continuous and discrets systems

continuous and discrets systems

1. NAME :- YOGESH KUMAR REGAR CLASS :- B-TECH MECHANICAL ENG TOPIC :- Discrete and Continuous Simulation 2014SUBTME005 Yogesh kumar regar

2. Basic concepts Static or dynamic models Stochastic, deterministic or chaotic models Discrete or continuous change/models Yogesh kumar regar 4. Examples

3. 1. Static or Dynamic models Dynamic : State variables change over time (System Dynamics, Discrete Event, Agent-Based, Econometrics?) Static : Snapshot at a single point in time (Monte Carlo simulation, optimization models, etc.) Yogesh kumar regar

4. 2. Deterministic, Stochastic or Chaotic Deterministic model is one whose behavior is entire predictable. The system is perfectly understood, then it is possible to predict precisely what will happen. Stochastic model is one whose behavior cannot be entirely predicted. Chaotic model is a deterministic model with a behavior that cannot be entirely predicted Yogesh kumar regar

5. 3. Discrete or Continuous models Discrete model : the state variables change only at a countable number of points in time. These points in time are the ones at which the event occurs/change in state. Continuous : the state variables change in a continuous way, and not abruptly from one state to another (infinite number of states). Yogesh kumarregar

6. Yogesh kumar regar Fluid flow in a pipe, motion of an aircraft or trajectory of a projectile, are examples of continuous systems. To understand continuity, students are advised to refer some basic book on continuity. Continuous Examples

7. (ii) Discrete Examples of discrete systems are, a factory where products are produced and marketed in lots. . Motion of an aircraft is continuous but if there is a sudden change in aircraft’s level to weather conditions, is a discrete system. Another example of discrete system is firing of a gun on an enemy target. It is important to conduct experiments to confirm theoretically developed mathematical models.

8. Not only the experiments are required for the validation of the theoretical models but various parameters required for the development of theoretical models are also generated by experimental techniques. For example to study the performance of an aircraft, various parameters like drag, lift and moment coefficients are needed, which can only be determined experimentally in the wind tunnel. Thus theory and experiment both are complementary to each other and are required for correct modeling of a system. In case of marketing and biological models in place of experiments, observations and trends of the system over a time period, are required to be known for modeling the system.

9. BEST EXAMPLE ON DISCRETE AND CONTINUOUS SYSTEM Strategies to Model Ore Processing Plants A mine and its associated ore processing plant are typical environments where simulation provides important benefits.  Simulation is used in these plants to address many important business considerations: Major Investments Strategic Decisions which have a major impact on project profitability Understanding Interdependent and Complex Systems Wait times at key resources Stockpiles and tank limitations Headings availability at a given time Traffic in the mine

10. Transporting the Ore with Trucks –> Discrete System

11. The truck moves towards the shovel Waits for its turn to get loaded Gets loaded Moves towards the crusher Waits for its turn to unload Unloads in the crusher Goes back to the shovel These operations represent a typical discrete system where entities (trucks) go through a process and Seize-Delay-Release resources (shovels and dump hopper pockets).

12. Ore Processing – Continuous System Strategies to Model Ore Processing Plants and Continuous Systems An ore processing plant is not discrete, but rather continuous. In Arena, it is possible to represent a flow of ore on a conveyor in a continuous manner. It is also possible to discretize the flow, as suggested by  Franzese and al. (2007). Here is a comparative analysis of the three methods: Discrete Mass – one entity = 1 unit of mass Discrete Time – one entity = mass moved during one unit of time Continuous – using the Flow Process Template

13. Continuous System

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