A Design Method of Static Output Feedback Sampling Controller for Automotive Suspension

Abstract

The present invention discloses a design method for an aperiodic sampled-data H-infinity controller based on the static output feedback of an automotive active suspension. The present invention relates to the problem of aperiodic sampled-data H-infinity control for the static output feedback of an automotive active suspension based on an uncertain disturbance model with time delay. The steps of the present invention are as follows: Step 1: Construct an integral quadratic constraint operator on the basis of a quarter-vehicle active suspension based on an uncertain disturbance model to quantify the uncertainty caused by sampled data and time delay; Step 2: Perform a model transformation and give corresponding exponential stability conditions for the closed-loop system; Step 3: Analyze the H-infinity performance index of the closed-loop system by using the integral quadratic constraint operator and the generalized KYP lemma; Step 4: Design a "two-stage heuristic" solution iteration algorithm based on a static output feedback controller; Step 5: Verify the reliability and feasibility of the controller through numerical simulation.

Description

Technical Field

[0001] The present invention relates to the field of automotive active suspension control, and particularly to a design method of an aperiodic sampling data H-infinity controller for an automotive active suspension system based on an uncertain disturbance model with time delay. Background Art

[0002] In recent years, with the continuous improvement of vehicle performance requirements, the research and application of vehicle active suspension systems have become increasingly important. In order to effectively reduce the impact of road disturbances on passengers, the suspension system, as an important part of the vehicle, plays an extremely important role in improving vehicle handling stability, ride comfort, driving safety, etc. However, due to signal transmission delays and the limitations of sampling data periods, the control effect of active suspension systems is often affected, thereby reducing stability and control performance.

[0003] In response to this problem, many scholars have conducted research. For example, a state feedback controller that meets the requirements of H-infinity performance and output constraints was proposed based on stochastic stability theory; an adaptive tracking control scheme for a nonlinear active suspension system with parameter fuzziness, actuator saturation, and bounded external disturbances was proposed; for a disturbed vehicle active suspension system, an output feedback finite-time control method was proposed to improve the suspension stability performance; an adaptive event-triggered fuzzy uncertain control method based on the system was proposed to cope with actuator failures, effectively saving more resources while ensuring the expected performance; in order to analyze the performance of a simulated quarter-vehicle active suspension under multiple cyberattacks, some scholars proposed a fully distributed hierarchical event-triggered intrusion-tolerant scheme.

[0004] Among many studies, the H-infinity performance index has always been the main choice for optimizing the performance of active suspension systems because it establishes a constraint condition involving disturbance inputs and system outputs, and reflects the performance index of the active suspension system by dealing with the H-infinity norm of the transfer function from disturbance inputs to state variable outputs. Its main advantage is to provide guarantee for the robustness of the system, ensuring the stability and good operation of the system under uncertain and disturbed conditions. However, in the design of controllers for multi-objective vehicle active suspensions, there are still many problems to be solved. For example, state feedback control cannot measure all state variables, such as tire displacement and road disturbance inputs. Dynamic output feedback uses measurable signals to control the suspension system, but in the design process, it is not easy to select appropriate performance weight functions. The obtained controller has high order, which not only increases the complexity of the system, but also greatly increases the cost of the actual hardware system.

[0005] With the development of computers and digital controllers, there have been many mature research types in sampled-data control, such as using small-gain type integral quadratic constraints to characterize the properties of operators to analyze the system stability of sampled data with time-delay signals. There is also the input delay method; the loop-based functional method; the switched system method and the stochastic system method are of great significance for the performance research of active suspensions. In the literature (journal: IEEE Transactions on Control Systems Technology; authors: Huijun Gao, Weichao Sun and Peng Shi; publication time: 2010; article title: Robust Sampled-Data H∞ Control for Vehicle Active Suspension Systems; page numbers: 238-245), an H-infinity controller for a non-periodic sampled-data system was proposed using the input delay method. In addition, the input delay method was also used for model transformation to analyze the fuzzy sampled-data control of the system (journal: IEEE / CAA Journal of Automatica Sinica; authors: Wenfeng Li, Zhengchao Xie, Yucong Cao, Pak Kin Wong and Jing Zhao; publication time: 2021; article title: Sampled-Data Asynchronous Fuzzy Output Feedback Control for Active Suspension Systems in Restricted Frequency Domain; page numbers: 1052-1066). Compared with state feedback and dynamic output feedback, the static output feedback controller has a structure that is easy to understand and implement, which has attracted a lot of attention to its design. The robust H-infinity static output feedback research for the finite frequency constraint and control gain perturbation system.

