LESSON PLANACADEMIC YEAR: 2014-15 FACULTY NAME: O. V. SIRISHA SUBJECT: MODERN CONTROL THEORY BRANCH: IV-II EEE Subject Code: (9A02803) With Effect from: 22-12-2014 T P C Last working Day: 4 0 4 LECTURE HOURS : 80 I NO OF WEEKS: 14 Aim: This course aims to provide students with a fundamental background on modern control theory and its applications and present how control theory is related to practical engineering problems. II Course Objective: This course offers a continuation of control system analysis and design, with emphasis on PID control and compensator design (lead, lag, lead-lag), and an introduction to modern control theory, which covers basic concepts and principles of system modeling, analysis and controller design for linear time-invariant systems with the state space approach including state variable models, controllability, observability and stability analysis, state feedback control and observer design. In this chapter we describe a general process for designing a control system. A control system consisting of interconnected components is designed to achieve a desired purpose. To understand the purpose of a control system, it is useful to examine examples of control systems through the course of history. These early systems incorporated many of the same ideas of feedback that are in use today. Modern control engineering practice includes the use of control design strategies for improving manufacturing processes, the efficiency of energy use, advanced automobile control, including rapid transit, among others. We also discuss the notion of a design gap. The gap exists between the complex physical system under investigation and the model used in the control system synthesis. The iterative nature of design allows us to handle the design gap effectively while accomplishing necessary tradeoffs in complexity, performance, and cost in order to meet the design specifications. To study concepts and techniques of linear and nonlinear control system analysis and synthesis in state space framework. It will have preferential bias towards aerospace applications, especially towards aircrafts and missiles. However, the theory as well as many demonstrative examples studied in this course will be generic. III Course contents: Full order observer and reduced order observer. Output regulator problem. Derivation of describing functions for Dead zone. Minimum time. UNIT – III MODAL CONTROL Effect of state feedback on controllability and observability. Saturation. Control variable inequality constraints. Minimum principle. Types of nonlinearities. UNIT –VII OPTIMAL CONTROL Formulation of optimal control problem. UNIT-V PHASE-PLANE ANALYSIS Introduction to phase-plane analysis. UNIT-VIII CALCULUS OF VARIATIONS Minimization of functionals of single function. State regulator problem. minimum fuel problems. UNIT-VI STABILITY ANALYSIS Stability in the sense of Lyapunov. Concepts of describing functions. Lyapunov‘s stability and Lypanov‘s instability theorems. relay with dead zone and Hysteresis – Jump Resonance. Method of Isoclines for Constructing Trajectories. Control and state variable inequality constraints. Tracking problem. time invariant case. hence only 13 weeks are available out of which 2 weeks of conducting mid examinations .JNTUA SYLLABUS 2009 UNIT – I STATE VARIABLE DESCRIPTION Concept of State – State Equations for Linear Continuous time Models – Non uniqueness of state model – State diagrams for continuous time state models – Solution of state equations – State transmission matrix. minimum energy control. as per JNTU norms 4periods/week allotted the total lecture hours available are 11*4=44 periods but the actual number of hours required are 17*4=65 periods the number of extra hours are mode available by providing 7 lecture hours / week making the