United Arab Emirates University College of Engineering

1. United Arab Emirates UniversityCollege of Engineering Design and Performance Analysis of Inverted Wedge Control System Faculty Advisor:Dr. Hazem Nounou Co-Ordinator:Dr. Mamdouh Ghannam Group members :Abeer Hassan 980223143 Aysha Kemadish 980724683 Esteklal Ali 980723249 Fatima Al-Sayed 980724305 Hasna Saleh 980724407

2. Table of Contents • Introduction • Background Information • Fuzzy Controller • Model Predictive Controller (MPC) • Results and Analysis • Conclusion

3. Objectives for this Semester • Searching about the Fuzzy Controller • Searching about the Model Predictive Control (MPC) • Design and test the Fuzzy Controller • Design and test the MPC • Compare the all performance of all controllers

4. Fuzzy Control:is a nonlinear control that can be used for complex system. It is kind of logic using grading statement to have grades of membership from 0 to 1. Linguistic variables:describe the input and outputs of the fuzzy system. The fuzzy controlcan be used to realize lower development costs, superior features and better end product performance.

5. Input u(t) Output y(t) Inference mechanism Reference Input r(t) Process Defuzzification Fuzzification Rule-base Block Diagram of the Fuzzy Controller

6. Input (r) Output(y) Current (I) error Inverted Wedge System gain Fuzzy Controller Input gain + - gain Change of error Block Diagram of the Controller and the Inverted Wedge

7. Error -3 -2 -1 0 1 2 3 Change of Error Cart Position -1 -3 -2 -1 0 1 2 3 1 Cart Speed -1 1 Inputs

8. -3 -2 -1 0 1 2 3 Output -1 1 Output

10. Error -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Cart Position Cart Speed -1 -1 Change of Error 1 1

11. Force change in error Error -3 - -2 -1 - 0 1 2 3 -3 - 3 3 3 2 2 1 0 -2 - 3 3 2 2 1 0 - 1 -1 - 3 2 2 1 0 - 1 - 2 0 2 2 1 0 - 1 - 2 - 2 1 2 1 0 - 1 - 2 - 2 - 3 2 1 0 - 1 - 2 - 2 - 3 - 3 3 0 - 1 - 2 - 2 - 3 - 3 - 3

12. Advantages of the Fuzzy Controller • Providing a nonlinear mapping between the state value and controller output • Reducing the development time • Simplifying the design complexity

13. Applications • Water Level Control • Fault Detection • Medical • Image Processing • Communication Signal Processing

14. The system • It has a fuzzy controller with two inputs, the error (e) and the change of error (c). • The outputof the fuzzy controller is the current (input of the Inverted Wedge).

15. What do we want • We want the inverted Wedge to track the reference input. • We simulate the system as a continuous time systemthat is controlled by a fuzzy controller that is implemented ona digital computer with a sampling interval of T.

16. The MATLAB can be used to illustrate -How to code a fuzzy controller (for two inputs and one output. -illustrating some approaches to simplify the computations, for triangular membership functions, and either center-of-gravity or center-average defuzzification - How to tune the input and output gains of a fuzzy controller. - How an improper choice of the scaling gains (or rule base) can result in an unstable system.

17. System initilization • Number of input membership functions for the error and the change of error. • Scaling gains for tuning membership functions for e , change of e and u (ge,gce,gu) • Place centers of membership functions of the fuzzy controller. • HOW TO IMPROVE THE PERFORMANCE • Controlling the width of the triangular input membership function bases. • Controlling the half of the triangular.

23. Model Predictive Control (MPC) • It is the class of advanced control techniques that is used mostly in the process industry. • It classified as linear and nonlinear control. • It is a methodology that refers to a class of control algorithms in which a dynamic model of the plant is used to predict and optimize the future behavior of the process. • It depends on the Time delay.

24. Objective: Minimize the difference between the predicted and desired response. How to implement MPC: MPC strategy yields the optimization of a performance index with respect to some future control sequence , using prediction of the output signal based on a process model.

26. Applications • MPC has received a strong position when it comes to industrially. • telecommunication networks

28. What is the fuzzy logic Toolbox? The fuzzy logic toolbox is a collection of functions built on the MATLAB. The fuzzy logic Toolbox allows user to do several things, but the most important thing is creating and editing Fuzzy Inferences Systems (FIS) using different categories of tools: 1. Command line functions. 2. Graphical interactive tools. 3. Simulink blocks.