[0006] To overcome the problems existing in multi-objective suspension control, an active suspension control strategy based on aperiodic sampling data is proposed. First, an integral quadratic constraint operator is constructed to quantify the uncertainties caused by sampling data and time delay, and the conditions for exponential stability are given. Second, based on the constructed integral quadratic constraint operator, the model is transformed, and the proposed controller aims to achieve the feedback control of the system. This controller has the characteristics of low order, few feedback signals, simple control problem, easy physical implementation, etc. It can effectively handle the influence of time-delay signals, improve the control accuracy and stability of the system, and has important practical application value. Finally, through numerical simulation, the delay signal is processed based on aperiodic sampling data combined with integral quadratic constraint, and static output feedback is used for control to verify the improvement of the system control performance and stability, providing strong support for achieving a higher level of vehicle handling performance and ride comfort, and having a higher practical application prospect. Summary of the Invention

[0007] The present invention discloses a design method of an aperiodic sampling data H-infinity controller for an automotive active suspension static output feedback, which relates to the aperiodic sampling data H-infinity control problem of an automotive active suspension static output feedback based on an uncertain perturbation model with time delay.

[0008] A sampling controller design method based on an automotive active suspension static output feedback is given, including the following steps:

[0009] Step 1: Establish a mathematical model of an automotive suspension with uncertain perturbation;

[0010] Step 2: Give the H-infinity control performance constraint conditions and exponential stability conditions of the suspension system;

[0011] Step 3: Give the construction process of the equivalent feedback interconnection of the closed-loop system;

[0012] Step 4: Give an iterative algorithm for solving the static output feedback controller;

[0013] The mathematical simulation of vehicle dynamics is one of the key links in controller design. The goal of developing a vehicle dynamics model is to simulate the behavior of a real vehicle as much as possible. According to ISO2631, the human body is very susceptible to vertical oscillations in the range of 4 - 8 Hz. It is assumed that the motions of the four wheels of the vehicle are uncoupled, and the suspension dynamics are considered separately in the frequency range related to the vertical motion of the vehicle. According to the automotive suspension sampling controller design method based on the system, the specific process of establishing the active suspension mathematical model in Step 1 considers a quarter-vehicle active suspension system with time delay. According to Newton's second law, the dynamic equations of the sprung mass and the unsprung mass are described as:

[0014]

[0015] Among them, m s is the sprung mass, m u is the unsprung mass, z s is the displacement of the sprung mass, z u is the displacement of the unsprung mass, z r is the road displacement input, c s is the damping coefficient of the spring damper, c t is the damping coefficient of the tire, k s is the suspension spring stiffness, k t is the tire stiffness, and u(t) is the acting force input by the actuator; by defining the following state variables: x1(t) = z s (t) - z u (t), x2(t) = z u (t) - z r (t), The disturbance input is The state variable x(t) = col{x1(t), x2(t), x3(t), x4(t)} is obtained, and the dynamic equation (1) is rewritten as the following state space model of the active suspension system:

[0016]

[0017] Among them,

[0018] The described design method of an automotive static output anti-sampling controller is characterized in that the specific process of the second step is as follows: The performance constraint conditions and stability conditions are:

[0019] The main objectives of the vehicle active suspension system control design are human ride comfort, the dynamic deflection of the suspension, and the relative dynamic tire load. Consider the following performance requirements:

[0020] 1) Ride comfort: The human body acceleration is a suitable choice for this performance index because the ride comfort of the human body is usually determined by the vertical acceleration of the whole body, and the ride comfort is related to the body acceleration and is used as the performance output of the state space model (2), denoted as z1(t); when designing the controller, the main objective is to make as small as possible, and the H-infinity criterion is applied to evaluate the output effect;

[0021] 2) Suspension stroke: To prevent damage to the suspension structure, the condition |z s (t) - z u (t)| ≤ z max constraint is required, where x 1max represents the maximum suspension deflection;

[0022] 3) Road keeping: For driving safety, the dynamic tire load should be low to provide continuous and firm contact between the wheel and the road, denoted as k t (z u (t)-z r (t)) / 9.8(m s +m u )≤x 2max , where x 2max is the maximum tire deflection;

