Aims and learning outcomes
This course aims at giving to participants all the mathematical tools required in the analysis and design of control systems, together with the basics on technological aspects related to their realization.
A classic mechatronic problem, i.e., the design of a motion control system, is used as a case study to show a realistic application of these tools.
The first part of the course deals with the basics on systems theory for continuous time and discrete time systems, and introduces the control system design problem, focusing on the tools required to analyze stability and performance of feedback control systems. Time domain and frequency domain design approaches are then introduced. The indirect digital controller design problem, i.e., the transformation of a continuous time control system into a digital one, closes this part.
The second part of the course presents an application of frequency and time domain control methodologies to a mechatronic problem, i.e., motion planning and control of a servomechanism, and introduces the basics on technological aspects related to the realization of control systems. In particular, hardware technologies, related to conditioning, filtering, analog-to-digital and digital-to-analog conversion, and software technologies, related to control system design, communication networks and Programmable Logic Controllers (PLCs), are discussed.
1. Systems theory overview (continuous time systems): Fundamentals of continuous time dynamical systems. Solutions and equilibrium points. Lyapunov stability. Linear Time Invariant (LTI) systems: solutions and equilibrium points, stability analysis. Stability of equilibria of nonlinear systems. LTI systems in the frequency domain. Structural properties of LTI systems: observability and controllability. Realization and canonical forms.
2. Frequency domain design: Frequency response. Introduction to control systems. Loop stability analysis. Loop transient and steady-state performance analysis. Control system design. Feedforward compensation. Cascaded control. PID regulators. Root locus.
3. Time domain design: Introduction to state space design. Full-state feedback. Observer design. Combining observer and control law. Introduction of a reference input. Adding a feedforward action.
4. Systems theory overview (discrete time systems): Introduction to discrete time systems. Linear Time Invariant (LTI) systems: solutions and equilibrium points, stability analysis. Stability of equilibria of nonlinear systems. LTI systems in the frequency domain. Time response of a first order system. Frequency response.
5. Digital control systems: Introduction to digital control systems. Analog-to-digital conversion: effects of sampling on the closed loop system. Digital-to-analog conversion. Indirect digital controller design: selecting the sampling rate and determining the transfer function of the digital regulator. Elements of direct digital controller design.
6. Motion planning: Introduction to motion planning: point-to-point motion planning and trajectory planning. Point-to-point motion planning with polynomial functions and trapezoidal velocity profiles. Using splines for trajectory planning. Trajectory scaling.
7. Motion control: Introduction to motion control problems. Models of an electric motor and of rigid and elastic transmissions. P/PI (position/velocity) control: tuning for rigid and elastic transmissions, using motor and load feedback, intrinsic performance limits. PID regulators: standard form and anti-windup techniques.
8. Advanced motion control: Notch filters. Torque disturbance observer. Use of pole placement techniques to design the motion control system. Input shaping.
9. Industrial robotics: Industrial robots. Kinematic and dynamic models. Joint space and Cartesian space motion planning. Elements of robot control: independent joint control, computed torque, PD control, inverse dynamic control.
10. Hardware technologies for automation: Operational amplifiers, instrumentation amplifiers, and isolation amplifiers. Elements of cables and cable selection. Differential and single-ended measurements. Standard systems used for signal transmission from sensor to controller. Analog and digital I/O conditioning and filtering. Analog-to-digital and digital-to-analog converters.
11. Software technologies for automation: Hardware and software architecture of a control system. Industrial communication networks: Ethernet and Fieldbus. Programmable Logic Controllers (PLCs): ladder logic and ladder diagrams. Real-time and embedded systems.
Automatic Control A includes all the previous topics; Automatic Control B includes only topics 1, 2, 3, 4, 5.
The course provides training sessions based on computer simulation tools.