The course is aimed at providing the basic elements and methods for the modelling and the analysis of mechanical systems equipped with actuators and active control. In order to reach this objective, the main issues dealt with in the course are:

• modelling a mechanical system coupled with dynamic model of actuator and control logic
• assessment of the stability of an uncontrolled and controlled mechanical system in time domain
• classic control techniques for evaluating stability, static and dynamic performance of a controlled mechanical system
• introduction to the basic of modern control

By the end of the course, students will learn contents and practices according to what defined in the leaning objectives.

In terms of acquired knowledge and understanding, students will be able to:

• Analyse and discuss about the interaction between a mechanical system and its control.
• Show how to represent in mathematical terms a controlled mechanical system including actuator’s dynamics, through Laplace transform, transfer function and state matrix.
• Discuss about the basic principles and methods of classic control for time domain and frequency domain approach, including standard PD and PI control, through Bode, Nyquist and root locus representation, combining these three approaches.
• Discuss about the basis for the practical tuning of a PID control.
• Show how to model an actuator on the basis of the relevant physical laws.
• Describe the models of the most common actuators’ types (hydraulic, electrical, pneumatic).
• Discuss about the basis of modern control.

 Concerning the ability to apply the acquired knowledge and understanding, students will be able to:  

• Build a dynamic model of an actuator coupled with a mechanical system.
• Design a PD and PI control system, selecting the best choice and comparing the performance of the controlled system.
• Apply the practical tuning of a PID controller.
• Select the most suitable actuator for a control application.
• Recognise the nature of instability problems in an uncontrolled and a controlled mechanical system.
• Describe and communicate the results of performance analysis and the control design also in graphical terms.

The course contents are delivered through lectures, exercise courses and some lab activities.

The course covers the following topics divided in modules as per the description below:

Module 1: Introduction to the control of mechanical systems

Topic 1.1

Basic concepts of a dynamic system, input and output variables. Control variable and observed variables.

Topic 1.2

Control of a mechanical system: feed-back and feed-forward. Effects of the control action on dynamic performance and disturbance rejection.

Module 2: Stability of mechanical systems

Topic 2.1

State dependent force fields: conservative and non-conservative.

Topic 2.2

Mechanical systems under the influence of force fields: general description, equations of motion and linearization, solution of the equations of motion, discussion of stability, position and velocity force fields. Fluid forces on a rigid body including aerodynamic instability (single d.o.f. and flutter instability of a profile).

Module 3: Classic control

Topic 3.1

Simulation models. State variables. Harmonic transfer function. Laplace and Fourier transform. Frequency response function. Block diagram representation. Bode and Nyquist diagram. Control system stability analysis of the closed chain through Root Locus, Nyquist criterion, Bode criterion.

Routh method.

Topic 3.2

Requirements of a controlled dynamic LTI (linear time invariant) SISO (single input single output) system: synthesis of the control logic, definition of performance and robustness indexes.

Module 4: PD and PI controller

Topic 4.1

Application to 1 d.o.f. and 2 d.o.fs vibrating systems. Performance assessment of the controlled system in time domain and frequency domain. Input and output disturbance rejection.

Topic 4.2

PID control: practical tuning rules.

Module 5: Actuators

Topic 5.1

Hydraulic actuators: basic components, performances, models, hydraulic circuits in automation processes.

Topic 5.2

Electric actuators: basic components, performances, characteristic curves. DC and AC drives: control and power electronics, models for synchronous brushless motors. Control of electric drives: basic principles, criteria for torque and speed control, performances.

Topic 5.3

Pneumatic actuators: basic components (cylinders, valves, …), model of model of a controlled cylinder with on/off and proportional valve.

Module 6: Modern approach to the synthesis of a controller

Topic 6.1

Controllability and observability of a system, Pole placement method.

Students must have acquired the following skills in:

• Kinematics, dynamics and vibration of mechanical systems composed of rigid bodies with one and 2-n degrees of freedom.
• Matrix algebra, eigenvalues and eigenvector calculation, systems of ordinary linear differential equations.
• Knowledge on meaning of FFT transform and frequency domain treatment of mechanical systems.

Students will pass the course after successfully take a written test and an oral exam. A positive evaluation in the written test is mandatory for accessing the oral exam.

Written Test

In the written test it is requested to model and analyse the equations of a controlled mechanical systems with actuator, at three different levels, single d.o.f mechanical system with a) simplified actuator model and b)  full dynamic actuator model, c) 2 d.o.fs mechanical system. Aim of the written test is to verify the applied knowledge and understanding of controlled mechanical system with regard to modelling, stability and performance analysis, with all the tools in Laplace, frequency and time domain.

Oral exam

The oral exam is organised through open questions to be answered to in a written format, including comments, equations and graphical representations, about all the topics of the knowledge and understanding, as well as the capability of communicating knowledge and results in a technical, concise and proper way.

Some PC laboratory activities will be proposed during the course on stability analysis and control with electrical actuators. Students are required to present, at the oral test, a report on the numerical applications developed in the computer room or a report of the laboratory activity based on experimental data set. This activity focuses on their ability in technical reporting and communicating results, as well as critical analysis of the obtained results. 

Final Grading

To pass the course, students must successfully pass the written test and the oral exam.

Authors: Giorgio Diana, Ferruccio Resta