[0023] 4) Actuator power limit: Due to the high power consumption of the active suspension system, the power applied to the actuator by the active suspension control should also be limited, i.e., |u(t)|≤u max ;

[0024] Considering the above four constraints and reflecting them in the input-output of the system, the state space shown below can describe the vehicle active suspension system:

[0025]

[0026] Among them,

[0027] Due to the time delay in the data transmission process, the sensor cannot update the actuator in real time after receiving the signal. To explore the non-periodic sampling data control problem of the active suspension system;

[0028] Considering when the sampling data sequence {s k} satisfies Among them, h and are two real numbers greater than zero, h k is the time-varying sampling data interval; the update order {a k} of the actuator satisfies a k :=h k +τ k , Among them is the maximum value of the time delay; x(s0) is used to represent the initial state in the sampling data sequence, and x v represents the initial state of the corresponding execution sequence at time s0 after being affected by the time delay, indicating that the initial state is not necessarily zero. Thus, the state when the signal reaches the actuator can be obtained is

[0029]

[0030] After being controlled by the state variable affected by the time delay u(t)=Ky(t)=KCx(s k ), there is

[0031]

[0032] Among them, x(s0) represents the initial state in the sampled data sequence, and x v represents the initial state at time s0 after the corresponding execution sequence is affected by time delay. It means that the initial state is not necessarily zero. When k = 0, x(s0) ≠ x v , and

[0033] Consider designing a static output feedback controller. Since it is different from state feedback, static output feedback does not require measuring all system state variables, requires fewer sensors, and has lower costs. The static output feedback design obtained by comparison is simpler, easier to implement, and provides better robustness. In addition, static output feedback achieves better suspension control by adjusting the output of the system, thereby improving the stability and comfort of the vehicle.

[0034] The construction process of the equivalent feedback interconnection of the closed-loop system given in step three is as follows:

[0035] First, to address the consequences brought by time delay, for the closed-loop system construct a feedback interconnection model of the closed-loop system with the operator generated by sampled data and time delay:

[0036]

[0037] Among them, And let the function have

[0038]

[0039]

[0040] For the original system (3), substitute u x (t) into the feedback interconnection model; thus, the problem is reduced to a non-periodic sampled data control problem regarding time delay in the active suspension system. Design a static output feedback controller (5) and construct a feedback interconnection term.

[0041] When w(t) = 0, the feedback interconnection term is exponentially stable; for any non-zero disturbance w(t) ∈ L 2e [0, ∞) and |w(t)| < w max is bounded. Under zero initial conditions, there exists a disturbance attenuation performance index γ > 0 such that ||z1(t)||2 < γ||w(t)||2; meanwhile, ensure the constraint ||z2(t)||2 ≤ [1 1] T , |u(t)| ≤ u max , and both the control input and control output are valid for t ≥ 0.

[0042] As described above, the algorithm for solving the controller is given, and the exponential stability and H-infinity performance index of the closed-loop system are analyzed based on the integral quadratic constraint; considering that the feedback interconnection model is exponentially stable when w(t) = 0, it is equivalent to the feedback interconnection structure:

[0043]

[0044] where obtain the feedback interconnection structure; since the feedback interconnection structure cannot guarantee the condition of the initial state being zero, the integral quadratic constraint cannot be directly used; to solve this problem, corresponding to the feedback interconnection, consider the non-homogeneous system with zero initial conditions, and use the Bohl-Perron principle to perform a series of transformations on the feedback interconnection to obtain a structure relative to the case of zero initial state, and combine it with the integral quadratic constraint to obtain the dissipation inequality for the time-domain α-IQC where, △ satisfies the time-domain definition of α-IQC, which means △ α satisfies the definition of the time-domain integral quadratic constraint.

