### Abstract

This paper develops a robust gain-scheduled proportional–integral–derivative (PID) controller design method for a linear-parameter-varying (LPV) system with parametric uncertainty. It is recognized in the literature that the robust fixed-order controller design can be formulated as a feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP hard problem in general. Previous researchers have applied a linearization method, such as a variable change technique or a congruence transformation, to transform the BMI into a LMI. The applicability of the linearization method depends on the specific structure of the problem at hand and cannot be generalized. This paper instead formulates the gain-scheduled PID controller design as a feasibility problem of a quadratic matrix inequality (QMI) constraint, which covers the BMI constraint as a special case. An augmented sequential LMI optimization method is proposed to search for a feasible solution of the QMI constraint iteratively. As an illustrative application, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real-world output feedback control design system.

Original language | English (US) |
---|---|

Pages (from-to) | 67-76 |

Number of pages | 10 |

Journal | Systems and Control Letters |

Volume | 126 |

DOIs | |

State | Published - Apr 2019 |

### Fingerprint

### Keywords

- Convex optimization
- LPV system
- Linear matrix inequality
- PID controller
- Quadratic matrix inequality
- Robust control

### Cite this

*Systems and Control Letters*,

*126*, 67-76. https://doi.org/10.1016/j.sysconle.2019.02.006

**A quadratic matrix inequality based PID controller design for LPV systems.** / Wang, Yan; Rajamani, Rajesh; Zemouche, Ali.

Research output: Contribution to journal › Article

*Systems and Control Letters*, vol. 126, pp. 67-76. https://doi.org/10.1016/j.sysconle.2019.02.006

}

TY - JOUR

T1 - A quadratic matrix inequality based PID controller design for LPV systems

AU - Wang, Yan

AU - Rajamani, Rajesh

AU - Zemouche, Ali

PY - 2019/4

Y1 - 2019/4

N2 - This paper develops a robust gain-scheduled proportional–integral–derivative (PID) controller design method for a linear-parameter-varying (LPV) system with parametric uncertainty. It is recognized in the literature that the robust fixed-order controller design can be formulated as a feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP hard problem in general. Previous researchers have applied a linearization method, such as a variable change technique or a congruence transformation, to transform the BMI into a LMI. The applicability of the linearization method depends on the specific structure of the problem at hand and cannot be generalized. This paper instead formulates the gain-scheduled PID controller design as a feasibility problem of a quadratic matrix inequality (QMI) constraint, which covers the BMI constraint as a special case. An augmented sequential LMI optimization method is proposed to search for a feasible solution of the QMI constraint iteratively. As an illustrative application, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real-world output feedback control design system.

AB - This paper develops a robust gain-scheduled proportional–integral–derivative (PID) controller design method for a linear-parameter-varying (LPV) system with parametric uncertainty. It is recognized in the literature that the robust fixed-order controller design can be formulated as a feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP hard problem in general. Previous researchers have applied a linearization method, such as a variable change technique or a congruence transformation, to transform the BMI into a LMI. The applicability of the linearization method depends on the specific structure of the problem at hand and cannot be generalized. This paper instead formulates the gain-scheduled PID controller design as a feasibility problem of a quadratic matrix inequality (QMI) constraint, which covers the BMI constraint as a special case. An augmented sequential LMI optimization method is proposed to search for a feasible solution of the QMI constraint iteratively. As an illustrative application, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real-world output feedback control design system.

KW - Convex optimization

KW - LPV system

KW - Linear matrix inequality

KW - PID controller

KW - Quadratic matrix inequality

KW - Robust control

UR - http://www.scopus.com/inward/record.url?scp=85063622857&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063622857&partnerID=8YFLogxK

U2 - 10.1016/j.sysconle.2019.02.006

DO - 10.1016/j.sysconle.2019.02.006

M3 - Article

AN - SCOPUS:85063622857

VL - 126

SP - 67

EP - 76

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

ER -