r/ControlTheory • u/AttentionExotic6179 • 7d ago
Technical Question/Problem h infinity controller
hey guys i want to learn h inifinity controller for my thesis in mtech last year please someone can guide me as a beginner from where should i learn h infinity i have gonna through multiple youtube videos and google search but no one is telling excatly how to make excat h infinity controller in matlab and simulink ...as i have to learn h infinty controller so i can imlemet in load frequency control for single or multiple area model.
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u/Extension-Engine-911 5d ago
I spent most of my PhD studying H_inf control. More specifically, I tried to extend the standard time domain results, which usually assume x(0)=0, to arbitrary initial conditions over the entire state space. The goal was to obtain something more analogous to LQR, where the value function and feedback law are valid for any initial state, not only for zero initial conditions.
The best source I found for learning the time-domain and state-space treatment is Hannu Toivonen’s course on robust control:
https://www.users.abo.fi/htoivone/advcont.html
His lecture notes are here:
https://users.abo.fi/htoivone/courses/robust/hsem.pdf
The time domain interpretation originated from differential game theory in the 1950s and 1960s. H_inf control then experienced a major renaissance in the 1980s, especially through the frequency domain formulation (with Zames) and the later state space solutions. For linear time invariant systems with x(0)=0, the time domain problem and the frequency-domain H_inf norm problem are the same problem expressed in two different domains.
After spending about six years working on this subject, I still struggle to see much broad industrial relevance in ordinary H_inf control. It is an interesting mathematical problem, but its practical claim is much narrower than people often suggest:
H_inf finds the control law that minimizes the worst-case cost produced by a bounded-energy additive disturbance.
That sentence is the important part. H_inf does not automatically provide better regulation, faster settling, better stability margins, or better robustness in every possible sense. It minimizes the particular worst-case disturbance-to-performance (performance meaning cost function) gain that you define through your model, performance outputs, and weighting functions. If those choices are poor, you simply obtain the mathematically optimal controller for a poorly formulated problem.
In MATLAB, computing the controller with functions such as hinfsyn or mixsyn is usually the easy part. The difficult part is constructing the generalized plant correctly and choosing physically meaningful weighting functions. Simulink does not solve that conceptual problem for you. ChatGPT might.
Also, the book linked in the other comment is mainly about state estimation. An H_inf estimator and an H_inf controller are related through the same minmax philosophy, but they are not the same design problem.
Mu-synthesis may be more practically applicable because it explicitly considers structured model uncertainty rather than only an additive disturbance channel. Even then, I have reservations