[0045] For the stability of the automotive active suspension system, there are the following steps:

[0046] The first step: The closed-loop system is a linear time-invariant system defined by the feedback interconnection structure (6), is a causal operator such that is well-posed; assume that △ satisfies the time-domain α-IQC through δ is a given scalar, R = R > 0, the scalar α ≥ 0, if one of the following cases holds, then T > 0, the scalar α ≥ 0, if one of the following cases holds, then is α-exponentially stable;

[0047] 1) There exists a matrix P = P T > 0 such that L α ≤ 0;

[0048] 2) There exists a matrix P = P T ≥ 0 such that L α < 0,

[0049] where

[0050] When designing the controller of this system, the main goal is to reduce the influence of ground disturbances on the human body acceleration. It is also necessary to consider the constraints to ensure the suspension performance, such as the suspension dynamic stroke and tire deflection. The following analyzes these two aspects. When non-zero w(t) ∈ L 2eWhen \(t\in[0,\infty)\), we consider that the disturbance attenuation performance index \(\gamma>0\) under zero initial conditions satisfies \(\left\|z_{1}(t)\right\|_{2}<\gamma\left\|w(t)\right\|_{2}\); to ensure the robustness of the system, the H-infinity control method is adopted to establish the transfer function between the output variable and the disturbance, and to ensure the stability and superiority of the system in the presence of uncertainties and disturbances; at the same time, by optimizing the performance index \(\gamma\), the error between the reference signal and the system output is reduced to obtain better tracking performance.

[0051] Step 2: To analyze the performance index \(\gamma\) of the active suspension, for the feedback interconnection structure (6) that is exponentially stable when \(w(t) = 0\), when the feedback interconnection structure (6) is given scalars \(\alpha\geq0\), \(\gamma>0\) and \(\rho>0\), and \(w(t)\in L\) 2e [0,\infty), if the matrices \(P\), \(Q\) and \(R\) are all positive definite and symmetric, the following inequalities hold;

[0052]

[0053]

[0054]

[0055]

[0056] Step 3: For the vehicle active suspension system (3), a static output feedback controller is designed, and a two-stage solution algorithm is given. The designed controller stabilizes the system and meets the finite frequency domain requirements. For the given \(\varPhi\), \(\varPsi\) and \(\varPi\), the state space of the vehicle active suspension can be realized. When there exist matrices \(P>0\), \(Q>0\), \(P\) s >0, the existence of a controller that further stabilizes the vehicle active suspension system (3) and meets the finite frequency domain index is satisfied and s when

[0057]

[0058]

[0059] where

[0060] \(\gamma=\begin{bmatrix}K&0&I\end{bmatrix}\) T \(\begin{bmatrix}L&0&F\end{bmatrix}\), \(\gamma\) s =\begin{bmatrix}K&I\end{bmatrix}\) T \(\begin{bmatrix}L&F\end{bmatrix}\), from which the static output feedback control gain matrix \(K = F\) T \(LC\). For the given \(F\) that satisfies the conditions, using the generalized KYP lemma and the heuristic two-step method, the above two inequalities hold, and the finally obtained \(K = F\) T \(LC\) is used as the desired static output feedback control gain matrix.

[0061] Based on the generalized KYP lemma, a heuristic algorithm for synthesizing a static output feedback controller is studied. The controller solution algorithm adopts a two-stage idea. In the first step, an initial controller is obtained, and there is a feasible solution as the initial value. In the second step, the output feedback controller is solved to give the optimal solution of the designed iterative algorithm. An iterative algorithm for solving the static output feedback controller is given:

[0062]

[0063]

[0064] The beneficial effects of the present invention are as follows: The controller effectively handles the uncertainties brought by non-periodic sampling data and time delays based on integral quadratic constraints, increases the output feedback gain, suppresses the influence of external disturbances on the system, and enhances the anti-interference ability of the system. The static output feedback achieves the optimal control performance by minimizing the H-infinity performance index. To sum up, compared with the dynamic output feedback and state feedback in the suspension system, the H-infinity static output feedback control has the advantages of robustness, improved control performance, and simplified design, improving the robustness and control performance of the system. Brief Description of the Drawings

[0065] Figure 1 is the quarter-car active suspension experimental equipment.

[0066] Figure 2 is the quarter-car data signal sampling-holding model of the automotive active suspension.

[0067] Figure 3 is the performance signal of the active suspension system using the controller through K q obtained in the last 9 s.

[0068] Figure 4 is the last 9 seconds of the active suspension system through K q control input signal of the controller.

[0069] Figure 5 is the diagram of the suspension deflection and sprung mass velocity state variables. Detailed Description of the Invention

[0070] The following describes the specific implementation manners of the present invention with reference to the accompanying drawings, so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed descriptions of known functions and designs may obscure the main content of the present invention, these descriptions will be omitted here.