no. Constrained minimization. Phase-plane analysis of nonlinear control systems. Design of State Feedback Control through Pole placement. Parameter Optimization. IV Lesson plan Layout: The course is spread over a period of seventeen weeks out of this last four weeks will be untied by students for their project work. Direct method of Lypanov for the Linear and Nonlinear continuous time autonomous systems. of lecture hours to 11*7=77periods>68 . UNIT – II CONTROLLABILITY AND OBSERVABILITY Tests for controllability and observability for continuous time systems – Time varying case. . Singular points. backlash. virtually 11 weeks are available to complete the lesson contents . Minimum energy. Controllability and observability of state models in Jordan canonical form and other canonical forms. Infinite time Regulator. Principle of Duality. UNIT – IV DESCRIBING FUNCTION ANALYSIS Introduction to nonlinear systems. V. QUIZ. at the end of the face two the second mid examination will be conducted.3 2.7 Tests for observability for BB&C 3&4 6/01/15 To 27/01/15 BB&C TB1 TB1 TB1 TB1 BB&C TB1 01 BB&C TB1 02 BB&C TB1 S2 REMA RKS .2 Concept of State 01 BB&C 1. SLIP TEST 01 1.The course work will be completed in two phases.5 State diagrams for continuous time state models 02 22/11/14 to 5/01/15 BB&C 1.8 Problems 03 BB&C TB1 A1 TB1 TB1 TB1 TB1 TB1 S1 UNIT.3 State Equations for Linear Continuous time Models 02 BB&C 1.1 Introduction 01 BB&C 1.2 BB&C 1. In the first phase before the first mid 4 units would be covered in first six weeks the fist mid will be conducted in seventh week In the second phase after the first mid examination remaining four units should covered in five weeks available. OF PERIO DS UNIT – I STATE VARIABLE DESCRIPTION Importance of lesson plan TENTA TIVE DATE AND WEEK NUMBE R MODE OF TEACHI NG TEXT BOOKS/ REFEREN CE BOOKS ASSIGN MENT.6 Solution of state equations 01 BB&C TB1 1. 01 BB&C TB1 Q1 1.7 State transmission matrix.4 Minimum energy control 01 2.1 Introduction 01 BB&C 22 Tests for controllability for continuous time systems 02 BB&C Time varying case 01 2.4 Non uniqueness of state model 01 1. LESSON PLAN TOPICS AND COVERAGE WEEKS/WEEK TITLE OF THE UNIT/CH APTER S.NO LESSON DETAILS NO.II CONTROLLABILITY AND OBSERVABILITY Total number of periods required for unit 1 = 12 2.5 Time invariant case 01 2.6 Principle of Duality 2. TEST. 8 2.7 Examples BB&C BB&C 4&5 RB1 RB1 BB&C RB1 BB&C RB1 BB&C RB1 01 BB&C RB1 01 BB&C RB1 28/01/15 To 11/02/15 Q2 A3 UNIT –IV DESCRIBING FUNCTION ANALYSIS Total number or periods required for unit 3 = 11 4.2 Types of nonlinearities 01 BB&C 4.1 Effect of state feedback on controllability 02 3.5 Examples 02 3. 02 BB&C Derivation of describing functions for saturation 01 BB&C Derivation of describing functions for backlash 01 BB&C 4.continuous time systems 2.2 Effect of state feedback on observability 02 3.4 Full order observer 01 3.5 4.3 Concepts of describing functions 01 BB&C 4.6 TB2 TB2 S3 TB2 Q3 TB2 TB2 5&6 4.4 Derivation of describing functions for Dead zone.8 Derivation of describing functions for relay with dead zone 02 Derivation of describing functions for Hysteresis – Jump Resonance 12/02/15 To 27/02/15 BB&C A4 TB2 BB&C TB2 01 Total number of periods required for unit 4 = 10 UNIT-V PHASE I-MID EXAMINATIONS 30 marks 5.7 4.9 Controllability and observability of state models in Jordan canonical form and other canonical forms.1 Introduction to nonlinear systems 01 BB&C 4.6 Reduced order observer 3.1 Introduction to phase-plane analysis 01 BB&C TB2 .3 Design of State Feedback Control through Pole placement 02 3. 02 Problems 01 BB&C A2 TB1 BB&C TB1 UNIT –III MODAL CONTROL Total number or periods required for unit 2 = 12 3. 