1. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two Feedback and control theory Learning summary By the end of this chapter you should have learnt about: Feedback and the concept of control engineering Illustrations of modelling and block diagram concepts The s domain: a notation borrowed from mathematics Block diagrams and the s notation: the heater controller and tensioning system Working with transfer functions and the s domain Building a block diagram: part 1 Building a block diagram: part 2 Conversion of the block diagram to the transfer function of the system

2. Feedback and control theory Learning summary The control algorithm and proportional-integral- derivative (PID) control Response and stability of control systems A framework for mapping the response of control systems: the root locus method. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two

3. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two 5.3 Illustrations of modelling and block diagram concepts – key points By the end of this section you should have learnt: the concepts of closed-loop control and feedback, and their typical applications the difference between positive and negative feedback the concept of a block diagram representing the characteristics of a control system and the manner in which feedback is provided.

4. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two 5.4 The s domain: a notation borrowed from mathematics – key points By the end of this section you should have learnt: the concept of the Laplace transform and its role in the solution of differential equations the basic rules relating to application of Laplace transforms to problems involving integration, differentiation and time-shifting how to transform a range of expressions from the time domain into the s domain.

5. 5.5 Block diagrams and the s notation: the heater controller and tensioning system – key points By the end of this section you should have learnt: the use of block diagrams involving the s domain the construction of the block diagram of a system involving dynamic behaviour such as mechanical or thermal inertia. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two

6. 5.6 Working with transfer functions and the s domain – key points By the end of this section you should have learnt: how to simplify a block diagram containing a feedback loop to give a simplified block diagram involving a single transfer function how to find the values of an expression in the s domain at times t = 0 and t =. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two

7. 5.7 Building a block diagram: part 1 – key points By the end of this section you should have learnt: the concept of a transfer function the transfer functions of a range of simple components the concept of linearization. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two

8. 5.8 Building a block diagram: part 2 – key points By the end of this section you should have learnt: to construct a block diagram for systems or subsystems based on the transfer functions of each of its components or features how to assemble the block diagram for a complex system from the diagrams for its various subsystems to appreciate that distinguishing the input and output of particular processes is not always straightforward. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two

9. 5.9 Conversion of the block diagram to the transfer function of the system – key points By the end of this section you should have learnt: the relationship between the transfer function of a closed-loop system and the transfer functions of its main and feedback paths the procedure for simplifying a block diagram with one or more loops in order to reduce it to a block diagram involving a single transfer function. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two

10. 5.11 The control algorithm and proportional-integral-derivative (PID) control – key points By the end of this section you should have learnt: how to assemble a collection of transfer function boxes relating to separate aspects of a control system how to form a complete block diagram for that system how to rearrange and simplify that system to find the transfer function of the system the importance of the control algorithm the purpose of the three terms in a PID controller typical effects of the three contributions to PID control. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two

11. 5.12 Response and stability of control systems – key points By the end of this section you should have learnt: the issues of response, damping and stability the meaning of the terms ‘characteristic polynomial’ and ‘characteristic equation’ how to determine the natural frequency and damping of a second-order system from the characteristic equation the meaning of a Bode plot and a Nyquist plot the meanings of gain margin and phase margin the principle of the Nyquist stability criterion Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two

12. 5.12 Response and stability of control systems – key points how to apply the Routh–Hurwitz stability criterion to a given characteristic polynomial. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two

13. 5.13 A framework for mapping the response of control systems: the root locus method – key points By the end of this section you should have learnt: how to draw root locus plots and interpret them in terms of system stability and response. Unit 5: Feedback and control theory An Introduction to Mechanical Engineering: Part Two