[0071] The present invention discloses a design method for an aperiodic sampled-data H-infinity controller based on the static output feedback of an automotive active suspension, which involves the problem of aperiodic sampled-data H-infinity control for the static output feedback of an automotive active suspension based on an uncertain disturbance model with time delay. First, construct an integral quadratic constraint operator on the basis of a quarter-vehicle active suspension with an uncertain disturbance model to quantify the uncertainties caused by sampled data and time delay; Second: perform model transformation and give corresponding exponential stability conditions for the closed-loop system; Third: use the integral quadratic constraint operator and the generalized KYP lemma to analyze the H-infinity performance index of the closed-loop system; Fourth: design a "two-stage heuristic" solution iterative algorithm based on a static output feedback controller; Fifth: verify the reliability and feasibility of the controller through numerical simulation.

[0072] The specific steps provide a design method for a sampled-data controller based on the static output feedback of an automotive suspension, including the following aspects:

[0073] Step 1: Establish a mathematical model of an automotive suspension with uncertain disturbances;

[0074] Step 2: Give the H-infinity control performance constraint conditions and exponential stability conditions of the suspension system;

[0075] Step 3: Give the construction process of the equivalent feedback interconnection of the closed-loop system;

[0076] Step 4: Give an iterative algorithm for solving the static output feedback controller;

[0077] The mathematical simulation of vehicle dynamics is one of the key links in controller design. The goal of developing a vehicle dynamics model is to simulate the behavior of a real vehicle as much as possible. According to ISO2631, the human body is very susceptible to vertical oscillations in the range of 4 - 8 Hz. It is assumed that the motions of the four wheels of the vehicle are uncoupled, and the suspension dynamics are considered separately for the frequency range related to the vertical motion of the vehicle. According to the design method of the sampled-data controller for an automotive suspension, in the specific process of establishing the mathematical model of the automotive active suspension in Step 1, considering a quarter-vehicle active suspension system with time delay, according to Newton's second law, the dynamic equations of the sprung mass and the unsprung mass are described as:

[0078]

[0079] By rewriting it into the state-space model of the active suspension system as shown below:

[0080]

[0081] For a design method of a sampled-data controller based on the static output feedback of an automotive suspension, the specific process in Step 2 is given

[0082] The main objectives of the control design of a vehicle active suspension system are human ride comfort, the dynamic deflection of the suspension, and the relative dynamic tire load. Considering the following performance requirements:

[0083] 1) Ride comfort: Body acceleration is a suitable choice for this performance index because human ride comfort is usually determined by the vertical acceleration of the whole body, and ride comfort is related to body acceleration and is used as the performance output of the state - space model (2); when designing the controller, the main goal is to make as small as possible, and the H - infinity criterion is applied to evaluate the output effect;

[0084] 2) Suspension travel: To prevent damage to the suspension structure, the condition z s (t)-z u (t)≤z max constraint is required;

[0085] 3) Road holding: For driving safety, the dynamic tire load should be low to provide a continuous and firm contact between the wheels and the road;

[0086] 4) Actuator power limitation: Due to the high power consumption of the active suspension system, the power applied to the actuator by the active suspension control should also be limited;

[0087] Considering the above four constraints and reflecting them in the input - output of the system, the following state - space can describe the vehicle active suspension system:

[0088]

[0089] Due to the time - delay in the data transmission process, the sensor cannot update the actuator in real - time after receiving the signal. To explore the non - periodic sampling data control problem of the active suspension system;

[0090] Considering when the sampling data sequence {s k} satisfies The update sequence {a k} of the actuator satisfies a k :=h k +τ k , Let x(s0) represent the initial state in the sampling data sequence, and x v represent the initial state at time s0 of the corresponding execution sequence after being affected by the time - delay, indicating that the initial state is not necessarily zero. Thus, the state when the signal reaches the actuator is as

[0091]

[0092] The state variables affected by time delay are controlled by \(u(t) = Ky(t)=KCx(s k ), and after being controlled by the controller, there is

[0093]

[0094] Considering the design of a static output feedback controller, since different from state feedback, static output feedback does not require measuring all system state variables, needs fewer sensors, and has lower costs. The static output feedback design obtained by comparison is simpler, easier to implement, and provides better robustness. In addition, static output feedback achieves better suspension control by adjusting the output of the system, thereby improving the stability and comfort of the vehicle.

