Uncertainties
always exist in practical industrial processes which
result in many difficulties for controller design. To enhance the
ability of closed-loop systems to handle uncertainties, an active
disturbance rejection control (ADRC) design based on probabilistic
robustness (PR) is proposed in this paper. The necessity of the proposed
design method is explained by introducing the problem formulation.
Then the principle and parameter stability region of ADRC are introduced.
On the basis of these fundamentals, a design method of ADRC based
on PR is proposed for uncertain systems and the corresponding design
procedure is summarized, which is applicable for uncertain single-input
single-output (SISO), multi-input multi-output (MIMO) and nonlinear
systems. The simulation results for SISO, MIMO, and nonlinear systems
illustrate that the proposed ADRC always has a larger estimated value
of the probability than other comparative controllers which means
that the proposed ADRC design method can not only ensure the satisfactory
control performance for nominal systems, but also meet control requirements
for all uncertain systems with the largest probability. In addition,
the superiority of the proposed ADRC design is also verified by comparative
experiments based on the Peltier temperature control platform. The
proposed ADRC design method can offer a practical solution and shows
a promising future for uncertain systems in practical industrial processes.