Constrained optimal control: an application to semiactive suspension systems

Abstract

This article applies three different control techniques to the design of a quarter-car semiactive suspension system. The three techniques, originally developed to solve a constrained optimal control problem, are optimal gain switching, discontinuous variable structure control and explicit model predictive control. All of them divide the state space into convex regions and assign a linear or affine state feedback controller to each region. The partition of the state space is computed off-line. During the on-line phase, the controller switches between the subcontrollers according to the current state. All the above techniques gave satisfactory results when applied to the design of semiactive suspension systems. A detailed comparison in terms of computational complexity, performance and simplicity of the design is proposed in the article.

Keywords:

• semiactive suspensions
• constrained optimal control
• optimal gain switching
• discontinuous variable structure control
• explicit model predictive control

Acknowledgements

We would like to thank Michal Kvasnica for his prompt and very helpful support concerning the use of the MPT toolbox.

We would also like to thank an anonymous referee for his/her help in determining appropriate values of the design parameters for the dVSC controller.

Notes

Notes

1. A bounded polyhedron 𝒫 ⊂ ℝ ⁿ , 𝒫 = { x ∈ ℝ ⁿ ∣ Ax ≤ B } is called a polytope.

2. A common practice, as we do in this section, is that of choosing .

3. Even though closed-loop stability and constraint satisfaction are not guaranteed, MPT provides a function to extract the set of states which satisfy the constraints for all time and another function to analyse these states for stability.

4. Note that an observer causes performance loss, notably with respect to the actuator saturation. This problem is not considered here when comparing the three different approaches.

5. In both cases (fourth-order and second-order models) suitable values for matrix R ₁ leading to good performance were provided by an anonymous reviewer.