[0095] For the automotive active suspension system, use the following steps to analyze its stability and obtain the control gain matrix in combination with the designed algorithm;

[0096] The first step: The closed-loop system is a linear time-invariant system defined by the feedback interconnection (6), is a causal operator such that is well-posed; assume that \(\Delta\) satisfies the time-domain \(\alpha\)-IQC through , \(\delta\) is a given scalar, \(R = R T > 0\), the scalar \(\alpha\geq0\), if one of the following cases holds, then is \(\alpha\)-exponentially stable;

[0097] 1) There exists a matrix \(P = P T > 0\) such that \(L α \leq0\);

[0098] 2) There exists a matrix \(P = P T \geq0\) such that \(L α < 0\),

[0099] where

[0100] When designing the controller of this system, the main goal is to reduce the influence of ground disturbances on human body acceleration. It is also necessary to consider the constraints to ensure the suspension performance, such as the suspension dynamic stroke and tire deflection. The following analyzes these two aspects. When the non-zero \(w(t)\in L 2e [0,\infty)\), we consider that the disturbance attenuation performance index \(\gamma>0\) under zero initial conditions satisfies \(\|z_1(t)\|_2<\gamma\|w(t)\|_2\); to ensure the robustness of the system, the H-infinity control method is used to establish the transfer function between the output variable and the disturbance, and to ensure the stability and superiority of the system in the presence of uncertainties and disturbances; at the same time, by optimizing the performance index \(\gamma\), the error between the reference signal and the system output is reduced to obtain better tracking performance.

[0101] For the transfer function G(s), where γ represents the disturbance attenuation performance index to be optimized, and the smaller its value, the stronger the disturbance attenuation ability of the system. Further, it is ensured by the transfer function inequality and by transforming it into a linear matrix inequality

[0102]

[0103] Step 2: To analyze the performance index γ of the active suspension, for the feedback interconnection structure (6) that is exponentially stable when w(t) = 0, when the feedback interconnection structure (6) is given scalars α≥0, γ>0, and ρ>0, and w(t) ∈ L 2e [0,∞), if the matrices P, Q, and R are all positive definite and symmetric, then the following inequalities hold;

[0104]

[0105]

[0106]

[0107]

[0108] Step 3: For the vehicle active suspension system (3), a static output feedback controller is designed, and a two-stage solution algorithm is given. The designed controller stabilizes the system and meets the finite frequency domain requirements. For the given Φ, ψ, and Π, the state space of the vehicle active suspension can be realized. When there exist matrices P>0, Q>0, P s >0, P, Q, P s when, the existence of a controller for the vehicle active suspension system (3) that is stable and further meets the finite frequency domain index is ensured and

[0109]

[0110]

[0111] where

[0112] γ = [K 0 I] T [L 0 F], γ s = [K I] T [L F], from which the static output feedback control gain matrix K = F T LC is obtained. For the given F that satisfies the conditions, using the generalized KYP lemma and the heuristic two-step method, the above two inequalities hold, and finally the obtained K = F T LC is used as the desired static output feedback control gain matrix.

[0113] A heuristic algorithm for synthesizing a static output feedback controller is studied based on the generalized KYP lemma. The controller solving algorithm adopts a two-stage idea. In the first step, an initial controller is obtained, and there is a feasible solution as the initial value. In the second step, the output feedback controller is solved to give the optimal solution of the designed iterative algorithm. An iterative algorithm for solving the static output feedback controller is given:

[0114]

[0115]

[0116] To verify the effectiveness of the proposed control method, the specific numerical values of the selected device parameters are shown in the following table:

[0117] Table 1: System design parameters, devices are attached Figure 1

[0118]

[0119]

[0120] A. Numerical simulation

[0121] Through numerical simulation comparison, using the proposed static output feedback controller solving algorithm, the control gain matrix of the finite frequency domain output feedback control is solved by MATLAB as

[0122] K = 10 4 ×[0.16360 -1.35960].