3 Lyapunov’s stability theorems 01 BB&C 6.4 Numerical problems 01 28/02/15 To 12/03/15 5.4 7.1 Introduction 01 BB&C 6.1 Introduction 01 Black board TB1 7.6 Direct method of Lypanov for the Linear continuous time autonomous systems 02 Direct method of Lypanov for the Nonlinear continuous time autonomous systems 02 Numerical problems 01 6.5 Numerical problems 01 6. Minimum energy Minimum fuelproblems 01 Black board TB1 Infinite time Regulator Output regulator problem.1 Introduction 01 Black board TB1 .7 6.2 Method of Isoclines for Constructing Trajectories 02 BB&C 5. 01 BB&C 5.4 Lyapunov’s instabilitytheorems 01 BB&C 6.3 Minimum time.5 10 26/03/15 To 6/04/15 Black board Black board Q5 TB1 A7 TB1 UNI T- Total number of periods required for unit 7 = 06 8.2 Formulation of optimal control problem 02 Black board TB1 7.PLANE ANALYSIS 5. 01 Tracking problem Parameter Optimization 01 7.2 Stability in the sense of Lyapunov 02 BB&C 6.5 Phase-plane analysis of nonlinear control systems.3 Method of Isoclines for Singular points 02 7&8 5.6 Numerical problems 02 BB&C BB&C BB&C TB2 TB2 S4 TB2 TB2 TB2 A5 UNIT-VI STABILITY ANALYSIS Total number of periods required for unit 5 = 09 6.8 8&9 13/03/15 To 25/03/15 BB&C TB1 TB1 Q4 TB1 TB1 TB1 BB&C TB1 S5 BB&C TB1 BB&C TB1 A6 UNIT – VII OPTIMAL CONTROL Total number of periods required for unit 6 = 11 7. Based upon then the internal marks are evaluate External Exam pattern:(70m) The external examination are conducted by the university at the end of semester in the 18 th week onwards. Explain highlights of classical control theories. 4. Review system.2 8. The internal marks Consists of objective and descriptive questions. modelling. Lyapunov methods 5.5 Control and state variable inequality constraints 8. . In the objective questions can be 10 or 20 and valied for 10marks. For passing in each individual subjects he has to secure the minimum of 40marks which comprises a minimum of 28marks from the external exam. linear system stability. Analyze the system stability. the student will have to answer choosing any five question. modern control theory 2. classification of systems. Minimum principle 01 8.VIII CALCULUS OF VARIATIONS Minimization of functional of single function 01 Constrained minimization. Out of the two mid exams marks the best marks is take in to consideration for finalizing the internal marks . equilibrium points. The patron of the external exam carry only descriptive questions of eight in number covering one question from each unit. mathematical representation of systems.3 Black board TB1 11 7/04/15 To 15/04/15 S6 Black board TB1 Black board TB1 A8 02 Black board TB1 Total number of periods required for unit 8 = 06 VI EXAM PATTERNAND MARKS Internal mid Examination: (30m) The internal mid exams are divided in to first and second mid exams as shown in the details of lesson contents. Solve system state equations. 01 8. The remaining 20marks are meant for descriptive questions which will be 5 in number and should answer 3 questions. students will be able to: 1. 3. Apply optimal control to statement of the optimal control problems. The student will be getting the total of internal plus external marks in the result sheet.4 Controlvariableinequali tyconstraints. is totally evaluated for 70 marks. VII LEARNING OUTCOMES: Upon successful completion of the course. X TEACHER’S NAME O. 1996. 2nd edition. 1998. Oxford Press. TB2.com PRINCIPAL . Modern Control Engineering – by K. 1997. RB2. Modern Control System Theory – by M. Gopal. 2003. Digital Control and State Variable Methods – by M.TEXT BOOKS: VIII TB1. Prentice Hall of India.V. New Age International Publishers.Gopal. Systems and Control by Stainslaw H.J. Tata Mc Graw-Hill Companies. New Age International (P) Ltd. IX REFERENCE BOOKS: RB1. RB3. Zak . Gopal. Nagarath and M. Control Systems Engineering by I.SIRISHA STAFF CONTACT NUMBER 9441847974 HOD EMAIL-ID [email protected] edition. Ogata.