on the gradient vector. The conditions of aperiodic robust stability are obtained as a system of inequalities on the uncertain parameters of the automatic control system, which are a condition for the existence of the Lyapunov vector-function. A numerical example of synthesis of aperiodic robustness of a multidimensional control object is given. The example shows the main stages of the developed synthesis method, the study of the system stability at different values of the coefficients k, confirming the consistency of the proposed method. Transients in the system satisfy all requirements