[0123] By observing the control gain matrix obtained by the algorithm solving, the numerical values of the control effect and performance index γ on the H-infinity controller are obtained, which illustrates the effectiveness of the proposed controller method. Comparing with the static output feedback controller proposed in Ref. [1] (Journal: IEEE Transactions on Cybernetics; Authors: Hongjiu Yang, Peng Li, Yuanqing Xia and Ce Yan; Publication time: 2021; Article title: H ∞ Static Output Feedback for Low-Frequency Networked Control Systems With a Decentralized Event-Triggered Scheme; Pages: 4227 - 4236) is

[0124] K Yang = 10 4 ×[-0.0026 -1.0694],

[0125] And the state feedback controller is given by [2] (Journal: International Journal of Systems Science; Authors: Hongyi Li, Honghai Liu, Steve Hand, and Chris Hilton; Publication Time: 2010; Article Title: Multi-objective H ∞ control for vehicle active suspension systems with random actuator delay; Pages: 2214 - 2227).

[0126] K Li = 10 4 × [-5.5911 0.2482 -2.4751 0.1443],

[0127] When the aperiodic sampling system with a sampling upper limit interval is regarded as and the magnitude of the time delay The value of the H-infinity control performance index γ = 2.3954, which shows better performance compared to other controllers and can better improve the handling stability and riding comfort of the vehicle while ensuring driving safety.

[0128] B. Experimental simulation verifies the effect of the controller

[0129] Using the Quanser device for simulation verification, according to Algorithm 1, the control gain matrix based on the quarter-active suspension device parameters is obtained as

[0130] K = 10 4 × [-25.599 0 -71.0107 0].

[0131] By analyzing and comparing the suspension system states generated by the active suspension system without a controller in the first 9 s and the system with a control input in the next 9 s, as shown in the appendix Figure 3 It effectively reduces the tire deflection, has a good control effect, and improves the riding comfort of the human body; The appendix Figure 4 shows the control input u(t) of the aperiodic sampling data; The appendix Figure 5 gives the state diagrams of the state variables x1 and x3 considered in the static output feedback. It can be seen that the body acceleration generated by the suspension system equipped with the finite-frequency domain static output feedback controller shows good disturbance rejection performance compared to the passive suspension without a controller.

[0132] The above results show that the advantages of the proposed H-infinity control gain in the automotive active suspension system are as follows: The controller effectively handles the uncertainties brought by the aperiodic sampling data and time delay based on the integral quadratic constraint, increases the output feedback gain, suppresses the influence of external disturbances on the system, and enhances the anti-interference ability of the system. The static output feedback achieves the optimal control performance by minimizing the H-infinity performance index. In summary, compared with the dynamic output feedback and state feedback in the suspension system, the H-infinity static output feedback control has the advantages of robustness, improved control performance, and simplified design, which improves the robustness and control performance of the system.

[0133] The present invention studies the active suspension control strategy based on aperiodic sampling data. First, an integral quadratic constraint operator is constructed to quantify the uncertainties brought by the sampling data and time delay, and the conditions for the exponential stability of the system are given; secondly, an H-infinity static output feedback controller is designed to achieve feedback control, effectively handle the influence of the time delay signal, and improve the accuracy and stability of the system. Finally, the simulation verification shows that processing the time delay signal based on the aperiodic sampling data combined with the integral quadratic constraint and using the static output feedback for control improves the effect and stability of the active suspension system, providing strong support for achieving a higher level of vehicle handling performance and ride comfort.

[0134] The above is only a preferred and feasible embodiment of the present invention, and it does not limit the scope of the rights of the present invention. Any equivalent structural changes made by using the content of the specification and drawings of the present invention are included in the scope of the rights of the present invention.

