How can you use classical and modern control theory effectively?

1 Classical control theory

Classical control theory is based on the use of mathematical models that describe the dynamics of a system using differential equations. These models can be represented by transfer functions, block diagrams, or state-space equations. Classical control theory focuses on the frequency domain analysis of system stability, response, and performance using tools such as Bode plots, Nyquist plots, and root locus. Classical control theory is useful for designing simple and robust controllers, such as proportional-integral-derivative (PID) controllers, that can handle linear and time-invariant systems.

2 Modern control theory

Modern control theory is based on the use of advanced mathematical techniques that can handle nonlinear, time-varying, and uncertain systems. These techniques include optimal control, adaptive control, robust control, and nonlinear control. Modern control theory focuses on the state-space domain analysis of system controllability, observability, and optimality using tools such as Lyapunov functions, Hamilton-Jacobi equations, and Riccati equations. Modern control theory is useful for designing complex and adaptive controllers, such as model predictive control (MPC), sliding mode control (SMC), and neural network control (NNC), that can cope with system disturbances, uncertainties, and constraints.

3 How to choose between classical and modern control theory

When deciding which control theory is best or most suitable for a given problem, there is no definitive answer. The choice depends on various factors, such as the system characteristics, the controller objectives, the available resources, and the trade-offs involved. Generally speaking, classical control theory should be used if the system is linear, time-invariant, and well-known, and the controller objectives are simple and well-defined. On the other hand, modern control theory should be used if the system is nonlinear, time-varying, and uncertain, and the controller objectives are complex and flexible. If the system has both linear and nonlinear components, or if the controller objectives can be decomposed into subproblems that can be solved by different methods, then a combination of classical and modern control theory may be the best option.

4 How to design a controller using classical control theory

Designing a controller using classical control theory requires several steps. Firstly, the system model must be identified using physical laws, experimental data, or system identification methods. Secondly, a suitable controller structure should be chosen, such as PID, lead-lag, or notch. Thirdly, the controller parameters must be determined through analytical methods like root locus or frequency response, or numerical methods like trial and error or optimization algorithms. Finally, the controller performance should be tested and validated using simulation or experimentation.

5 How to design a controller using modern control theory

Designing a controller using modern control theory requires several steps. Firstly, the system model must be identified by utilizing physical laws, experimental data, or system identification methods. Next, a suitable controller structure must be chosen, such as MPC, SMC, or NNC. After that, the controller parameters must be determined by employing analytical methods, like Lyapunov or Hamilton-Jacobi, or numerical methods, like linear matrix inequalities or optimization algorithms. Lastly, the controller performance must be tested and validated through simulation or experimentation.

6 How to improve your control theory skills

To improve your control theory skills, you need to practice and learn from multiple sources, including books and textbooks on the fundamentals and applications of control theory, like Modern Control Engineering by Ogata, Feedback Control of Dynamic Systems by Franklin et al., and Nonlinear Systems by Khalil. Additionally, online courses and tutorials offer interactive and hands-on learning of control theory concepts and methods, such as Control of Mobile Robots by Coursera, Control Systems Engineering by Udemy, and Control Tutorials for MATLAB and Simulink by Michigan University. You should also use software and tools to model, simulate, and implement control systems, like MATLAB, Simulink, LabVIEW, and Arduino. Finally, projects and challenges can help you test your knowledge and creativity in solving real-world control problems, like balancing a robot or controlling a smart grid.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?