This book presents a collection of exercises on dynamical systems, modelling and control. Each topic covered includes a summary of the theoretical background and exercises with solved problems on fractional calculus and simple tools for nonlinear systems. Topics covered include: mathematical models; PID controller synthesis; controller synthesis by pole placement; fractional order systems and controllers and many others. This book is essential reading for advanced students with courses in modelling and control in engineering, applied mathematics, biomathematics and physics.1. Block Diagram Algebra and System Transfer Functions 2. Mathematical Models 3. Analysis of Continuous Systems in the Time Domain 4. Root Locus Analysis 5. Frequency Domain Analysis 6. PID Controller Synthesis 7. State Space Analysis of Continuous Systems 8. Controller Synthesis by Pole Placement 9. Discrete Time Systems and Z Transform 10 Analysis of Non-linear Systems with the Describing Function Method 11. Analysis of Nonlinear Systems with the Phase Plane Method 12. Fractional Order Systems and Controllers