Claims

1. A design method for a static output feedback sampling controller of an automotive suspension, characterized in that It includes the following steps: Step 1: Establish a mathematical model of an automotive suspension with uncertain disturbances; Step 2: Give the H-infinity control performance constraints and exponential stability conditions of the suspension system; Step 3: Give the construction process of the equivalent feedback interconnection of the closed-loop system; Step 4: Give an iterative algorithm for solving the static output feedback controller; The specific process of Step 1 is as follows: Considering a quarter-vehicle active suspension system with time delay, according to Newton's second law, the dynamic equations of the sprung mass and the unsprung mass are described as: where, m s is the sprung mass, m u is the unsprung mass, z s is the displacement of the sprung mass, z u is the displacement of the unsprung mass, z r is the road displacement input, c s is the damping coefficient of the spring damper, c t is the damping coefficient of the tire, k s is the suspension spring stiffness, k t is the tire stiffness, u(t) is the force input by the actuator; by defining the following state variables: x1(t) = z s (t) - z u (t), x2(t) = z u (t) - z r (t), the disturbance input is the state variable x(t) = col{x1(t), x2(t), x3(t), x4(t)} is obtained, and the dynamic equation (1) is rewritten as the following state - space model of the active suspension system: Among them, The specific process of Step 2 is as follows: The performance requirements include: ride comfort, suspension travel, road driving safety, and actuator power limitation; Considering the above four constraints and reflecting them in the input and output of the system, the vehicle active suspension system is expressed as: Among them, Due to the time lag in the data transmission process, the sensor cannot update the actuator in real time after receiving the signal. To explore the problem of non-periodic sampling data control of the active suspension system, consider when the sampling data sequence {s k} satisfies where and are two real numbers greater than zero, and h k is the time-varying sampling data interval; the update order {a k} of the actuator satisfies where is the maximum value of the delay; thus, after the state variable affected by the time lag is controlled by the u(t) = Ky(t) = KCx(s k ), there is where x(s0) represents the initial state in the sampled data sequence, x v represents the initial state at time s0 of the corresponding execution sequence after being affected by the time delay, indicating that the initial state is not necessarily zero, and when k = 0, x(s0) ≠ x v , and The specific process of the third step is as follows: To address the consequences brought about by time delay, for the closed-loop system construct a feedback interconnection model of the closed-loop system G with respect to the operator Δ generated by the sampled data and the time delay: Among them, And let the function have Therefore, the problem is reduced to a non-periodic sampled-data control problem with time delay in the active suspension system. Design a static output feedback controller (4) and construct a feedback interconnection model (5).

2. A design method for an automotive suspension static output feedback sampling controller according to claim 1, characterized in that: Give the process of the algorithm for solving the controller. Analyze the exponential stability and H-infinity performance index of the closed-loop system based on integral quadratic constraints. Considering that the feedback interconnection model (5) is exponentially stable when w(t)=0, give relevant definitions and obtain the stability theorem, which is equivalent to the feedback interconnection structure: Among them obtain the feedback interconnection structure; Since the feedback interconnection (6) cannot guarantee the condition that the initial state is zero, the integral quadratic constraint cannot be directly used. To solve this problem, a case-by-case discussion is carried out: When w(t) = 0, for the closed-loop system is a linear time-invariant system defined by the feedback interconnection structure (6), Δ: is a causal operator such that is well-posed; assuming that Δ is Satisfy time domain α-IQC, δ is a given scalar, R = R T >0, scalar α≥0, if any of the following conditions holds, then is α-exponentially stable; 1) There exists a matrix P = P T > 0 such that L α ≤ 0; 2) There exists a matrix P = P T ≥ 0, such that L α < 0, Among them When non - zero \(w(t)\in L\) 2e [0,\infty)\), we consider that the disturbance attenuation performance index \(\gamma>0\) under zero initial conditions satisfies \(\left\|z_{1}(t)\right\|_{2}<\gamma\left\|w(t)\right\|_{2}\); To ensure the robustness of the system, the H - infinity control method is adopted to establish the transfer function between the output variable and the disturbance, ensuring the stability and superiority of the system in the presence of uncertainties and disturbances; At the same time, by optimizing the performance index \(\gamma\), the error between the reference signal and the system output is reduced to obtain better tracking performance; To analyze the performance index γ of the active suspension, consider when w(t) ∈ L 2e [0, ∞), for the feedback interconnection structure (6), given scalars α ≥ 0, γ > 0, and ρ > 0, if the matrices P, Q, and R are all positive definite and symmetric, then the following inequality holds For the vehicle active suspension system (3), a static output feedback controller is designed, and a two-stage solution algorithm is given. The designed controller stabilizes the system and meets the finite frequency domain requirements. For the given Φ, ψ, and Π, the state space realization of the vehicle active suspension. When there exist matrices P, Q, P s > 0 with P > 0, Q > 0, P s , the vehicle active suspension system (3) is stable, and the existence of a controller that further meets the finite frequency domain specifications is also Among them Υ = [K 0 I] T [L 0 F], Υ s = [K I] T [L F], from which the static output feedback control gain matrix K = F T LC. A heuristic algorithm for synthesizing a static output feedback controller is studied based on the generalized KYP lemma. The controller solving algorithm adopts a two-stage idea. In the first step, an initial controller is obtained, and there is a feasible solution as the initial value. In the second step, the output feedback controller is solved, and the optimal solution of the designed iterative algorithm is given.

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