29. Categories of tools • Command line functions: Using M-file • Graphical interactive tools: the Graphical User Interface (GUI) based tools provide an environment for fuzzy inference system design, analysis and implementation. • Simulink blocks: setting of blocks for use with the simulink simulation software. • This block now automatically generates a customized block diagram representation for most FISs.

30. Why use the fuzzy logic? • It is conceptually easy to understand. • It is flexible. • It is tolerant of imprecise data. • Every thing is imprecise if you look closely enough, but more than that, most things are imprecise even on careful inspection. Fuzzy reasoning builds this understanding into the process rather than tacking it into the end. • It can model nonlinear functions of arbitrary complexity. • It can be built on top of the experience of experts. • It is based on natural language. • The basis of fuzzy logic is the basis human communication.

31. FIS (Fuzzy Inference System) FIS: is the MATLAB object that contains all the fuzzy inference system information such as variable names and membership function definitions, fuzzy logic operators and If-Then rules. • It is the process of formulating the mapping from a given input to an output using fuzzy logic. • The mapping provides a basis from which decision can be made. • To implement the fuzzy inference in fuzzy logic Toolbox there are two types of inference system which are Mamdani-type and Sugeno-type.

32. Types of FIS • There are two types of FIS: • Mamdani Fuzzy Inference System (FIS): type of fuzzy inference in which the fuzzy sets from the consequent of each rule are combined through the aggregation operator and the resulting fuzzy set is defuzzified to yield the output of the system. • Sugeno Fuzzy Inference System (FIS):

33. input name range input1 MFs name type params FIS name type andMethod orMethod defuzzMethod impMethod aggMethod input2 MFs name type output name range rules Antecedent consequent output MFs name type FIS Structure

34. Block diagram of the fuzzy

35. Function of Fuzzy Controller (Arguments) • Addvar: a = addvar(a,varType,varName,varBounds) • The FIS name • The type of the variable (input or output) • The name of the variable • The vector describing the limiting range for the variable • Addmf: a = addmf(a,varType,varIndex,mfName,mfType,mfParams) • A MATLAB variable name of a FIS structure in the workspace • A string representing the type of the variable you want to add the • membership function to (input or output) • A string representing the name of the new membership function • A string representing the type of the new membership function • The vector of parameters that specify the membership function. • Addrule a = addrule(a,ruleList) • The FIS name. • A matrix of one or more rows, each of which represents a given rule.

38. The output

40. Fuzzy Controller

42. Model Predictive Controller The Model Predictive Control (MPC) strategy yields the optimization of a performance index with respect to some future control sequence, using predictions of the output signal based on a process model, coping with amplitude constraints on inputs, outputs and states. Model Predictive Control (MPC) was first proposed by industry to deal with the control of multivariable systems with a large number of inputs and outputs subject to constraints. In the last few years a theoretical basis for MPC has emerged which provides strong stability and robustness guarantees.

43. What is MPC? • Practically, MPC is the dual of an expert system. Almost every aspect is based on a different principle. More specifically: • MPC uses a model of the process; an expert system uses a model of the operator. • MPC is predictive; an expert system is algebraic. • MPC is closed-loop control; an expert system is open-loop control. • MPC is algorithm-based; an expert system is rules-based. • MPC accepts set points for controlled variables; an expert system only accepts ranges for the controlled variables. • MPC includes dynamics; an expert system does not. • MPC is robust1, which means inaccurate models have little impact on performance.

44. Input (r) Output(y) Current (I) Model Predictive Controller Inverted Wedge System +/- Block Diagram of the Controller and plant

45. MPC functions • SCMPC FUNCTION: • It simulate Closed Loop systems for constrained problems. • SCMPC designs an MPC-type controller for constrained problems • and simulates the closed-loop system with hard constraints • (inputs and outputs) using quadratic programming. • SCMCSIM FUNCTION: • It simulate closed-loop systems with saturation constraints. • State-space closed-loop simulation for MPC with saturation • constraints on manipulated variables. Otherwise, unconstrained. • SMPCCON FUNCTION: • It calculate MPC controller gains for unconstrained case. • It Uses a state-space model of the process.

48. A Rule –Base: If ” premise “ then ”Consequent” Linguistic Variables:between the positive and negative values. An inference mechanism: It is a means of combining the certainties of different inputs, using the minimum, multiplication and average represent the premise.

49. Fuzzification inference: which converts controller input into information that the inference mechanism can easily use to activate and apply rules. . Defuzzification Inference: Its convert the result of the inference mechanism into actual output of the fuzzy system. Center of gravity: calculate the areas, take the center of each area, take the average.

50. Controller Unit Water Tank Sensor Water Level Control